SOLUTION: find the equation of variation if y varies jointly as w and the square of x and inversely as z, and y=9 when x=5, x=3 and z=10

Algebra ->  Equations -> SOLUTION: find the equation of variation if y varies jointly as w and the square of x and inversely as z, and y=9 when x=5, x=3 and z=10      Log On


   

Question 960784: find the equation of variation if y varies jointly as w and the square of x and inversely as z, and y=9 when x=5, x=3 and z=10
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
To review:
"y varies as x" means y+=+kx
"y varies jointly as x and y" means y+=+kxy
"y varies as x+%2B+y" means y+=+k%28x+%2B+y%29
"y varies inversely as x" means y++=+k%2Fx

find the equation of variation:
if y+ varies jointly as w+and the x%5E2, then
y+=kwx%5E2
and ify+ varies inversely as z, then
y+=kwx%5E2%2Fz
and if +y=9+when x=5, x=3 and z=10, we have
9+=kw%2A5%5E2%2F10
90+=kw%2A25
90%2F25+=kw
kw=18%2F5+
kw=3.6
w=3.6%2Fk

9+=kw%2A3%5E2%2F10
90+=kw%2A9
90%2F9+=kw
w=10k
find k
3.6%2Fk=10k

k=0.6%7D%7D+or+%7B%7B%7Bk=-0.6%7D%7D+%0D%0A%0D%0Anow+find+%7B%7B%7Bw
w=10k=>w=10%2A0.6=>w=6
or
w=10k=>w=10%2A%28-0.6%29=>w=-6
so, y+=0.6%2A6x%5E2%2Fz or y+=-0.6%2A%28-6%29w%5E2%2Fz (both are same)
y+=3.6x%5E2%2Fz