$course$/top/CSDPS $course$/top/CSDPS/Sec 5 $course$/top/CSDPS/Sec 5/Fonction exponentielle Nombre de bactéries Dans une certaine culture, le nombre de bactéries double toutes les #m minutes. Initialement, le nombre de bactéries était de #b.

Au bout de combien de minutes comptera-t-on #n bactéries ?


Au bout de {#1} minutes, le nombre de bactéries sera de #n.

]]> Vous devez résoudre la fonction exponentielle «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»n«/mi»«mo»=«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«msup»«mn»2«/mn»«mfrac»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»m«/mi»«/mrow»«/mfrac»«/msup»«/math»

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">;</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">n</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>700</mn><mo>.</mo><mo>.</mo><mn>1000</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>875</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mo>=</mo><mn>10</mn><mo>&#xD7;</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><mi>arrondir</mi><mfenced><mrow><mfenced><mrow><mi>log</mi><mfenced><mfrac><mi mathvariant="normal">n</mi><mi mathvariant="normal">b</mi></mfrac></mfenced><mo>&#xF7;</mo><mi>log</mi><mfenced><mn>2</mn></mfenced></mrow></mfenced><mo>&#xD7;</mo><mi mathvariant="normal">m</mi></mrow></mfenced></math></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calculs et notes auxiliaires</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Population d'un village La population d’un village augmente de #p % annuellement. En 2020, la population était de #h habitants et habitantes.

Quelle sera la population de ce village en l’an #a?


La population sera de {#1} habitants.

]]> Vous devez calculer la base de la fonction exponentielle : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mfenced»«mrow»«mn»100«/mn»«mo»+«/mo»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfenced»«mn»100«/mn»«/mfrac»«/math»=#v

Ensuite, calculez «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»h«/mi»«mo»§#183;«/mo»«mo»#«/mo»«msup»«mi»v«/mi»«mrow»«mo»#«/mo»«mi»x«/mi»«/mrow»«/msup»«mo»=«/mo»«mo»#«/mo»«mi»r«/mi»«/math»

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">;</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">v</mi><mo>=</mo><mfenced><mrow><mn>100</mn><mo>+</mo><mi mathvariant="normal">p</mi></mrow></mfenced><mo>&#xF7;</mo><mn>100</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>05</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">h</mi><mo>=</mo><mn>100</mn><mo>&#xD7;</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>60</mn><mo>;</mo><mn>70</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6200</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>2040</mn><mo>.</mo><mo>.</mo><mn>2060</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2042</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><mi mathvariant="normal">a</mi><mo>-</mo><mn>2020</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>=</mo><mi>arrondir</mi><mfenced><mrow><mi mathvariant="normal">h</mi><mo>&#xD7;</mo><msup><mi mathvariant="normal">v</mi><mi mathvariant="normal">x</mi></msup></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18137</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calculs et notes auxiliaires</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Résolution de fonction exponentielle Trouvez la valeur de x qui vérifie l'équation suivante :

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«msup»«mi»b«/mi»«mrow»«mn»2«/mn»«mi»x«/mi»«/mrow»«/msup»«mo»=«/mo»«mo»#«/mo»«mi»p«/mi»«/math»


La valeur de x est : {#1}

]]> La réponse est «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«msub»«mi»log«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msub»«mfenced»«mrow»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfenced»«/mrow»«mn»2«/mn»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>=</mo><msup><mi mathvariant="normal">b</mi><mn>4</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>=</mo><mfrac><mrow><mi>log</mi><mfenced><mi mathvariant="normal">p</mi></mfenced></mrow><mrow><mi>log</mi><mfenced><mi mathvariant="normal">b</mi></mfenced><mo>&#xD7;</mo><mn>2</mn></mrow></mfrac></math></input></command></group></task></session></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calculs et notes auxiliaires</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Un investissement payant Mme Tremblay investit #v $ à un taux d’intérêt annuel de #p % calculé tous les 6 mois. Les intérêts s’ajoutent au capital.

Dans combien d'années peut-elle espérer avoir accumulé une somme de #s $?


Elle espérer avoir accumulé une somme de #s $ dans {#1} années.

