Question 39285This question is from textbook College Algebra
: Cost of material. A rectangular box with volume 320ft^3 is built with a square base and top. The cost is $1.50/ft^2 for the bottom, $2.50/ft^2 for the sides, and $1/ft^2 for the top. Let x=the length of the base, in feet.
a) Express the cost of the box as a function of x.
b) Find the domain of the function.
This question is from textbook College Algebra
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Cost of material. A rectangular box with volume 320ft^3 is built with a square base and top. The cost is $1.50/ft^2 for the bottom, $2.50/ft^2 for the sides, and $1/ft^2 for the top. Let x=the length of the base, in feet.
a) Express the cost of the box as a function of x.
Cost = cost of bottom + cost of top +4(cost of one side)
cost of bottom= $1.5x^2
cost of top =$1(x^2)
To get cost of side need to know the height of a side, as follows.
V=lwh
320=x^2h
h=320/x^2
Area of one side is base(height)=x(320/x^2)=320/x
Cost of 4 sides is 4($2.5)(320/x)=3200/x
EQUATION:
Cost =1.5x^2+x^2+3200/x
= 2.5x^2+3200/x
b) Find the domain of the function.
Domain of the FUNCTION is all Real numbers except x=0
Domain of the function as a model of the problem is
x>0
Cheers,
Stan H.
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