Question

y varies inversely with x. If y = 2.4 and k (the constant of variation) = 8.88, what is x? Round to the nearest tenth, if necessary.

Answer 1

Answer:

3.7

Step-by-step explanation:

Inversely means we are taking the constant and dividing it.

So y varies inversely with x means "y=k/x".

k is a constant.  We can find the constant if they give us a point on this curve.

The constant is a number that doesn't change no matter your input and output.

$y=\frac{k}{x}$

So they actually give us k=8.88 and y=2.4 so let's input this:

$2.4=\frac{8.88}{x}$

We need to solve this equation for x.  You can do your favorite thing in cross-multiply. But how, Freckles?  Well just slap a 1 underneath that 2.4.  You can do that because 2.4/1 is still 2.4.

$\frac{2.4}{1}=\frac{8.88}{x}$

Cross-multiply:

$2.4x=8.88(1)$

$2.4x=8.88$

Divide both sides by 2.4:

$x=\frac{8.88}{2.4}$

$x=3.7$ when $y=2.4$.