Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
n = 75n
What will be an ideal response?
First we show that the statement is true when n = 1.
For n = 1, we get 75 = 7(5?1) = 75
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is true for some positive integer k.
We need to show that the statement holds for k + 1. That is, we need to show that
So we assume that 
is true and multiply the next term, 
to both sides of the equation.
k
(k + 1) = 75k
(k + 1)
(k + (k + 1)) = 75k
(2k + 1) = 7(5k + 5k + 5))
7(5(2k + 1)) = 7(5(2k + 1))
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Solve the problem.A sanding machine disk can be described as the volume generated by rotating the area bounded by 
and the y-axis about the y-axis (measurements in in.). Locate the centroid of the disk to the nearest 0.001.
A. 0.507 in. above the center of the larger surface B. 0.247 in. above the center of the larger surface C. 0.493 in. above the center of the larger surface D. 0.986 in. above the center of the larger surface
Classify the surface. Select the correct answer.
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If r || s and m
= 73°, find m
.
What will be an ideal response?
Simplify the expression.(-40) ÷ (-5)
A. 8 B. 9 C. -9 D. -8