]]> Vous devez résoudre l'équation «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»v«/mi»«mo»§#183;«/mo»«mo»#«/mo»«msup»«mi»i«/mi»«mrow»«mn»2«/mn»«mi»x«/mi»«/mrow»«/msup»«/math», où f(x)=#s

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">v</mi><mo>=</mo><mn>100</mn><mo>&#xD7;</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>10</mn><mo>,</mo><mn>90</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">i</mi><mo>=</mo><mfrac><mrow><mn>100</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mi mathvariant="normal">p</mi><mn>2</mn></mfrac></mstyle></mrow><mn>100</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>015</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">s</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mo>&#xD7;</mo><mi mathvariant="normal">v</mi></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><mi>arrondir</mi><mfenced><mfrac><mrow><mi>log</mi><mfenced><mstyle displaystyle="true"><mfrac><mi mathvariant="normal">s</mi><mi mathvariant="normal">v</mi></mfrac></mstyle></mfenced><mo>&#xF7;</mo><mi>log</mi><mfenced><mi mathvariant="normal">i</mi></mfenced></mrow><mn>2</mn></mfrac></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calculs et notes auxiliaires</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSDPS/Sec 5/Fonction logarithmique Concentration en ions d'hydrogène La concentration en ions d’hydrogène d'une solution est donnée par l'équation «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mi»H«/mi»«mo»=«/mo»«mi»log«/mi»«mfenced»«mfrac»«mn»1«/mn»«mi»H«/mi»«/mfrac»«/mfenced»«/math».

Le jus de citron a un pH de #pH. Quelle est la concentration molaire en ions d’hydrogène de ce jus ?


La concentration molaire en ions d’hydrogène de ce jus est {#1} mol/L.

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">;</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pH</mi><mo>=</mo><mn>2</mn><mo>+</mo><mfrac><mn>1</mn><mn>10</mn></mfrac><mo>&#xD7;</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">H</mi><mo>=</mo><mfrac><mn>1</mn><msup><mn>10</mn><mi>pH</mi></msup></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>0</mn><mo>.</mo><mn>007943</mn></mrow></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">false</option><option name="relative_tolerance">false</option><option name="tolerance_digits">2</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calculs et notes auxiliaires</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Désintégration d'un élément radioactif Un élément radioactif de #g g se désintègre et il ne reste que #a/#b de sa masse initiale après #n ans.

Dans combien d’années ne restera-t-il que 1/#b de la masse initiale ?


Dans {#1} ans, il ne restera que #m grammes.

]]> Il faut résoudre l'équation «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»m«/mi»«mo»=«/mo»«mo»#«/mo»«mi»g«/mi»«mo»§#183;«/mo»«msup»«mfenced»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/mfenced»«mfrac»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/mfrac»«/msup»«/math»

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mi mathvariant="normal">a</mi><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>.</mo></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">g</mi><mo>=</mo><mn>10</mn><mo>&#xD7;</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo>.</mo></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mo>=</mo><mfrac><mi mathvariant="normal">g</mi><mi mathvariant="normal">b</mi></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">n</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>10</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><mfenced><mrow><mi>log</mi><mfenced><mfrac><mn>1</mn><mi mathvariant="normal">b</mi></mfrac></mfenced><mo>&#xF7;</mo><mi>log</mi><mfenced><mfrac><mi mathvariant="normal">a</mi><mi mathvariant="normal">b</mi></mfrac></mfenced></mrow></mfenced><mo>&#xD7;</mo><mi mathvariant="normal">n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>45</mn><mo>.</mo><mn>23</mn></mrow></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calculs et notes auxiliaires</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Résolution d'une équation logarithmique Résolvez l'équation suivante : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»log«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msub»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»p«/mi»«/mrow»«/mfenced»«mo»=«/mo»«mo»#«/mo»«mi»e«/mi»«/math»


La valeur de x est {#1}

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul&#xa0;sans&#xa0;titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>2</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>50</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">e</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>=</mo><msup><mi mathvariant="normal">b</mi><mi mathvariant="normal">e</mi></msup><mo>+</mo><mi mathvariant="normal">p</mi></math></input></command></group></task></session></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calculs et notes auxiliaires</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSDPS/Sec 5/Fonction polynomiale de degré 2 Équation d'une quadratique

Du haut d’un rocher, un projectile est lancé, et le graphique ci-contre nous renseigne sur  la hauteur en mètres atteinte par ce dernier en fonction du temps écoulé en secondes depuis le lancement.

Quelle est l’équation générale de la trajectoire suivie par le projectile ?

