SOLUTION: 74. An open box is to be made from a square piece of cardboard of dimensions 30 inches by 30 inches by cutting out squares of area x^2 from each corner. a. Express the volume V of

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Question 54909This question is from textbook Applied College Algebra
: 74. An open box is to be made from a square piece of cardboard of dimensions 30 inches by 30 inches by cutting out squares of area x^2 from each corner.
a. Express the volume V of the box as a function of x.
b. State the domain of V.This question is from textbook Applied College Algebra

Answer by funmath(2925) About Me  (Show Source):
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74. An open box is to be made from a square piece of cardboard of dimensions 30 inches by 30 inches by cutting out squares of area x^2 from each corner.
a. Express the volume V of the box as a function of x.
b. State the domain of V.
Each side of the square would look like x--------x, if the length started out as 30 inches, then each side would be 30-2x.
V=L*W*H
The height is x.
Length and width are the same because it has a square base.
a. V%28x%29=%2830-2x%29%2830-2x%29%2Ax
V%28x%29=%2830-2x%29%5E2%2Ax
b.Each dimension has to be greater than 0.
x>0 and 30-2x>0
30-2x>0
-30+30-2x>0-30
-2x>-30
-2x/-2<-30/-2
x<15in
Therefore
0%3Cx%3C15in is the domain.
Interval notation: (0,15in)
Happy Calculating!!!