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

February 22, 2026

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

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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 \( h(t) \):
#### 1225
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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