Graph Quadr 2

L'équation générale de cette fonction est f(x) = {1:NM:=-1}«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» {1:MC:=+~-}{1:NM:=6}x + {1:NM:=7}


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 0.3333333 0 Fusée pyrotechnique

Au cours d’un feu d’artifice, une fusée pyrotechnique s’élève d’une hauteur h (en mètres) qui varie en fonction du nombre t de secondes écoulées depuis sa mis à feu selon l’équation h(t) = -2t2 + 16t. Pour faire éclater cette fusée à la hauteur maximale qu’elle peut atteindre, après combien de secondes de vol doit-elle exploser ?


La fusée doit exploser après {4:SHORTANSWER:=4} secondes.


]]> 0.3333333 0 Équation d'une quadratique Quelle est la règle associée à la fonction quadratique décrivant la relation entre la hauteur f(x) atteinte par une balle de golf et le temps écoulé (x) depuis qu’elle a quitté le sol ?

Graph quadr 1

Le règle de la fonction f(x) est : f(x) = {#1} «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» + {#2} x + {#3}

]]> 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 ou 
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mn»3«/mn»«mi»x«/mi»«mo»(«/mo»«mi»x«/mi»«mo»-«/mo»«mn»3«/mn»«mo»)«/mo»«/math»
]]> 3.0000000 1.0000000 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul&#xa0;sans&#xa0;titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>=</mo><mo>-</mo><mn>3</mn><mi>x</mi><mfenced><mrow><mi>x</mi><mo>-</mo><mn>3</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>·</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>9</mn><mo>·</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1"><![CDATA[{"elements":[],"constraints":[],"displays":[{"id":"traceur1","center":[0,0],"background_color":"#FFFFFF","axis_color":"#717171","grid_primary_color":"#C6C6C6","grid_secondary_color":"#E2E2E2","axis_x":true,"horizontal_axis_label":"","horizontal_axis_values_position":"below","horizontal_axis_step":"auto","grid_x":true,"horizontal_grid_step":"auto","axis_y":true,"vertical_axis_label":"","vertical_axis_values_position":"left","vertical_axis_step":"auto","grid_y":true,"vertical_grid_step":"auto","width":41.16,"height":21,"external":false,"grid_subdivisions":2}],"handwriting":[]}]]]]><![CDATA[></construction></constructions></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calculs et notes auxiliaires</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Équation quadratique

Du haut d’un rocher, un projectile est lancé, et le graphique ci-contre nous renseigne sur  la hauteur en mètres atteinte par ce dernier en fonction du temps écoulé en secondes depuis le lancement.

Quelle est l’équation générale de la trajectoire suivie par le projectile ?

Graph Quadr 2

L'équation générale de cette fonction est f(x) = {#1}«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math»  {#2}x + {#3}

]]> 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 Donc
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»-«/mo»«mn»1«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»6«/mn»«mi»x«/mi»«mo»+«/mo»«mn»7«/mn»«/math»
]]> 3.0000000 0.3333333 0 <question><localData><data name="inputField">textField</data></localData></question> Équation d'une parabole - Dynamique Quelle est l’équation qui représente la courbe tracée dans le graphique ci-dessous? #traceur1


Le sommet de la courbe se trouve à (#h, #k) et passe par (0, #c).

]]>



]]> 4.0000000 0.3333333 0 true true abc Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. y = #a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» #Symboleb #b1 x #Symbolec #c1

]]> <p>y = #a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» #Symboleb #b1 x #Symbolec1 #c1

]]> <p>y = #a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» #Symboleb1 #b1 x #Symbolec #c1

]]> <p>y = #a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» #Symboleb1 #b1 x #Symbolec1 #c1

