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Home » Solve for \(x\): \(2^x+1 = 32\). - jntua results

Solve for \(x\): \(2^x+1 = 32\). - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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The volume \(V_{\text{sphere}}\) of a sphere with radius \(r\) is:
V_{\text{sphere}} = \frac{4}{3}\pi r^3
For the sphere with radius \(2x\):
V_1 = \frac{4}{3}\pi (2x)^3 = \frac{4}{3}\pi (8x^3) = \frac{32}{3}\pi...
The volume \(V_{\text{hemisphere}}\) of a hemisphere with radius \(r\)...
V_{\text{hemisphere}} = \frac{1}{2} \cdot \frac{4}{3}\pi r^3 = \frac{2...
For the hemisphere with radius \(3x\):
V_2 = \frac{2}{3}\pi (3x)^3 = \frac{2}{3}\pi (27x^3) = 18\pi x^3
\frac{V_2}{V_1} = \frac{18\pi x^3}{\frac{32}{3}\pi x^3} = \frac{18}{\f...
Thus, the ratio is:

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