Question

y varies jointly as x and the inverse of z. When y = 6 and x = 3, z = 6. Find the constant of variation and determine the value for y when x = 6 and z = 8.

Answer 1

Back so soon? ;P

Answer 2

lol yeahhh

Answer 3

Suppose z varies directly as x and y and inversely as w, and z =8 when x =6, y =5 and w =10. Find z when x =3, y =4 and w = 5.

FORMULA:

product of "directly" or "jointly" variables
"Varies as" variable = k* --------------------------------------------
product of "inversely" variables

The "varies as" variable is z, so write:


z = k*-----

The "directly variables" are x and y, so write them on the top:

xy
z = k*-----


There is just one "inversely variable", w, so write it on the bottom:


xy
z = k*-----
w

Now we're ready to substitute the numbers for all the letters except the
constant k from this: "z =8 when x =6, y =5 and w =10". Substituting:

6*5
8 = k*-----
10


Solve for k:
30
8 = k*-----
10

8 = k*3

8
--- = k
3

Now go back to this equation:


xy
z = k*-----
w

and substitute 3/8 for the constant k.


3 xy
z = ---*----
8 w

or

3xy
z = -----
8w

Now we substitute in x =3, y =4 and w = 5, to find z:


3(3)(4)
z = --------
8(5)

Then finish it up:

36
z = ----
40

Reduce the fraction:


9
z = ----
10

The answer is 9/10.

Answer 4

Thanks ^-^

Answer 5

np

Answer 6

wait i dont think thats right tho...

Answer 7

That's because it isn't ^_^

Answer 8

y varies jointly as x and the inverse of z. When y = 6 and x = 3, z = 6. Find the constant of variation and determine the value for y when x = 6 and z = 8

\[\large y = \frac{kx}{z}\]

"When y = 6 and x = 3, z = 6. Find the constant of variation"

\[\large 6 = \frac{3k}{6}\]solve for 'k' here

Answer 9

thats wat my nots said and i found that on a math site

Answer 10

@conley1 no that is the correct approach....however they way you have it written with the "9/10 is your answer" made sierra think that was truely HER answer...

however @sierraleone17 as you can see...the example @conley1 has given does not have the same numbers as your question nor does it have the same variables

Answer 11

oh ok