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Home » 2; "This AP Stats Formula Sheet Got Students Scoring 5s—Break It Down Now!" - AMAZONAWS

2; "This AP Stats Formula Sheet Got Students Scoring 5s—Break It Down Now!" - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 Here, \( r = 3 \) meters and \( h = 5 \) meters.

📌 So, \( V = \pi \times 3^2 \times 5 = 45\pi \) cubic meters.

📌 The tank is drained at 2 cubic meters per minute.

📌 Time \( t \) to empty the tank is \( \frac{45\pi}{2} \) minutes.

📌 Approximating \( \pi \) as 3.14, \( t \approx \frac{45 \times 3.14}{2} = \frac{141.3}{2} = 70.65 \) minutes.

📌 #### 70.65

📌 A particle moves along a straight line with its position at time \( t \) given by \( s(t) = t^3 - 6t^2 + 9t \). Find the velocity of the particle at \( t = 4 \).

📌 Velocity is the derivative of position, \( v(t) = \frac{ds}{dt} \).

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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:
\boxed{\frac{27}{16}}
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