1. Apr 19, 2010

### phys-lexic

1. The problem statement, all variables and given/known data
[This is the final step in a "critical thinking" problem assigned as extra practice/intense application] Find the value of x, for the given equation, when f(x) = $$\frac{49}{6}$$$$\pi$$

f(x) = $$\left(x\right)$$$$\times$$$$\sqrt{49-x^2}$$ + 49sin$$^{-1}$$$$\left(\frac{x}{7}\right)$$

2. Relevant equations
(This is where I need help, I have tried moving around the values, sqaring both sides, applying e and ln; my T.A. could only think of plugging f(x) into a graphing calculator and tracing to y = $$\frac{49}{6}$$$$\pi$$)
*A big question I have is if trig-substitution (aside from integration) can be used, or another method I am not "equipped with," with simplifications.

3. The attempt at a solution
This is what is left after integrating a problem, the answer should be ~1.85 (from graphing/tracing). I tried simplifying using regular relationships:

sin$$^{-1}$$$$\left(\frac{x}{7}\right)$$ = $$\frac{1}{6}\pi$$ - $$\left(x\sqrt{49-x^2}\right)\div49$$

2. Apr 19, 2010

### Staff: Mentor

You're not going to be able to solve this by algebraic means. The simplest approach is to graph the function and see what value of x gives a y value of 49pi/6.

3. Apr 19, 2010

### tiny-tim

Hi phys-lexic!

Try the obvious substitution.

4. Apr 19, 2010

### phys-lexic

I understand algebraic means won't help, which is why I'm posting this question.

Trig-substitution is what I was thinking, but is that applicable when not integrating? (We were only introduced to trig-substitutions with integrals, for obvious reasons)

5. Apr 19, 2010

### tiny-tim

Yes!! You can always substitute, if you think it will make the problem easier.

6. Apr 19, 2010

### diggy

Would be a lot simpler if there was only a way to make that first term go to zero...

7. Apr 19, 2010