college algebra, CANNOT figure this out: a 2 inch by 4 inch by 7 inch iron block is plated with brass so that each of its three dimensions is increased by the same amount x. the volume of the plated block is 50% greater than the volume of the unplated block.
then it asks to give the function for the volume of the plated block. and i know that is (2+x)(4+x)(7+x)
and then it asks what are the three dimensions of the plated block. and the answers are 2.4941, 4.4941, and 7.4941.

Question

mathmate · Answer

So you need to solve for the thickness x, such that
1.5(2*4*7) = (2+x)(4+x)(7+x)
or 
f(x)=(2+x)(4+x)(7+x)-84=0
Graphing tells us that there is a root around 0.5.
Use Newton's method to converge to the root:
f'(x)=3x^2+26x+50,
x=0.5-f(0.5)/f'(0.5)=0.4941

anonymous · Answer

thank you so so much! like you have no idea. thank you!

mathmate · Answer

You're welcome!