My cousin asked me for help on a math question. I thought I figured it out but my answer seems too simple? Help? It's just algebra, polynomials and such. 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) = s^3 - 13s^s + 54s - 72 a.) Find V(10). This was easy, I just plugged 10 in for s and got 168 b.) If the new width is s-6 centimeters, then what are the new length and height? I figured they must be the same as the width since it's a cube, so s-6 c.) Find the volume when s = 10 by multiplying the length, width, and height. I figured plugging 10 in for s in respect to each side (s-6), so 4x4x4 is 64 Any help or confirmation is appreciated, from one nerd to another.
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Looks like you're on the right track. For b), you could probably find what s actually is, by setting (S-6)^3 = V(S), but your answer for length and height is technically correct. For c), looks like you did the right thing as well. You could check your answer by plugging s=10 into your new volume formula though.
here are my thoughts, assuming this is all that's given. a) correct, it's asking you to solve the V(s) formula for 10. b) incorrect, the original shape was a cube, each side was reduced by a number, but not the same number (new volume from part a) was 168, which is not a perfect cube). so you need to divide out (s-6) from the V(s) formula. so V(s)=(s-6)(s-something)(s-something)... working on it now c) this one is confusing. if s=10, the volume of the cube is 10^3=1000. if they want you to solve V(s) for s=10, you already did that in part a).... is there more to the question?
You just bothered. I think the insinuation is that each side is reduced by 6, unless its just some really crappy wording. Is there any non-trivial solutions for V(S)=(s-6)^3 ?
i think the wording is off, but you can't reduce the three dimensions by the same number and get the original V(s) equation.
Wait until numbers leave math altogether and are replaced by Greek symbols. I barely made it through non-linear Calculus in college (thank God it was the highest I had to go) and let me tell you, you ain't seen nothing yet.
Then I guess your answer is more likely to be the correct one. That's kind of a strange wording though. Maybe this thread should get turned into another one of those "math quiz" threads we had a while back. "Do not worry about your difficulties in mathematics, for I assure you mine are greater." - Albert Einstein
should've read like this i think: A cube has sides S, after reducing each side you get a rectangular prism of volume V(S)=S^3 - 13S^2 +54S - 72. a) solve V(S) for S=10. b) one side is S-6, what are the other two? c) if S=10, find volume by using the height, width, length found in part b. i could do math quiz answers, i would stink at coming up with questions.
I will approach it as V = len x wid x hgt. len = longest side = s width = middle length side = s - x height = shortest side = s - y so V = s(s-x)(s-y) = s( s^2 - s(y+x) + xy ) = s^3 - s^2(x+y) - sxy (Yes sexy)
B is a little confusing because on the original equation, How you know which side is reduced. If the equation is V(s-6) then... V = (s-6)^3 - 13( s-6)^2 + 54(s-6) - 72 V = (s-6)(s-6)(s-6) - 13(s-6)^2 + 54(s-6) -72 V = (s-6)(s^2 -12s +36) - 13 (s^2 - 12s +36) +54s - 324 - 72 V= (s^3 - 12s^2 + 36s - 6s^2 + 72s - 216) - (13s^2 + 156s - 468) + 54s - 396 V = (s^3 -18s^2 + 108s - 216) - (13s^2 + 156s -468) + 54s - 396 V = s^3 -(18s^2 + 13s^2) + (108s - 156s) + (468 - 216) + 54s - 396 V = (s^3 - 5s^2 - 48s + 252) + 54s -396 V = s^3 - 5s^2 + 6s - 144 Someone check my answer.
check your signs, you're not carrying some of your negatives through correctly. easier to write it out completely instead of having minus times a whole expression. s^3-12s^2+36s-6s^2+72s-216-13s^2+156s-468+54s-324-72 = s^3-12s^2-6s^2-13s^2+36s+72s+156s+54s-216-468-324-72 = s^3-31s^2+318s-648
