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Home » The profit function is a quadratic \( P = -2x^2 + 12x - 5 \), which opens downward. - Groen Casting

The profit function is a quadratic \( P = -2x^2 + 12x - 5 \), which opens downward. - Groen Casting

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Mar 01, 2026

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\(\cos^2(\theta) = 1 - \frac{9}{25} = \frac{16}{25}\).
\(\cos(\theta) = \frac{4}{5}\) (positive in the first quadrant).
Evaluate the sum \(\sum_{k=1}^{5} (2k + 1)\).
Compute each term: when \(k=1\), \(2(1)+1=3\); \(k=2\), \(5\); \(k=3\)...
Sum: \(3 + 5 + 7 + 9 + 11 = 35\).
Alternatively, use formula for arithmetic series:
First term = 3, last term = 11, number of terms = 5.
Sum = \(\frac{n}{2}(a + l) = \frac{5}{2}(3 + 11) = \frac{5}{2} \times...
Find the area of a regular hexagon with side length 6 cm.
A regular hexagon can be divided into 6 equilateral triangles.

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