An engineer is designing an open box (without top) with a square base. The box's volume must be 2900 in ^(3). The engineer wants to minimize the box's surface area. Note that the volume of the box is V=hx^(2). We can write the box's surface area, S(x), as a function of x : S(x)=4xh+x^(2) S(x)=4x((2900)/(x^(2)))+x^(2) S(x)=(11600)/(x)+x^(2) Use a gr

Question

An engineer is designing an open box (without top) with a square base. The box's volume must be 2900 in

^(3)

. The engineer wants to minimize the box's surface area. Note that the volume of the box is

V=hx^(2)

. We can write the box's surface area,

S(x)

, as a function of

x

:

S(x)=4xh+x^(2)
S(x)=4x((2900)/(x^(2)))+x^(2)
S(x)=(11600)/(x)+x^(2)

Use a graphing utility to find the value of

x

and

h

such that the box has a minimum surface area. Round your answers to two decimal places and include units. The box has a minimum surface area of

◻

when its base's side length is

◻

and the box's height is (Use in for inches and in

^(^())2

for square inches.)

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