Question

Write a mathematical expression for the statement 'Y varies jointly with x and the cube of z, and inversely with the square root of w'

Could someone help me understand what this one wants? I have no clue what the 'varie' means

Answer 1

the term is "vary"

when something varies with another, it means they change depending on the other
if x varies inversely to y, then \[x = \frac{ 1 }{ y }\]

Answer 2

Do you need more help?

Answer 3

if x varies jointly with y, then x is directly related to y

Answer 4

I think I'm sort of getting it. Then X would = Y, since they're directly related?

Answer 5

Yup
So what would the overall equation be?

Answer 6

Hm, we would write it as one equation? I would think it would be three seperate ones since Y changes.

Y=X
\[Y=z^{2}\]
then\[Y^{-1}= \sqrt{w}\]

Answer 7

Ah but the original equation said that 'Y varies jointly with x and the cube of z, and inversely with the square root of w'
Note "and"
This means that y varies with x,z^2 and rt(w) in one equation

Answer 8

I don't know how better to explain that, I was only using y=x to demonstrate y varies jointly with x

Answer 9

Hm,ok. I'll see how I can work that
That helps so much! Not only with this question but with my whole paper. Thank you!

Answer 10

So, whats the equation?

Answer 11

For some questions that require you to input numerical data, you will need to include a "constant"

\[y = \frac{ kxz ^{2} }{ \sqrt{w} }\]

Answer 12

k = constant

Answer 13

Oh, I see! The square of W goes on the bottome because it's the inverse. and the 'and' simply means they are multiplied together. For some reason I thought they would be added instead.