]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">a</mi><mo>&#x2260;</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b1</mi><mo>=</mo><mfenced open="|" close="|"><mi mathvariant="normal">b</mi></mfenced></math></input></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>.</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c1</mi><mo>=</mo><mfenced open="|" close="|"><mi mathvariant="normal">c</mi></mfenced></math></input></command><command name="plot"><properties><property name="color">{53,117,183}</property><property name="line_width">2</property><property name="name">courbe1</property><property name="plotter">traceur1</property><property name="xref">&quot;5&quot;</property></properties><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi><mo>=</mo><mi mathvariant="normal">a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi mathvariant="normal">b</mi><mi>x</mi><mo>+</mo><mi mathvariant="normal">c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>traceur1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>si</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&gt;</mo><mn>0</mn><mo>&#xA0;</mo><mi>alors</mi><mspace linebreak="newline" indentshift="1"/><mi>Symboleb</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mspace linebreak="newline" indentshift="1"/><mi>Symboleb1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mspace linebreak="newline" indentshift="0"/><mi>sinon</mi><mspace linebreak="newline" indentshift="1"/><mi>Symboleb</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mspace linebreak="newline" indentshift="1"/><mi>Symboleb1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mspace linebreak="newline" indentshift="0"/><mi>fin</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>si</mi><mo>&#xA0;</mo><mi mathvariant="normal">c</mi><mo>&gt;</mo><mn>0</mn><mo>&#xA0;</mo><mi>alors</mi><mspace linebreak="newline" indentshift="1"/><mi>Symbolec</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mspace linebreak="newline" indentshift="1"/><mi>Symbolec1</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mspace linebreak="newline" indentshift="0"/><mi>sinon</mi><mspace linebreak="newline" indentshift="1"/><mi>Symbolec</mi><mo>=</mo><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo><mspace linebreak="newline" indentshift="1"/><mi>Symbolec1</mi><mo>=</mo><mo>&quot;</mo><mo>+</mo><mo>&quot;</mo><mspace linebreak="newline" indentshift="0"/><mi>fin</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>&quot;</mo><mo>-</mo><mo>&quot;</mo></math></output></command><command 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mathvariant="normal">k</mi></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>.</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>.</mo><mn>55</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1"><![CDATA[{"elements":[{"id":"A","type":"point","coordinates":[-19,17],"wiris_cas_kernel_computed":"false"},{"id":"courbe1","value_content":"<math><lambda><bvar><ci>x</ci></bvar><domainofapplication><interval closure=\"closed\"><apply><minus/><infinity/></apply><infinity/></interval></domainofapplication><apply><plus/><apply><times/><apply><minus/><cn>5</cn></apply><apply><power/><ci>x</ci><cn>2</cn></apply></apply><apply><minus/><apply><times/><cn>3</cn><ci>x</ci></apply><cn>7</cn></apply></apply></lambda></math>","type":"function_graph","wiris_cas_kernel_computed":"false"}],"constraints":[],"displays":[{"styles":[{"color":"#3575B7","stroke_width":2,"xref":"5","external":true,"ref":"courbe1"}],"id":"traceur1","aspect_ratio":0.9911308605232216,"center":[0,0],"background_color":"#FFFFFF","axis_color":"#717171","grid_primary_color":"#C6C6C6","grid_secondary_color":"#E2E2E2","axis_x":true,"horizontal_axis_label":"","horizontal_axis_values_position":"below","horizontal_axis_step":"auto","grid_x":true,"horizontal_grid_step":"auto","axis_y":true,"vertical_axis_label":"","vertical_axis_values_position":"left","vertical_axis_step":"auto","grid_y":true,"vertical_grid_step":"auto","width":80.67359970092774,"height":81.75888061523438,"grid_subdivisions":2}],"handwriting":[]}]]]]><![CDATA[></construction></constructions></wiriscalc>]]></wirisCasSession><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSDPS/Sec 5/Optimisation Rémunération à l'épicerie Olivier est caissier et emballeur dans une épicerie. Le nombre d’heures qu’il travaille chaque semaine est soumis à différentes contraintes. Ces contraintes sont représentées par les inéquations et le polygone de contraintes ci-contre. X représente le nombre d’heures de travail par semaine comme caissier et Y représente le nombre d’heures de travail comme emballeur.


y ≥ 4

 x + y ≤ 16

 y ≤ 4 + 2x

 x ≥ 1

Quelles sont les coordonnées du point R ?


Le vecteur résultant est : ( {#1}, {#2} )

]]> 4.0000000 0.3333333 0 <question><localData><data name="inputField">textField</data></localData></question> Sommet d'un polygone de contraintes

Soit un polygone de contraintes et le système d’inéquations correspondant.

Chaque côté du polygone porte le numéro de la relation qui lui est associée.


Lequel des couples ci-dessous correspond à un sommet du polygone de contraintes?


]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. (8, 11)

]]> (7, 2)

]]> (12,7)

]]> (11, 6)

]]> Sommet d'un polygone de contraintes

Pendant ses vacances, Pierrette vend des casquettes bleues et des casquettes noires.

