SOLUTION: A rain gutter is to be made of a sheet that is 10in wide by turning up the edges 90 degrees. I have developed the formula for the cross sectional area by letting x define the u

Question 575890: A rain gutter is to be made of a sheet that is 10in wide by turning up the edges 90 degrees.
I have developed the formula for the cross sectional area by letting x define the unknown quantity of depth that is to be the independent value.
my formula is f(x)= 2x^2 + 10x

My question is, what happens to the cross sectional area as depth size increases?
What x and y values make sense for this problem? (restricted domain and range)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rain gutter is to be made of a sheet that is 10in wide by turning up the edges 90 degrees.
:
Using the depth as x,
then
(10-2x) = the width of the gutter
;
y = the cross sectional area
:
y = depth * width
y = x(10-2x)
y = -2x^2 + 10x
or
f(x) = -2x^2 + 2x
:
Graphing this would make it clear

You can see the domain is >0 to < 5, with max area when x= 2.5

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