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Home » Simplify: \( 50 = 5 \times \textHeight \). - Dyverse

Simplify: \( 50 = 5 \times \textHeight \). - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 h'(x) = 3x^2 - 6x + 2

📌 Set $ h'(x) = 0 $ to find where the slope is horizontal:

📌 3x^2 - 6x + 2 = 0

📌 Solve using the quadratic formula:

📌 x = \frac{6 \pm \sqrt{(-6)^2 - 4 \cdot 3 \cdot 2}}{2 \cdot 3} = \frac{6 \pm \sqrt{36 - 24}}{6} = \frac{6 \pm \sqrt{12}}{6} = \frac{6 \pm 2\sqrt{3}}{6} = 1 \pm \frac{\sqrt{3}}{3}

📌 The sum of the roots is:

📌 \left(1 + \frac{\sqrt{3}}{3}\right) + \left(1 - \frac{\sqrt{3}}{3}\right) = 2

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A' = \frac{\sqrt{3}}{4} (14)^2 = \frac{\sqrt{3}}{4} \times 196 = 49\sq...
\Delta A = A' - A = 49\sqrt{3} - 36\sqrt{3} = 13\sqrt{3}
\boxed{13\sqrt{3} \text{ square centimeters}}
A right triangle has a hypotenuse of length \( z = 10 \) cm and an ins...
A_{\text{circle}} = \pi c^2 = \pi (2)^2 = 4\pi
For a right triangle, the radius \( c \) of the inscribed circle is gi...
where \( a \) and \( b \) are the legs. But we also know:
A_{\text{triangle}} = \frac{1}{2}ab = r \cdot s
where \( r = c = 2 \) and \( s = \frac{a + b + z}{2} \) is the semi-pe...
Using the identity for right triangles:

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