Elle doit cependant respecter certaines contraintes traduites par les inéquations ci‑dessous et le polygone de contraintes ci‑contre.



 x «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 0         x + y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 40           x «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 3y

y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 0         x + y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8804;«/mo»«/math» 100        y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 10



Quelles sont les coordonnées du sommet P du polygone de contraintes?


]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. (65, 35)

]]> (70, 30)

]]> (75, 25)

]]> (80, 20)

]]> Sommet d'un polygone de contraintes

Soit un polygone de contraintes et le système d'inéquations correspondant.

Chaque côté du polygone et la relation correspondante sont identifiés par le même numéro.



Quel couple ci‑dessous correspond à un sommet du polygone de contraintes?



]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. (10, 20)

]]> (40, 80)

]]> (100, 30)

]]> (140, 10)

]]> Sommet d'un polygone de contraintes Le système d’inéquations et le polygone de contraintes ci‑dessous représentent une situation d’optimisation. On a associé chaque côté du polygone et l’inéquation correspondante par le même numéro.





Quelles sont les coordonnées du sommet R de ce polygone de contraintes?


]]> Résolution d'un système des 2 équations représentant les droites à l'intersection du point cherché.

]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. (16, 32)

]]> (16, 4)

]]> (9, 18)

]]> (18, 9)

]]> Sommet d'un polygone de contraintes Les contraintes d’une situation d’optimisation se traduisent par le système d’inéquations ci‑dessous.

x «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 0

y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 0

y < 9

x + y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«/math» 5

2x + 3y «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8804;«/mo»«/math» 30

Lequel des couples suivants représente une solution de ce système d’inéquations?


]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. (1, 9)

]]> (2, 2)

]]> (4, 5)

]]> (11, 5)

]]> Sommet d'un polygone de contraintes Les contraintes liées à une situation d’optimisation sont représentées par le système d’inéquation et le polygone de contraintes suivants. On a associé chaque côté du polygone et l’inéquation correspondante par le même numéro.





Quelles sont les coordonnées du sommet P de ce polygone de contraintes?


]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. (4, 9)

]]> (7, 7)

]]> (2, 5)

]]> (8, 2)

]]> $course$/top/CSDPS/Sec 5/Trigonométrie Coordonnées de points dans le cercle Quelles sont les coordonnées exactes de P(-120°)?

]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte.

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mfrac»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«mn»2«/mn»«/mfrac»«mo»,«/mo»«mfrac»«mrow»«mo»-«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«/math»


]]>

]]>

]]> Le cercle trigonométrique Quel est le point, sur le cercle trigonométrique, qui a comme coordonnées (0, 1)? 4.0000000 0.3333333 0 true true none 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte.

]]>

]]>

]]> ]]> Les degrés Parmi les grandeurs d'angles suivantes, laquelle est équivalente à 70°?

]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. 450°

]]> -70°

]]> 650°

]]> 700°

]]> Les radians Dans un cercle de rayon 1, un angle au centre intercepte un arc de 3 radians; quelle est (en degrés) la valeur de cet angle au centre?

]]> 4.0000000 0.5000000 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. 3

]]>

]]> 120

]]>

]]> 171,9

]]> 3,1416

]]>

]]> Les radians

Le rayon d’un cercle de centre O est de 12 cm. Un arc AB de ce cercle mesure 18 cm. Quelle est, en radians, la mesure de l’angle AOB?


]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. 1,5 rad

]]> 0,67 rad

]]> 12 rad

]]> 18 rad

]]> Points de mêmes coordonnées Parmi les points suivants, lequel a les mêmes coordonnées que le point «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mfrac»«mrow»«mn»7«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»4«/mn»«/mfrac»«/mfenced»«/math»?

]]> 4.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte.

]]>

]]>

]]>

]]> Quadrants dans le cercle trigonométrique Soit P  la fonction d’enroulement de la droite réelle sur le cercle trigonométrique. Dans quel quadrant le point P(23) est-il situé?

]]> 1.0000000 0.3333333 0 true true abc 1 Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. 1

]]> 2

]]> 3

]]> 4

]]> Des tours sur un cercle Combien de tours complets fait-on lorsqu'on parcourt une distance de #a«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#960;«/mi»«/math»?

