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Spencerg325
05.02.2021 •
Mathematics
Bonjour, voilà la question: une boite sans couvercle de contenance 0,5L, a la forme d'un pavé droit de base carrée de coté x cm et de hauteur h cm. 1a- justifier que x^2*h=500 b- en déduire que l'aire extérieure de la boite (fond plus parois latérales) est, pour tout x € ]0;+infini[ : A(x)=x^2 + (2000/x) 2- trouver les dimensions de la boite pour lesquelles l'aire extérieure est minimale et préciser cette aire. si quelqu'un sais répondre à une de ces questions ça m'aidera beaucoup, merci d'avance!
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Ответ:
x=y/4+8/3
y= 4x-32/3
Step-by-step explanation:
2x-1/3=1/2y+5
Add 1/3 =0.333333333 to both sides.
2x-1/3=1/2+5+1/3
Add 5 and 1/3≈0.333333333 to get 16/3 ≈5.333333333.
2x=1/2y+16/3
The equation is in standard form.
2x=y/2+16/3
Divide both sides by 2.
2x/2=y/2+16/3/2
Dividing by 2 undoes the multiplication by 2.
x=y/2+16/3/2
Divide y/2+16/3 by 2
x= y/4+8/3
2x-1/3=1/2y+5
Swap sides so that all variable terms are on the left hand side.
1/2+5=2x-1/3
Subtract 5 from both sides.
1/2y=2x-1/3-5
Subtract 5 from -1/3 ≈−0.333333333 to get -16/3 −5.333333333.
1/2=2x-16/3
Multiply both sides by 2.
1/2y/1/2=2x-16/3/1/2
Dividing by 1/2 =0.5 undoes the multiplication by 1/2 =0.5
y=2x-16/3/1/2
Divide 2x-16/3 by 1/2 = 0.5 by multiplying 2x-16/3 by the reciprocal of 1/2=0.5
y = 4x-32/3