SOLUTION: Given that y is directly proportional to the cube of x and inversly proportional to the square of z, if x decreases by 35.9% and z increases by 5.8%, by what factor does y change?

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Question 956610: Given that y is directly proportional to the cube of x and inversly proportional to the square of z, if x decreases by 35.9% and z increases by 5.8%, by what factor does y change?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equation is:

y = k * x^3 / z^2

when x decreased by 35.9%, then the value of x becomes x - .359 * x which is equal to .641 * x.

when z increased by 5.8%, then the value of z becomes z + .058 * z which is equal to 1.058 * z.

the new equation becomes:

y = k * (.641 * x)^3 / (1.058 * z)^2

this becomes:

y = (k * .641^3 * x^3) / (1.058^2 * x^2)

this is the same as:

y = (.641^3 / 1.058^2) * k * (x^3 / z^2)

simplify to get:

y = (.2352896118 * k * x^3) / z^2

y changes by a factor of .2352896118.

let's do an example to see if this holds true.

let x = 9 and let z = 5

when this happens, y is equal to 87.48

you get:

87.48 = k * 9^3 / 5^2

solve for k to get k = 3.

k is the constant of variation and so never changes.

now let y = k * (.641 * x)^3 / (1.058 * z)^2

when x = 9 and when z = 5 and when k = 3, this equation becomes:

y = (3 * (.641 * 9)^3) / (1.058 * 5)^2

this becomes:

y = (3 * 5.769^3) / 5.29^2 which becomes:

y = 20.58313524

the original value of y was 87.48

the new value of y is 20.58313524

the new value of y divided by the original value of y is equal to 20.58313524 / 87.48 which is equal to .2352896118.

the new value of y is equal to .2352896118 times the original value of y.

i believe that's what you are looking for.

that's the factor that the value of y was changed by.