]]> 4.0000000 0.3333333 0 true true abc Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #y

]]> #a

]]> #b <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">,</property><property name="digit_group_separator"> </property><property name="float_format">,mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">;</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>70</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>53</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><mfrac><mi mathvariant="normal">a</mi><mn>2</mn></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>53</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>quotient</mi><mfenced><mrow><mfenced><mrow><mi mathvariant="normal">a</mi><mo>+</mo><mn>2</mn></mrow></mfenced><mo>;</mo><mn>2</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>si</mi><mo>&#xA0;</mo><mi mathvariant="normal">x</mi><mo>&#x2208;</mo><mi mathvariant="normal">&#x2115;</mi><mo>&#xA0;</mo><mi>alors</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">y</mi><mo>=</mo><mfrac><mi mathvariant="normal">a</mi><mn>2</mn></mfrac><mspace linebreak="newline" indentshift="0"/><mi>sinon</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">y</mi><mo>=</mo><mi>quotient</mi><mfenced><mrow><mi mathvariant="normal">a</mi><mo>;</mo><mn>2</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>fin</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>26</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Un angle négatif et son quadrant Dans quel quadrant du cercle trigonométrique se situe le côté terminal d’un angle de #a°?

]]> 4.0000000 0.3333333 0 true true abc Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #y

]]> #m

]]> #n

]]> #o

]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Untitled calc</mtext></math></title><properties><property name="decimal_separator">,</property><property name="digit_group_separator"></property><property name="float_format">,f</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator"> </property><property name="lang">en</property><property name="precision">2</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>999</mn><mo>.</mo><mo>.</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>while</mi><mo>&#xA0;</mo><mfenced><mfrac><mi mathvariant="normal">a</mi><mn>90</mn></mfrac></mfenced><mo>&#x2208;</mo><mi mathvariant="normal">&#x2124;</mi><mo>&#xA0;</mo><mi>do</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>999</mn><mo>.</mo><mo>.</mo><mo>-</mo><mn>1</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>end</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><mi mathvariant="normal">a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>589</mn></math></output></command><command><input><math 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]]> 4.0000000 0.3333333 0 0 #b]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">;</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>60</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">x</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>&#xB7;</mo><mi mathvariant="normal">a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mn>360</mn><mo>&#xB7;</mo><mi mathvariant="normal">x</mi><mo>&#xF7;</mo><mfenced><mrow><mn>2</mn><mo>&#xB7;</mo><pi/></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">b</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="mixedfractions">true</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">false</option><option name="relative_tolerance">false</option><option name="tolerance_digits">2</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Période de fonction sinus Quelle est la période de la fonction f(x) = #a sin(#b(x - #h) + #k?

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»2«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mfenced open=¨|¨ close=¨|¨»«mi»b«/mi»«/mfenced»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»2«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mfenced open=¨|¨ close=¨|¨»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfenced»«/mfrac»«/math»

]]> 4.0000000 0.3333333 0 0 #r <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">;</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">a</mi><mo>&#x2260;</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&#x2260;</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">h</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">h</mi><mo>&#x2260;</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">k</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">k</mi><mo>&#x2260;</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>&#xB7;</mo><pi/></mrow><mfenced open="|" close="|"><mi mathvariant="normal">b</mi></mfenced></mfrac></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>8976</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="mixedfractions">true</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">false</option><option name="relative_tolerance">false</option><option name="tolerance_digits">2</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mfrac><mrow/><mrow/></mfrac></math></input></command></group></task></session></wiriscalc>]]></data></localData></question> $course$/top/CSDPS/Sec 5/Vecteurs Calculs - vecteurs Soit les vecteurs «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math»= (#a, #b) et «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»= (#c, #d). Déterminez les composantes du vecteur résultant #k«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» + #j«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math».


Le vecteur résultant est : ( {#1}, {#2} )

]]> (#k • #a + #j • #c, #k • #b + #j • #d)

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">a</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">c</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">c</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">d</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">d</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">k</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">k</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">j</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>9</mn><mo>.</mo><mo>.</mo><mn>9</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">j</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>=</mo><mi mathvariant="normal">k</mi><mo>&#xB7;</mo><mi mathvariant="normal">a</mi><mo>+</mo><mi mathvariant="normal">j</mi><mo>&#xB7;</mo><mi mathvariant="normal">c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">g</mi><mo>=</mo><mi mathvariant="normal">k</mi><mo>&#xB7;</mo><mi mathvariant="normal">b</mi><mo>+</mo><mi mathvariant="normal">j</mi><mo>&#xB7;</mo><mi mathvariant="normal">d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Différence de vecteurs Soit les vecteurs «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math»= (#a, #b) et «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»= (#c, #d). Déterminez les composantes du vecteur résultant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» - «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math».


