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Home » Thus, the region's area is $ \boxed25(\pi - 2) $. - RTA

Thus, the region's area is $ \boxed25(\pi - 2) $. - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 A rocket's altitude in meters after t seconds is modeled by the function \( h(t) = -5t^2 + 150t + 100 \). What is the maximum altitude the rocket reaches?

📌 The function is a quadratic in the form \( h(t) = at^2 + bt + c \), with \( a = -5 \), \( b = 150 \), and \( c = 100 \).

📌 Since \( a < 0 \), the parabola opens downward, so the maximum occurs at the vertex: \( t = -\frac{b}{2a} = -\frac{150}{2(-5)} = 15 \) seconds.

📌 Now substitute \( t = 15 \) into \( h(t) \):

📌 \( h(15) = -5(15)^2 + 150(15) + 100 = -5(225) + 2250 + 100 = -1125 + 2250 + 100 = 1225 \) meters.

📌 The sum of the first n terms of a geometric sequence is given by \( S_n = 3^n - 1 \). Find the 5th term of the sequence.

📌 The general formula for the sum of the first n terms is \( S_n = a \frac{r^n - 1}{r - 1} \).

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