A+ Answers
Question 15
Suppose you are proving that an integer derived in a certain way is even, and that you are at a point in the proof that you have the integer expressed as 7(4k2 + 4k + 1) + 1. How should you rewrite this expression to show that the integer is even?
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28k2 + 28k + 7 + 1 |
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28k2 + 28k + 8 |
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20(k2 + k) + 8(k2 + k + 1) |
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2(14k2 + 14k + 4) |
Question 16
Which one of the following gives a recursive algorithm for computing an, where n is a positive integer and a is a real number?
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procedure power(a: real number, n: positive integer) if n = 1 then power(a, n) := a else power(a, n) := a∙power(a, n) |
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procedure power(a: real number, n: positive integer) for i = 1 to n power := a∙power |
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procedure power(a: real number, n: positive integer) power := a for i = 2 to n power := a∙power |
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procedure power(a: real number, n: positive integer) if n = 1 then power(a, n) := a else power(a, n) := a∙power(a, n – 1) |
Question 17
Let f be the function such that f(0) = 1, f(1) = 4, and
f(n) = f(n – 1)∙f(n – 2) + 1 for all integers n greater than 1. Which one of the following is true?
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f(3) = 4 and f(4) = 105 |
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f(3) = 5 and f(4) = 21 |
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f(3) = 21 and f(4) = 106 |
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f(3) = 20 and f(4) = 105 |
Question 18
If {an} is the sequence defined by an = (n + 5)/2 for all positive integers n, which one of the following is a recursive definition for the sequence?
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a1 = 1 and, for n = 2, 3, 4, . . . , an = an–1 + 5/2
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a1 = 1 and, for n = 2, 3, 4, . . . , an = an–1 + 1/2
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a1 = 3 and, for n = 2, 3, 4, . . . , an = an–1 + 5/2
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a1 = 3 and, for n = 2, 3, 4, . . . , an = an-1 + 1/2 |
Use the graph below to match each quantity with the correct value.
:
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total number of vertices? |
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number of edges connecting a and c? |
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number of edges connecting a and b? |
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degree of vertex e? |
