- #1
phys-lexic
- 29
- 0
really complicated "solve for x" problem.. please help..
[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) = [tex]\frac{49}{6}[/tex][tex]\pi[/tex]
f(x) = [tex]\left(x\right)[/tex][tex]\times[/tex][tex]\sqrt{49-x^2}[/tex] + 49sin[tex]^{-1}[/tex][tex]\left(\frac{x}{7}\right)[/tex]
(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 = [tex]\frac{49}{6}[/tex][tex]\pi[/tex])
*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.
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[tex]^{-1}[/tex][tex]\left(\frac{x}{7}\right)[/tex] = [tex]\frac{1}{6}\pi[/tex] - [tex]\left(x\sqrt{49-x^2}\right)\div49[/tex]
Homework Statement
[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) = [tex]\frac{49}{6}[/tex][tex]\pi[/tex]
f(x) = [tex]\left(x\right)[/tex][tex]\times[/tex][tex]\sqrt{49-x^2}[/tex] + 49sin[tex]^{-1}[/tex][tex]\left(\frac{x}{7}\right)[/tex]
Homework 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 = [tex]\frac{49}{6}[/tex][tex]\pi[/tex])
*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.
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[tex]^{-1}[/tex][tex]\left(\frac{x}{7}\right)[/tex] = [tex]\frac{1}{6}\pi[/tex] - [tex]\left(x\sqrt{49-x^2}\right)\div49[/tex]