I have a right triange with sides of x and y. I know y is a constant (500) and that dtheta/dt (where theta is the angle opposite from side x) is also constant (8pi rad/s). I have already found dx/dt for a specified x, but the next problem asks me to relate dx/dt to x. How do I do this?

Question

anonymous · Answer

if i am picturing it right 
$$\tan(\theta)=\frac{x}{y}=\frac{x}{500}$$

anonymous · Answer

correct

anonymous · Answer

Sorry for the formatting; I hadn't figured out the interface when I posted...

anonymous · Answer

i guess i am confused
if you found $\frac{dx}{dt}$ for a specific $x$ why can't you find it for a general $x$?

anonymous · Answer

I may have just got it... thinking...

anonymous · Answer

i think you are being asked to put $x$ where you put the number you used for $x$ and write that 
i think

anonymous · Answer

Got it. $$\frac{dx}{dt}=\frac{4\pi d^{2}}{250}+100$$ When I differentiate the original problem, I get an answer in terms of $\theta$ and $\frac{d\theta}{dt}$. $\frac{d\theta}{dt}$ is known and theta can be found in terms of $x$ because of pythagorean theorem stuff. I found $\theta$ in terms of the hypotenuse and then the hypotentus in terms of $x$.

anonymous · Answer

good work but why is that 100 there?

anonymous · Answer

maybe i did it wrong'
i have 
$$\tan(\theta)=\frac{x}{500}$$ so 
$$\sec^2(\theta)\theta '=\frac{x'}{500}$$

anonymous · Answer

Oops... it is actually 100. $$\frac{dx}{dt}=\frac{4\pi h^{2}}{250}$$ and
$$h^{2}=x^{2}+y{2}$$ so $h^{2}$ is replaced with $x^{2}+250000$ and then the fraction is split to cancel the 250 from the denominator

anonymous · Answer

oops... it is actually 1000

/me facepalms

anonymous · Answer

okay