Find an equation of variation in which $y$ varies jointly as $t$ and $r$ and inversely as the square of $w$, and $y=2$ when $t=4, r=9,$ and $w=6$.

Question

Find an equation of variation in which $y$ varies jointly as $t$ and $r$ and inversely as the square of $w$, and $y=2$ when $t=4, r=9,$ and $w=6$.

I can set this up as two separate equations, $y=ktr$, and $y=\dfrac k{w^2}$. Then I can:

solve it as $k=\dfrac 1{18}$ for the first equation and $k=72$ for the second equation.
Set the $y's $ equal to each other, which gives me $ktr=\dfrac k{w^2}$, which simplifies to $trw^2=1$, which is incorrect.

Both seem wrong; how do I solve this?

Both k are different how did you cancel – Archis Welankar Nov 15 '16 at 05:19 — Archis Welankar, Nov 15 '16 at 05:19
Does this answer your question? Joint Proportionality – ryang Jun 25 '23 at 14:21 — ryang, Jun 25 '23 at 14:21

score 0 · Answer 1 · answered Nov 15 '16 at 05:21

0

I would combine them together into a single equation, with a single constant $K$ to solve for: $$ y = K \cdot \frac{tr}{w^2} $$

answered Nov 15 '16 at 05:21

Adriano

1 Answers1