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Home » How Kendra Saunders Became the Fitness Icon You #1 Search For Every Day! - Midis

How Kendra Saunders Became the Fitness Icon You #1 Search For Every Day! - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Compute \(\tan 75^\circ\) using angle addition formulas.

📌 \tan 45^\circ = 1, \quad \tan 30^\circ = \frac{1}{\sqrt{3}}

📌 Rationalize the denominator:

📌 \]Question: A weather balloon is modeled as a sphere with radius $ r $ meters, and it ascends such that its volume increases at a rate proportional to $ \sin \theta $, where $ \theta $ is the angle of elevation from the ground. If the volume increase rate is given by $ \frac{dV}{dt} = k \sin \theta $, and $ \theta = 60^\circ $, compute the rate of volume increase in terms of $ k $ and $ r $.

📌 Solution: The volume of a sphere is given by $ V = \frac{4}{3} \pi r^3 $. Differentiating with respect to time $ t $, we get:

📌 We are given that $ \frac{dV}{dt} = k \sin \theta $, and $ \theta = 60^\circ $, so $ \sin \theta = \frac{\sqrt{3}}{2} $. Substituting:

📌 k \cdot \frac{\sqrt{3}}{2} = 4\pi r^2 \frac{dr}{dt}

📌 Solving for $ \frac{dr}{dt} $:

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\frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{\frac{1}{3}}{\frac{2}{3}}...
So the sum is \( 3 \cdot \frac{1}{2} = \frac{3}{2} \).
Thus, the minimum value is \( \boxed{\frac{3}{2}} \).
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\sqrt{51} - \sqrt{1} = \sqrt{51} - 1

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