SOLUTION: Consider a rectangular box with a volume of 300 cubic centimeters. Suppose that the base is a rectangle with sides x centimeters and 3x centimeters. Let h(x) give the height of the
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Question 490573: Consider a rectangular box with a volume of 300 cubic centimeters. Suppose that the base is a rectangle with sides x centimeters and 3x centimeters. Let h(x) give the height of the box in centimeters and let A(x)be the total area of the six sides of the box. Find h(x) and A(x).
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Consider a rectangular box with a volume of 300 cubic centimeters.
Suppose that the base is a rectangle with sides x centimeters and 3x centimeters.
Let h(x) give the height of the box in centimeters and let A(x)be the total area of the six sides of the box.
Find h(x) and A(x).
:
Using the given volume, find the h in terms of x
L * W * h = 300
3x * x * h = 300
3x^2h = 300
divide both sides by 3
x^2h = 100
divide both sides by x^2
h(x) =
:
Area of the sides
A = 2(L*W) + 2(L*h) + 2(W*h)
L=3x; W=x
A = 2(3x*x) + 2(3x*h) + 2(x*h)
A = 6x^2 + 6xh + 2xh
A = 6x^2 + 8xh
Replace h with
A = 6x^2 + 8x*
A(x) = 6x^2 +
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