Determine the equation of combined variation. Then solve for the missing value. x varies directly with y and inversely with z.x = 20 when y = 8 and z = 4.Find x when y = 4 and z = 8.@awkwardpanda

Question

awkwardpanda · Answer

We have x = k*y/z for some k. 

Since x = 20 when y = 8 and z = 4, we know 20 = k*8/4 = 2*k, 

so k = 10. 

Therefore, x = 10*y/z. 

So when y = 4 and z = 8 

we get x = 10*4/8 = 40/8 = 5.

-anyone correct me if I'm wrong-

anonymous · Answer

We have the relations:
$$\eqalign{
&x\propto y \
&x\propto\frac{1}{z}
}$$
So then to put all in one equation we have:
$$x=\frac{ky}{z}$$
Where k is an real number and a constant. We can solve for $k$ by plugging in $(x=20),(y=8),(z=4)$
$$\eqalign{
&x=\frac{ky}{z} \
&20=\frac{8k}{4} \
&20=2k \
&k=10 \
}$$
So then the complete formula is:
$$x=\frac{10y}{z}$$
They give you y and z and so you can solve for x!

awkwardpanda · Answer

Wait. Nevermind, Keith got it.

anonymous · Answer

you are correct i am gann post another one @awkwardpanda

awkwardpanda · Answer

Alright..

anonymous · Answer

ok are you ready for another one @awkwardpanda