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maths GCSE help ( higher maths question)

hii! we did our mock a few weeks ago. my teacher gave the whole class a sheet of the questions which the whole class got wrong on the test and allowed us to try again.
there was one question she didn't go over and i tried to find the answer online to help me solve it but no results came up.

the question is:

x is directly proportional to the square of y
y is directly proportional to the cube of z

z=2 when x=32

find a formula for x in terms of z.

thankyou!
Original post by harlz_chalamet
hii! we did our mock a few weeks ago. my teacher gave the whole class a sheet of the questions which the whole class got wrong on the test and allowed us to try again.
there was one question she didn't go over and i tried to find the answer online to help me solve it but no results came up.

the question is:

x is directly proportional to the square of y
y is directly proportional to the cube of z

z=2 when x=32

find a formula for x in terms of z.

thankyou!


For each of those two proportionalities you should be able to write down an equation involving a constant of proportionality. Then eliminate y between the two.

Have a go and see what you can do.
Original post by ghostwalker
For each of those two proportionalities you should be able to write down an equation involving a constant of proportionality. Then eliminate y between the two.

Have a go and see what you can do.

i get that:

x=ky^2
y=kz^3

and then i would substitute the numbers in. but i don't understand what i would do after.
so

32=ky^2

y=k2^3
y=k8
Original post by harlz_chalamet
i get that:

x=ky^2
y=kz^3

and then i would substitute the numbers in. but i don't understand what i would do after.
so

32=ky^2

y=k2^3
y=k8


First off the constant of proportionality will not be the same for the two relationships. So, lets call the first one "k" and the second one "m".
Your first two equations are otherwise correct.

Since we want a relationship between x and z, you now want to combine those two equations and eliminate y.
(edited 2 years ago)

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