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Texoce
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April 2019
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Coucou j'ai besoin d'aide pour l'exercice 99 svp je comprend pas
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isapaul
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Bonjour
ABCD et un carré de 5 cm de côté
BM = DN = x
1)
on a
Aire ABCD = 5² = 25 cm²
Aire CNPM = (5-x)²
Aire ABM = (AB * MB)/2 = (5x)/2
Aire AND = (AD * DN)/2 ) = (5x)/2
2)
Aire Flèche = Aire ABCD - Aire MCNP - Aire ABM - Aire AND
Aire Flèche = 25 - (5 - x)² - (5x)/2 - (5x)/2
Aire Flèche = 25 - 25 - x² + 10x - 5x
Aire Flèche = -x² + 5x
3)
A(x) = - (x-5/2)²+25/4
A(x) = - (x² - 10x/2 +25/4) +25/4
A(x) = -x² + 10x/2
A(x) = -x² +5x ce qu'il fallait démontrer...
4)
la dérivée sera A ' (x) = - 2x + 5 donc A' (x) = 0 pour x = 5/2 = 2.5
Sens de Variation et tableau
x 0 ___________________ 2.5 __________________________ 5
A ' (x) -5 positive 0 négative -5
A(x) 0 croissante 6.25 décroissante 0
figure 1 : A(1.4) = 5.04
figure 2 : A(2.9) = 6.09
figure 3: A(4.3) = 3.01
5)
A(x) = 5.25 soit
-x²+5x = 5.25
-x² + 5x - 5.25 = 0
delta = 25 - 21 = 4 donc racine delta ou Vdelta = 2
deux solutions
x ' = (-5 - 2)/-2 = 7/2 = 3.5
x " = ( -5 +2) /-2 = 3/2 = 1.5
2 votes
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isapaul
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Lista de comentários
Verified answer
BonjourABCD et un carré de 5 cm de côté
BM = DN = x
1)
on a
Aire ABCD = 5² = 25 cm²
Aire CNPM = (5-x)²
Aire ABM = (AB * MB)/2 = (5x)/2
Aire AND = (AD * DN)/2 ) = (5x)/2
2)
Aire Flèche = Aire ABCD - Aire MCNP - Aire ABM - Aire AND
Aire Flèche = 25 - (5 - x)² - (5x)/2 - (5x)/2
Aire Flèche = 25 - 25 - x² + 10x - 5x
Aire Flèche = -x² + 5x
3)
A(x) = - (x-5/2)²+25/4
A(x) = - (x² - 10x/2 +25/4) +25/4
A(x) = -x² + 10x/2
A(x) = -x² +5x ce qu'il fallait démontrer...
4)
la dérivée sera A ' (x) = - 2x + 5 donc A' (x) = 0 pour x = 5/2 = 2.5
Sens de Variation et tableau
x 0 ___________________ 2.5 __________________________ 5
A ' (x) -5 positive 0 négative -5
A(x) 0 croissante 6.25 décroissante 0
figure 1 : A(1.4) = 5.04
figure 2 : A(2.9) = 6.09
figure 3: A(4.3) = 3.01
5)
A(x) = 5.25 soit
-x²+5x = 5.25
-x² + 5x - 5.25 = 0
delta = 25 - 21 = 4 donc racine delta ou Vdelta = 2
deux solutions
x ' = (-5 - 2)/-2 = 7/2 = 3.5
x " = ( -5 +2) /-2 = 3/2 = 1.5