- #1
Nebuchadnezza
- 79
- 2
I was calculating some numbers, revolving around a sphere and some integration.
The case was to find out for what x-value a spherical bowl with a radius of 5m was half filled.
After doing the algebra, I narrowed it down to
[tex] x^3 - 15x^2 + 125 = 0 [/tex]
Now, my calculator says that the solution to this equation is.
[tex] x = 5 \sqrt{3}\sin\left(\frac{\pi }{9} \right) -5 \cos\left( \frac{\pi }{9} \right) +5 [/tex]
How do you figure that out? Kept trying a few variable changes, but nothing comes to mind.
Ofcourse this polynomial have more solutions, but this is the only solution where 0<x<5 the other ones where -2.2 and 14.
The case was to find out for what x-value a spherical bowl with a radius of 5m was half filled.
After doing the algebra, I narrowed it down to
[tex] x^3 - 15x^2 + 125 = 0 [/tex]
Now, my calculator says that the solution to this equation is.
[tex] x = 5 \sqrt{3}\sin\left(\frac{\pi }{9} \right) -5 \cos\left( \frac{\pi }{9} \right) +5 [/tex]
How do you figure that out? Kept trying a few variable changes, but nothing comes to mind.
Ofcourse this polynomial have more solutions, but this is the only solution where 0<x<5 the other ones where -2.2 and 14.