Mrs. Galicia is creating a bunny farm. The farm starts with 820 bunnies and is growing at a rate of 20.75% per month. How many m
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Triangle EFG can also be proven to be a right triangle by using the following: D. Prove that KL is equal to c by Pythagorean Theorem.
<h3>What is the Pythagorean Theorem?</h3>The Pythagorean theorem states that the square of the longest side of a right triangle, which is the hypotenuse (c²) equals the sum of the squares of the other two legs of the right triangle (a² + b²).
If we apply the Pythagorean theorem, we would find the length of KL. If KL has the same length as c in triangle EFG, then we can say that triangle EFG is also a right triangle.
Therefore, the answer is: D. Prove that KL is equal to c by Pythagorean Theorem.
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Consider a circle with radius centered at some point
on the
-axis. This circle has equation
Revolve the region bounded by this circle across the -axis to get a torus. Using the shell method, the volume of the resulting torus is
where .
So the volume is
Substitute
and the integral becomes
Notice that is an odd function, so the integral over
is 0. This leaves us with
Write
so the volume is