Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.5 + 10 + 15 + ... + 5n = 
What will be an ideal response?
First, we show the statement is true when n = 1.
For n = 1, we get 5 = 
= 5.
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 add the next term, 
to both sides of the equation.
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Use the fundamental identities to find the value of the trigonometric function.Find tan ?, given that cos ? = -0.25881905 and ? is in quadrant II.
A. -3.9910152 B. -3.7320507 C. 3.7320507 D. 3.9910152
Solve. Simplify the answer.Ian walked 
mile to his biology class, 
mile to his art class, 
mile to his calculus class, and then back to his dormitory. If he walked 1 mile altogether, how far did he walk from his calculus class to his dormitory?
A. 
mi
B. 
mi
C. 
mi
D. 
mi
Write the indicated event in set notation.When four coins are tossed, exactly three tails are obtained.[Hint: When four coins are tossed, the following 16 outcomes are possible:HHHH HHHT HHTH HHTTHTHH HTHT HTTH HTTTTHHH THHT THTH THTTTTHH TTHT TTTH TTTT]
A. 
B. 
C. 
D. 
Find dy/dx by implicit differentiation.x3 + 3x2y + y3 = 8
A. - 
B. 
C. - 
D. 