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pommekiwi
@pommekiwi
January 2021
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Bonjour j'ai un dm pour demain et je n'y arrive vraiment pas merci énormément .seconde
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no63
Salut
AM=AN=x
1) x appartient a [ 0 ;6 ]
2) aire du carré = x²
aire du rectangle hachuré = L*l
= (6-x)(10-x)
= x²-16x+60
3) aire hachurée = aire du carré + aire du rectangle hachuré
= x²+x²16x+60
= 2x²-16x+60
4) tableau
x 0 1 2 3 4 5 6
aire 60 46 36 30 28 30 36
5) le minimum de f est donné par -b/2a
=> 16/(2*2)= 4
valeur du minimum => f(4)= 28
6) je te laisses faire
7) a) aire ABCD= 60
aire hachurée >= (1/2)*60
2x²-16x+60>= 30
2x²-16x+30>=0
x²-8x+15>=0
b) (x-3)(x-5)
=> x²-5x-3x+15
=> x²-8x+15
c) x-3>=0 => x>=3
x-5>=0 => x>=5
tableau de signe
x 0 3 5 6
x-3 - 0 + +
x-5 - - 0 +
x²-8x+15 + 0 - 0 +
S= [ 0 ; 3 ] U [ 5 ; 6 ]
1 votes
Thanks 1
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AM=AN=x
1) x appartient a [ 0 ;6 ]
2) aire du carré = x²
aire du rectangle hachuré = L*l
= (6-x)(10-x)
= x²-16x+60
3) aire hachurée = aire du carré + aire du rectangle hachuré
= x²+x²16x+60
= 2x²-16x+60
4) tableau
x 0 1 2 3 4 5 6
aire 60 46 36 30 28 30 36
5) le minimum de f est donné par -b/2a
=> 16/(2*2)= 4
valeur du minimum => f(4)= 28
6) je te laisses faire
7) a) aire ABCD= 60
aire hachurée >= (1/2)*60
2x²-16x+60>= 30
2x²-16x+30>=0
x²-8x+15>=0
b) (x-3)(x-5)
=> x²-5x-3x+15
=> x²-8x+15
c) x-3>=0 => x>=3
x-5>=0 => x>=5
tableau de signe
x 0 3 5 6
x-3 - 0 + +
x-5 - - 0 +
x²-8x+15 + 0 - 0 +
S= [ 0 ; 3 ] U [ 5 ; 6 ]