what is the value of X when Q is the biggest?
Hello,
I assume that you want to know for which value of x has the angle $\displaystyle \theta$ a maximum.
From your sketch you see:
$\displaystyle \theta(x)=\arctan\left(\frac{420}{x}\right)-\arctan\left(\frac{380}{x}\right)$
You'll get an extremum if the first derivative of this function equals zero:
$\displaystyle \theta'(x)=\frac{1}{1+\left(\frac{420}{x} \right)^2}\cdot \left(\frac{-420}{x}\right)-\frac{1}{1+\left(\frac{380}{x} \right)^2}\cdot \left(\frac{-380}{x}\right)$
After a few and simple transformations you'll get:
$\displaystyle \theta'(x)=\frac{40·(159600 - x^2)}{(x^2 + 144400)·(x^2 + 176400)}$
That means: $\displaystyle \theta'(x)=0\text{ if }159600 - x^2=0$. Solve for x. I've got:
$\displaystyle x= 399.4996... \approx399.5 $
There is of course a negative solution of x but thisvalue isn't very realistic with your problem.
EB
Hello,
maybe this will help a little bit further: In this forum you can find a link to the LaTeX-tutorial.
(If I find the link in time I'll add it here)
Have a nice time!
EB
Edit: Well, Ihope I actually did find the right link: http://www.mathhelpforum.com/math-he...rial-latex.pdf