I was calculating some numbers, revolving around a sphere and some integration.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Algebra solution containing trig?

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