Question

suppose z varies directly with x and interversley with y when x=6 and y=2 and z=15 find z when x=4 and y=p????

Answer 1

Is the answer to your previous posting wrong?

Answer 2

I just did not quite understand it... I thought I did at first but if you wouldn't mind could you walk me through it?

Answer 3

If z varies directly with x, then z = C * x where C is the proportionality constant.
Do you follow this part?

Answer 4

yes

Answer 5

If z varies inversely with y, then z = D * 1 / y where D is the proportionality constant. Follow this?

Answer 6

That is what an INVERSE means. As y increases, z decreases. As y decreases, z increases. So they are related reciprocally or inversely.

Answer 7

ok

Answer 8

If z varies directly with x AND inversely with y then z = k * x / y where k is the proportionality constant.

Answer 9

alright

Answer 10

We are given one set of x, y and z. Substitute into the equation and find k.
Put x = 6, y = 2, z = 15 in z = k * x / y and find k.

Answer 11

15=k(6/2) is that right?

Answer 12

yes. simplify and solve for k.

Answer 13

how would I do that?

Answer 14

15=k(6/2)
simplify right hand side:
15 = k * 3
divide both sides by 3
5 = k or k = 5.

Answer 15

eureka!

Answer 16

Put k back in the original equation:

z = 5 * x / y

Now put the new set of values for x and y and find z.
x = 4, y = p

z = 5 * 4 / p = 20/p

Answer 17

so the answer would be 20/9?

Answer 18

In your original posting does it say find z when x=4 and y=p ?
or is y supposed to be some number and you made a typo?

Answer 19

whoops typo! it was supposed to be 9 thank you for being so patient with me I understand it a lot more now! :)

Answer 20

then z = 20 / 9.

You are welcome.