Le vecteur résultant est : ( {#1}, {#2} )

]]> (#a - #c, #b - #d)

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">a</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">c</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">c</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">d</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">d</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>=</mo><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">g</mi><mo>=</mo><mi mathvariant="normal">b</mi><mo>-</mo><mi mathvariant="normal">d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Somme de vecteurs Soit les vecteurs «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math»= (#a, #b) et «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»= (#c, #d). Déterminez les composantes du vecteur résultant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» + «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math».


Le vecteur résultant est : ( {#1}, {#2} )

]]> (#a + #c, #b + #d)

]]> 4.0000000 0.3333333 0 <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul&#xa0;sans&#xa0;titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">a</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">c</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">c</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">d</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">d</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>=</mo><mi mathvariant="normal">a</mi><mo>+</mo><mi mathvariant="normal">c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">g</mi><mo>=</mo><mi mathvariant="normal">b</mi><mo>+</mo><mi mathvariant="normal">d</mi></math></input></command></group></task></session></wiriscalc>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Norme d'un vecteur Déterminez la norme du vecteur \( \vec{v} \) = (#a, #b).

]]> 4.0000000 0.3333333 0 true true abc Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #c

]]> #d

]]> #e

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]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>=</mo><msqrt><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mn>0</mn><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced><mn>2</mn></msup></msqrt></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>616</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>=</mo><msqrt><mfenced open="|" close="|"><mrow><mi mathvariant="normal">a</mi><mo>+</mo><mi mathvariant="normal">b</mi></mrow></mfenced></msqrt></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">e</mi><mo>=</mo><msqrt><mfenced open="|" close="|"><mrow><mi mathvariant="normal">a</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced></msqrt></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>162</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>=</mo><msup><mi mathvariant="normal">a</mi><mn>2</mn></msup><mo>+</mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>58</mn><mo>.</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Norme d'un vecteur connaissant les extrémités Déterminez la norme du vecteur d'origine (#a, #b) et d'extrémité (#c, #d).

]]> 4.0000000 0.3333333 0 true true abc Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #e

]]> #f

]]> #g

]]> #h

]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">d</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>16</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">e</mi><mo>=</mo><msqrt><msup><mfenced><mrow><mi mathvariant="normal">c</mi><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><msup><mfenced><mrow><mi mathvariant="normal">d</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced><mn>2</mn></msup></msqrt></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>41</mn><mo>.</mo><mn>05</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mo>=</mo><msqrt><mfenced open="|" close="|"><mrow><mi mathvariant="normal">c</mi><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mo>+</mo><mfenced open="|" close="|"><mrow><mi mathvariant="normal">d</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced></msqrt></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>55</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">g</mi><mo>=</mo><msqrt><mfenced open="|" close="|"><mrow><msup><mfenced><mrow><mi mathvariant="normal">c</mi><mo>-</mo><mi mathvariant="normal">a</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><msup><mfenced><mrow><mi mathvariant="normal">d</mi><mo>-</mo><mi mathvariant="normal">b</mi></mrow></mfenced><mn>2</mn></msup></mrow></mfenced></msqrt></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>.</mo><mn>04</mn></math></output></command><command name="approximate"><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">h</mi><mo>=</mo><msqrt><msup><mi mathvariant="normal">d</mi><mn>2</mn></msup><mo>+</mo><msup><mi mathvariant="normal">b</mi><mn>2</mn></msup></msqrt></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn><mo>.</mo><mn>08</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Orientation d'un vecteur Déterminez l'orientation du vecteur «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math» = (#a, #b).

