Posted by Sandra on Friday, July 10, 2009 at 3:06pm.
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

algebra  Marth, Friday, July 10, 2009 at 3:20pm
a) use 10 for s.
V(10) = 10^3  13(10)^2 + 54(10)  72
V(10) = 1000  1300 + 540  72
V(10) = 168
b) Divide V(s) by (s6)
Using synthetic division:
6 1 13  54  72
 0  6  42  72
_____________________
 1  7  12  0
So, the new length and height can be found by s^2 7s + 12.
That can factored into (s3)(s4)
V(s) = (s6)(s3)(s4)
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