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Home » Solution: Rewrite the equation by completing the square. Group $ x $ and $ y $ terms: - Blask

Solution: Rewrite the equation by completing the square. Group $ x $ and $ y $ terms: - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \sin 45^\circ = \frac{\sqrt{2}}{2}

📌 \sin 180^\circ - \sin 45^\circ = 0 - \frac{\sqrt{2}}{2} = -\frac{\sqrt{2}}{2}

📌 The simplified expression is:

📌 Question:** The radius of a sphere is \(2x\) units and the radius of a hemisphere is \(3x\) units. What is the ratio of the volume of the hemisphere to the volume of the sphere?

📌 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 x^3

🔥 Popular Posts

Sum of real roots: \( 4 + 9 = 13 \)
oxed{13}
Question: A plant biologist studying drought resistance defines a func...
Solution: Assume \( \lim_{n o \infty} c_n = L \). Then taking limits:
L = f(L) = L - rac{L^3}{6}
\Rightarrow 0 = -rac{L^3}{6}
\Rightarrow L^3 = 0 \Rightarrow L = 0
We verify convergence. Since \( f(t) = t\left(1 - rac{t^2}{6}
ight) \), for \( t > 0 \), \( f(t) < t \) when \( 1 - rac{t^2}{6} < 1...
c_2 = f(0.5) = 0.5 - rac{(0.5)^3}{6} = 0.5 - rac{0.125}{6} = 0.5 - 0...

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