Mathematics, 23.04.2021 03:50 krystalhurst97
A proof by mathematical induction is supposed to show that a given property is true for every integer greater than or equal to an initial value. In order for it to be valid, the property must be true for the initial value, and the argument in the inductive step must be correct for every integer greater than or equal to the initial value. Consider the following statement. For every integer n ≥ 1, 3n − 2 is even. The following is a proposed proof by mathematical induction for the statement. Since the property is true for n = 1, the basis step is true. Suppose the property is true for an integer k, where k ≥ 1. That is, suppose that 3k − 2 is even. We must show that 3k + 1 − 2 is even. Observe that 3k + 1 − 2 = 3k · 3 − 2 = 3k(1 + 2) − 2 = (3k − 2) + 3k · 2. Now 3k − 2 is even by inductive hypothesis, and 3k · 2 is even by inspection. Hence the sum of the two quantities is even by (Theorem 4.1.1). It follows that 3k + 1 − 2 is even, which is what we needed to show. Identify the error(s) in the proof. (Select all that apply.) The inductive hypothesis is assumed to be true. (3k − 2) + 3k · 2 ≠ 3k(1 + 2) − 2 The property is not true for n = 1. 3k + 1 − 2 ≠ (3k − 2) + 3k · 2 3k − 2 is odd by the inductive hypothesis.
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Mathematics, 21.06.2019 22:30
9.4.34 question to estimate the height of a stone figure, an observer holds a small square up to her eyes and walks backward from the figure. she stops when the bottom of the figure aligns with the bottom edge of the square, and when the top of the figure aligns with the top edge of the square. her eye level is 1.811.81 m from the ground. she is 3.703.70 m from the figure. what is the height of the figure to the nearest hundredth of a meter?
Answers: 1
Mathematics, 21.06.2019 23:10
Frank is lending $1,000 to sarah for two years. frank and sarah agree that frank should earn a real return of 4 percent per year. instructions: a. the cpi (times 100) is 100 at the time that frank makes the loan. it is expected to be 113 in one year and 127.7 in two years. what nominal rate of interest should frank charge sarah?
Answers: 3
Mathematics, 21.06.2019 23:50
Find the interior angle of a regular polygon which has 6 sides
Answers: 1
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