# Directly Proportional

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Thread starter 1 month ago
#1
Q6 P134 Exam-Style Questions, Student Book, CGP, Mathematics Higher Level

Z is directly proportional to x^3
Z is also directly proportional to y^2
When y=8, x =5

Find the value of x when y is 27

Book answer is :
x = cuberoot of 1423.8... = 11.25

However, I'm not too sure how they got this. Could someone explain with their own in-depth workings please?
0
1 month ago
#2
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(Original post by DJFearRoss)
Q6 P134 Exam-Style Questions, Student Book, CGP, Mathematics Higher Level

Z is directly proportional to x^3
Z is also directly proportional to y^2
When y=8, x =5

Find the value of x when y is 27

Book answer is :
x = cuberoot of 1423.8... = 11.25

However, I'm not too sure how they got this. Could someone explain with their own in-depth workings please?
It would be better if you posted your attempt/thoughts/...
https://www.bbc.co.uk/bitesize/guide...srd/revision/3
0
Thread starter 1 month ago
#3
THanks
My workings out are:
z = kx^3 also z = jy^2
so kx^3 = jy^2

even after putting in the values of x & y , i've got 2 unknowns, so don't quite understand how I work this out.
0
1 month ago
#4
(Original post by DJFearRoss)
THanks
My workings out are:
z = kx^3 also z = jy^2
so kx^3 = jy^2

even after putting in the values of x & y , i've got 2 unknowns, so don't quite understand how I work this out.
You don't need to get k and j individually (indeed you can't). Divide though by k to get
x^3 = (j/k) y^2
Then work with the new proportionality constant m, where m = j/k.

You could just note the question effectively says x^3 is directly proportional to y^2.
Last edited by mqb2766; 1 month ago
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Thread starter 4 weeks ago
#5
"You could just note the question effectively says x^3 is directly proportional to y^2."

Thanks so much, that really helped! Makes sense. If x^3 and y^2 are both proportional to z, then they must both be proportional to each other, so there is a constant (m) there that needs to be calculated.

So:
x^3 is directly proportional to y^2
so x^3 = my^2
m = 1.953

x^3 = m27^2
x = 11.25
1
4 weeks ago
#6
(Original post by DJFearRoss)
"You could just note the question effectively says x^3 is directly proportional to y^2."

Thanks so much, that really helped! Makes sense. If x^3 and y^2 are both proportional to z, then they must both be proportional to each other, so there is a constant (m) there that needs to be calculated.

So:
x^3 is directly proportional to y^2
You are posting a lot of questions without working - PLEASE follow website guidelines and upload what you have done.
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Thread starter 4 weeks ago
#7
Sorry, that was the answer. I'm done. I just wanted to put my full workings there.
The point was to get the value of x.
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