SOLUTION: Suppose that y varies directly as x and inversely as z^2. If x and z are both decreased by 20%, then y? This is all I've got y=kx/z^2 ...I don't even know whether it's right.

Question 564767: Suppose that y varies directly as x and inversely as z^2. If x and z are both decreased by 20%, then y?
This is all I've got y=kx/z^2 ...I don't even know whether it's right.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you problem states that y varies directly as x and inversely as z^2.
the formula for that would be:
y = kx/z^2
you got started right because this agrees with what you showed.
if x and y are each reduced by 20%, then you get:
x - .2x = .8x
z - .2z = .8z
you would replace x with .8x and you would replace z with .8z to get:
y = k(.8x)/(.8z)^2
you would simplify this to:
y = .8kx / .64z^2 which you can further simplify to:
y = 1.25kx/z^2
let's see how this would pan out.
assume x = 64 and assume z = 8 and assume k = 1.
that makes the math simple.
your original equation of:
y = kx/z^2 becomes:
y = 1*64/8^2 which becomes:
y = 64/64 which becomes:
y = 1.
now assume that x and y are both decreased by 20%.
your equation of y = kx/z^2 becomes y = 1*(.8x) / (.8z)^2 which becomes:
y = .8*64 / (.8*8)^2 which becomes:
y = 51.2 / 6.4^2 which becomes:
y = 51.2 / 20.96 which becomes:
y = 1.25
we said that your equation became:
y = 1.25kx/z^2
since your original x = 64 and your original y = 8, this equation becomes:
y = 1.25(64)/(8^2) which becomes:
y = 80/64 which becomes:
y = 1.25
the answer comes out the same so the equation is good.
your answer is:
y = 1.25kx/z^2
a good reference on this type of problem can be found here:
http://regentsprep.org/Regents/math/algtrig/ATE7/indexATE7.htm
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