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Home » Thus, the value of \( f'(x) \) at \( x = 4 \) is 22. - Sterling Industries

Thus, the value of \( f'(x) \) at \( x = 4 \) is 22. - Sterling Industries

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 Solution: A regular hexagon inscribed in a circle has its side length equal to the radius of the circle. Since the side length of the hexagon is 5 cm, the radius $r$ of the enclosing circular dome is also 5 cm. The circumference $C$ of a circle is given by:

📌 Question: A cartographer uses satellite data to map a triangular atoll with side lengths 13 km, 14 km, and 15 km. To optimize GPS signal reception, a circular transmission range must cover the entire triangle. Find the radius of the circumcircle of this triangle, express your answer in simplified radical form.

📌 Solution: We are given a triangle with sides $a = 13$, $b = 14$, and $c = 15$. The circumradius $R$ of a triangle with sides $a$, $b$, $c$ is given by the formula:

📌 where $K$ is the area of the triangle. First, compute the semi-perimeter $s$:

📌 Now use Herons formula to find the area $K$:

📌 Solution: Let the side length of the original equilateral triangle be $s$. The area $A$ of an equilateral triangle is:

📌 After reducing each side by 4 mm, the new side length is $s = 12$ mm. The new area is:

📌 Question: An oceanographer analyzing spherical underwater sensor buoy designs compares a full buoy of radius $2r$ to a hemispherical float of radius $r$. What is the ratio of the volume of the buoy to the volume of the float?

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