Question

z varies inversely with x and directly with y.
When x=6 and y =2, z=5.
What is the value of z when x=4 and y=9?

Answer 1

Okay so

\[\large z = \frac{ky}{x}\]
plugging in everything we have
\[\large 5 = \frac{2k}{6}\]
and solvingfor k we get

\[\large k = 15\]

so our eneral equation will be

\[\large z = \frac{15y}{x}\]

now just plug in 4 for 'x' and 9 for 'y' and solve for 'z'

Answer 2

im confused on what you mean

Answer 3

on what I mean?

Answer 4

how do you plug it in

Answer 5

Oh, just replace the 'x' you see with 4...and replace the 'y' you see with 9

\[\large z = \frac{15(9)}{(4)}\]

Answer 6

so i multiply it but where did you get 15?

Answer 7

so would it be 135/4?

Answer 8

The 15 is what we solved for before...the *constant of variation*

Answer 9

ohh ok so is it 135/4??

Answer 10

Correct

Answer 11

ok thanks :)

Answer 12

i have another like that

Answer 13

do you mind helping me work it out

Answer 14

Of course not :)

Answer 15

z varies inversely with x and directly with y.
when x=2 and y=4 z=0.5
what is the value of z when x=4 and y=9

Answer 16

Alright so same thing here...

Varying inversely means division...and directly means multiplication

so

\[\large z = \frac{ky}{x}\]

same formula as before

make sense?

Answer 17

kinda

Answer 18

The 'k' still throwing you off?

Answer 19

yea

Answer 20

So the 'k' is something that is in EVERY variation problem...it is referred to as the constant of variation

It is a number that relates the variables

For example

say our equation was
\[\large y = kx\]

that 'k' is the number, that HAS to be multiplied to each 'x' we get, in order to get the exact 'y that we want

Answer 21

and how do you get k in the first place?

Answer 22

Well, notice how we are always given an initial condition

z varies inversely with x and directly with y.
***************** when x=2 and y=4 z=0.5****************
what is the value of z when x=4 and y=9

knowing that information...we are allowed to solve for 'k'

Answer 23

waite it says z varies inversely with the product of x and y

Answer 24

does that make a difference

Answer 25

sorry if im making this hard for you

Answer 26

No not at all, but now you're confusing me :P lol I'm going off the question you posted (not the original) but the one that is a few posts up...

Answer 27

z varies inversely with the product of x and y
when x=2 and y=4 z=0.5
what is the value of z when x=4 and y=9

Answer 28

sorry that one is the right one

Answer 29

Oh, then the post up there is incorrect! lol

alright...so yes....big difference

Answer 30

sorry

Answer 31

Remember how I said inversely means divide? well x and y are being multiplied together...but both are to be in the bottom of the fraction we make

so

\[\large z = \frac{k}{xy}\]

Answer 32

ok

Answer 33

but does that make sense? The 'k' will always be on top unless otherwise specified, any other variable is free game

Answer 34

nope not one word

Answer 35

Lmao....grr...hmm I'm not sure how to explain it lol...

Answer 36

let me try and find a website for you to look at ^_^

Answer 37

how about you just give me th answer lol

Answer 38

Neva ;P

Answer 39

oh ok

Answer 40

one more

Answer 41

Okay 1 more! :P

Answer 42

ok

z varies jointly with x and y .
when x=2 and y=3, z=60.
what is the value of z when x=4 and y=9?

Answer 43

\[\large z = kxy\]

\[\large 60 = k(2)(3)\]
\[\large k = 10\]

\[\large z = 10xy\]
\[\large z = 10(4)(9)\]

Answer 44

got it