The variable x varies directly as the square of r and inversely as the cube of t.

When r=3 and t=27, x=24. What is x when r is 2 and t is 8?

Please show solution as much as possible

Question

The variable x varies directly as the square of r and inversely as the cube of t.

When r=3 and t=27, x=24. What is x when r is 2 and t is 8?

Please show solution as much as possible

anonymous · Answer

so the equation would be
$$y=\frac{ r ^{2}k }{ t ^{3}}$$
so you want to find k to plug into the equation

anonymous · Answer

sorry replace y with x

anonymous · Answer

$$24=\frac{ 3^{2} k}{ 27^{3} }$$
$$24=\frac{ 9 k}{ 19683 }$$
9k=472392
k=52488

anonymous · Answer

so you replace k into the equation 
$$x=\frac{ x^{2} 52488}{ t^{3} }$$

anonymous · Answer

then replace the other variables
$$y=\frac{ 2^{2} 52488}{ 8^{3} }$$
$$y=\frac{ 4(52488)}{512 }$$
$$y=\frac{209952}{512}$$
y=about 410

elleblythe · Answer

@insanitycat it's not an exact value?

anonymous · Answer

no its a long decimal

anonymous · Answer

if in fraction form it would be y=6561/16