SOLUTION: Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is

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Question 202840: Decreasing cube. Each of the three dimensions of a
cube with sides of length s centimeters is decreased by a
whole number of centimeters. The new volume in cubic
centimeters is given by
V(s)  s3  13s2  54s  72.
a) Find V(10).
b) If the new width is s  6 centimeters, then what are the
new length and height?
c) Find the volume when s  10 by multiplying the
length, width, and height.
Have tried the following: For A.) v(10)=10^3-13(10)^2+54(10)-72 For B. and C. I am completely lost at where to even begin.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hi there,

Something must have not been copied correctly because there are a lot of box symbols all over the page. So I'm going to make a lot assumptions of what the problem really is.


a)


V%28s%29=s%5E3-13s%5E2%2B54s-72 Start with the given function.


V%2810%29=%2810%29%5E3-13%2810%29%5E2%2B54%2810%29-72 Plug in s=10 (ie replace each "s" with 10).


V%2810%29=1000-13%2810%29%5E2%2B54%2810%29-72 Cube 10 to get 1000.


V%2810%29=1000-13%28100%29%2B54%2810%29-72 Square 10 to get 100.


V%2810%29=1000-1300%2B54%2810%29-72 Multiply -13 and 100 to get -1300.


V%2810%29=1000-1300%2B540-72 Multiply 54 and 10 to get 540.


V%2810%29=168 Combine like terms.




b)


V=LWH Start with the volume equation.


s%5E3-13s%5E2%2B54s-72=L%28s-6%29H Plug in the given expressions


%28s%5E3-13s%5E2%2B54s-72%29%2F%28s-6%29=LH Divide both sides by s-6.


%28%28s-6%29%28s%5E2-7s%2B12%29%29%2F%28s-6%29=LH Factor the numerator


%28cross%28%28s-6%29%29%28s%5E2-7s%2B12%29%29%2Fcross%28%28s-6%29%29=LH Cancel out the common terms.


s%5E2-7s%2B12=LH Simplify


LH=s%5E2-7s%2B12 Rearrange the equation


LH=%28s-3%29%28s-4%29 Factor


So the new length and height are s-3 and s-4




c)

I'll let you attempt this one on your own. Repost if you still need help.


Note: the answer is going to be the same as the answer in part a) (so you'll have something to check)