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This is a contradiction unless we reinterpret the question: the volumes areEqual, so we solve:
Question: A mammalogist observes a group of monkeys forming a triangle while foraging in a forest clearing. The triangle has side lengths of 5 meters, 6 meters, and 7 meters. Find the radius of the circle that can be inscribed in this triangle.
Solution: The semiperimeter $ s $ of the triangle is:
The inradius $ r $ is given by $ r =
Solution: The volume $ V $ of a cone is $
Question: A mammalogist observes a troop of monkeys forming a triangle with side lengths in arithmetic progression: $ a - d $, $ a $, and $ a + d $. If the triangle is right-angled, find the value of $
Solution: Assume the triangle is right-angled with hypotenuse $ a + d $. Then by the Pythagorean theorem:
Question: A plant biologist models the growth efficiency of a genetically modified crop using the function $ E(x) =
Let $ u = x + 3 $, so $ u > 0 $. Then:
Square both sides (both sides are nonnegative):