Question

2.A rectangular box open at the top is to have volume of 32cubic feet. Find its
dimensions if the total surface area is minimum.
3.a.If u = x
2 + y
2 where x = s + 3t and y = 2s − t find ∂u
∂s and∂u
∂t .

b.If z = sin (
x
y
) , x = e
t
, y = t
2 find dz
dt
.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The dimensions must be close to (32)^1/3 or 3.17

Total surface of the box or 5×10.08 =50.4

S.A.= L*B +2(L*H) +2(B*H)=50.4

Let L=B =3

9+12H = 50.4

H = 41.4/12 = 3.45 increase ht. to 3.6

Dimensions of box 3×3×3.6