An open box is constructed of 3500 cm2 of cardboard. the box is a cuboid, with height hcm and square base of side xcm. what is the value of x which maximises the volume of the box?

34.16 cm

Step-by-step explanation:

side of square base = x

height = h

area, A = 3500 cm^2

Area = x² + 4xh = 3500

4 xh = 3500 - x²

h = (3500 - x²)/4x

Volume = Area of base x height

V = x² h

V = x² (3500 - x²)/4x

V = (3500 x - x³) / 4

Differentiate volume with respect to x

dV/dx = (3500 - 3x²) / 4

It is equal to zero for maxima and minima

3500 - 3x² = 0

x = 34.16 cm

Now differentiate again

d²V/dx² = 6x / 4

It is negative so the volume is maximum.

Thus, for x = 34.16 cm, the volume is maximum.

b

step-by-step explanation:

step-by-step explanation:

*calories burned = (weight)(calorie factor)*

calories burned = 180 (0.65)

calories burned = 117

the calories he used up is 117, which is 65% of his weight.