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Home » Total time for both journeys: \(3 + 2 = 5\) hours. - Aurero

Total time for both journeys: \(3 + 2 = 5\) hours. - Aurero

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 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, \( v(t) = \frac{ds}{dt} \).

📌 So, \( v(t) = \frac{d}{dt}(t^3 - 6t^2 + 9t) = 3t^2 - 12t + 9 \).

📌 At \( t = 4 \), \( v(4) = 3(4)^2 - 12(4) + 9 \).

📌 Calculating gives \( v(4) = 48 - 48 + 9 = 9 \).

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A_{\text{base}} = \pi (3)^2 = 9\pi \, \text{square meters}
The rise in water level \( h \) is given by the displaced volume divid...
h = \frac{V_{\text{sphere}}}{A_{\text{base}}} = \frac{\frac{32}{3} \pi...
#### \(\frac{32}{27}\)
A company offers two investment plans. Plan A offers 5% simple annual...
For Plan A, the future value after \( t \) years is:
A_A = 1000(1 + 0.05t)
For Plan B, the future value is:
A_B = 1000(1.04)^t
Setting \( A_A = A_B \):

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