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Home » Find the total time: \( 3 \text hours + 3.33 \text hours \approx 6.33 \text hours \) - 500apps

Find the total time: \( 3 \text hours + 3.33 \text hours \approx 6.33 \text hours \) - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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Dividing both sides by \(\sqrt{3}\), we get:
\frac{3}{2}s^2 = 54
Multiplying both sides by \(\frac{2}{3}\) gives:
s^2 = 36
s = 6
Thus, the length of each side of the hexagon is \(\boxed{6}\).
Question: A circle is inscribed in a right triangle with legs of lengt...
Solution: The area \(A\) of the triangle is given by:
A = \frac{1}{2} \times 9 \times 12 = 54
s = \frac{9 + 12 + 15}{2} = 18

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x^2 + y^2 = c^2 \sin^4\phi, \quad z = c \sin\phi \cos\phi
Let \(r = \sqrt{x^2 + y^2} = c \sin^2\phi\)
But from \(z = c \sin\phi \cos\phi = c \sin\phi \sqrt{1 - \sin^2\phi}\...
Set \(u = \sin\phi\), then:
r = c u^2, \quad z = c u \sqrt{1 - u^2}
u = rac{r^{1/2}}{\sqrt{c}}, \quad z = c \cdot rac{r^{1/2}}{\sqrt{c}}...
z^2 = c \cdot r \left(1 - rac{r^2}{c^2}
ight) = c r - rac{r^3}{c}
But \(r = rac{\sqrt{x^2 + y^2}}{1}\), so:
z^2 = c \sqrt{x^2 + y^2} - rac{(x^2 + y^2)^{3/2}}{c}

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