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Home » Solution: The volume of a hemisphere is $ V_{\texthemisphere} = \frac23 \pi r^3 $. - wispro

Solution: The volume of a hemisphere is $ V_{\texthemisphere} = \frac23 \pi r^3 $. - wispro

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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\frac{(1/3)^2}{1/3} + \frac{(1/3)^2}{1/3} + \frac{(1/3)^2}{1/3} = 3 \c...
Therefore, the minimum value is $ \boxed{1} $.
Question: Compute the sum of the roots of the equation
u\sqrt{u} - 6u + 7\sqrt{u} - 12 = 0,
given that all roots are real and non-negative.
Solution: Let $ \sqrt{u} = t $, so $ u = t^2 $. Substituting into the...
t^2 \cdot t - 6t^2 + 7t - 12 = 0 \Rightarrow t^3 - 6t^2 + 7t - 12 = 0
We are now to find the sum of the roots of the cubic equation
t^3 - 6t^2 + 7t - 12 = 0
By **Vieta’s Formula**, the sum of the roots is the coefficient of $ t...

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