]]> 4.0000000 0.3333333 0 true true abc Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #o

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]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">true</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">a</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&#x2260;</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">c</mi><mo>=</mo><mi>arctan</mi><mfenced><mfrac><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi></mfrac></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>arctan</mi><mo>⁡</mo><mfenced><mfrac><mn>1</mn><mi>a</mi></mfrac></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>si</mi><mo>&#xA0;</mo><mi mathvariant="normal">a</mi><mo>&gt;</mo><mn>0</mn><mo>&#xA0;</mo><mi>alors</mi><mspace linebreak="newline" indentshift="1"/><mi>si</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&gt;</mo><mn>0</mn><mo>&#xA0;</mo><mi>alors</mi><mspace linebreak="newline" indentshift="2"/><mi mathvariant="normal">o</mi><mo>=</mo><mi mathvariant="normal">c</mi><mspace linebreak="newline" indentshift="1"/><mi>sinon</mi><mspace linebreak="newline" indentshift="2"/><mi mathvariant="normal">o</mi><mo>=</mo><mn>360</mn><mo>+</mo><mi mathvariant="normal">c</mi><mspace linebreak="newline" indentshift="1"/><mi>fin</mi><mspace linebreak="newline" indentshift="0"/><mi>sinon</mi><mspace linebreak="newline" indentshift="1"/><mi>si</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&gt;</mo><mn>0</mn><mo>&#xA0;</mo><mi>alors</mi><mspace linebreak="newline" indentshift="2"/><mi mathvariant="normal">o</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi mathvariant="normal">c</mi><mspace linebreak="newline" indentshift="1"/><mi>sinon</mi><mspace linebreak="newline" indentshift="2"/><mi mathvariant="normal">o</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi mathvariant="normal">c</mi><mspace linebreak="newline" indentshift="1"/><mi>fin</mi><mspace linebreak="newline" indentshift="0"/><mi>fin</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">p</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi mathvariant="normal">o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>+</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">q</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi mathvariant="normal">o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>o</mi><mo>+</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi mathvariant="normal">o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>o</mi><mo>+</mo><mn>360</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Orientation d'un vecteur connaissant ses extrémités Déterminez l'orientation du vecteur «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math» , dont les coordonnées du point de départ sont (#a, #b) et celles du point d'arrivée sont (#c, #d).

]]> 4.0000000 0.3333333 0 true true abc Votre réponse est correcte. Votre réponse est partiellement correcte. Votre réponse est incorrecte. #o

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]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">,</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">true</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">a</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">a</mi><mo>&#x2260;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" indentshift="1"/><mi mathvariant="normal">b</mi><mo>=</mo><mi>al&#xE9;a</mi><mfenced><mrow><mo>-</mo><mn>20</mn><mo>.</mo><mo>.</mo><mn>20</mn></mrow></mfenced><mspace linebreak="newline" indentshift="0"/><mi>jusqu_&#xE0;</mi><mo>&#xA0;</mo><mi mathvariant="normal">b</mi><mo>&#x2260;</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r&#xE9;p&#xE9;ter</mi><mspace linebreak="newline" 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mathvariant="normal">p</mi><mo>=</mo><mn>180</mn><mo>+</mo><mi mathvariant="normal">o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>+</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">q</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi mathvariant="normal">o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>o</mi><mo>+</mo><mn>180</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi mathvariant="normal">o</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>o</mi><mo>+</mo><mn>360</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session><constructions><construction group="1">{&quot;elements&quot;:[],&quot;constraints&quot;:[],&quot;displays&quot;:[],&quot;handwriting&quot;:[]}</construction></constructions></wiriscalc>]]></wirisCasSession><localData><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Sheet 1</mtext></math></title><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></task></session></wiriscalc>]]></data></localData></question> Produit scalaire de vecteurs Soit les vecteurs «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math»= (#a, #b) et «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»= (#c, #d). Déterminez le produit scalaire #k«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» \( \bullet \) #j«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math».

]]> #k·#j·#a·#c + #k·#j·#b·#d = #g

]]> 4.0000000 0.3333333 0 0 #g]]> <question><wirisCasSession><![CDATA[<wiriscalc version="3.2"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Calcul sans titre</mtext></math></title><properties><property name="decimal_separator">.</property><property name="digit_group_separator"></property><property name="float_format">mg</property><property name="imaginary_unit">i</property><property name="implicit_times_operator">false</property><property name="item_separator">;</property><property name="lang">fr</property><property name="precision">4</property><property name="quizzes_question_options">true</property><property name="save_settings_in_cookies">false</property><property name="times_operator">·</property><property name="use_degrees">false</property></properties><session version="3.0" lang="fr"><task><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Feuille 1</mtext></math></title><group><command><input><math 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₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.001</option><option name="relative_tolerance">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<wiriscalc version="3.1"><title><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Auxiliary computations and notes</mtext></math></title><properties><property name="lang">en</property><property name="precision">4</property><property name="use_degrees">false</property></properties><session version="3.0" lang="en"><task><title><math 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