Algebra Question?

Question

I was wondering if anyone could help me out with this question, I really don't get what I'm supposed to do.

x varies directly as the square of s and inversely as t. How does x change when s is doubled? When both s and tare doubled?

Answer 1

I think that question means that the equation is X=(S^2)/t, because varying directly means that one increases as the other one does. Inversely is something increases when the other decreases.

So directly is "X=S^2" and Inversely is "X=1/t" If you combine it, then its that one at the beginning --> "X=(S^2)/t".

Now, you have to see what happens if S is doubled.
Try a number.
1=S for example --> X=(1^2)/t = 1/t
If it is doubled, then ---> X=(2^2)/t = 4/t
It's 4 times larger.
If you want to verify it, you can with other number.
3=S for fun --> X=(3^2)/t = 9/t
double that ---> X=(6^2)/t = 36/t
It is also 4 times larger right? =]

Now, When S AND T are doubled.
Also, Try a number.
1=S and 2=T ----> X=(1^2)/2 = 1/2
Now if they double -----> X=(2^2)/4 = 1
So if its doubled, then its 2 times larger.
You can verify it with other number.
2=S and 4=T ------> X=(2^2)/4 = 1
If you double them ----> X=(4^2)/8 = 2
It's also doubled.

So Final Answer:
1. Change of X when S is doubled: 4 times larger.
2. Change of X when S and T are doubled: It is doubled.