Mathematics, 05.05.2020 07:35 mya1318
Strong Induction (11 points) (1) (6 points) Let P(n) be the statement that a postage of n cents can be formed using just 3-cent stamps and 7-cent stamps. The Induction and Recursion parts of this exercise outline a strong induction proof that P(n) is true for n 18. (a) (1 points) Show that P(12), P(13), and P(14) are true, which com- pletes the base case. (b) (1 points) What is the inductive hypothesis? (c) (1 points) What do you need to prove in the inductive step? (d) (3 points) Complete the inductive step for k 14. (2) (5 points) Use strong induction to show that every positive integer can be written as a sum of distinct powers of two (i. e., 20 = 1; 21 = 2; 22 = 4; 23 = 8; 24 = 16; : : :). For example: 19 = 16 + 2 + 1 = 24 + 21 + 20 Hint: For the inductive step, separately consider the case where k +1 is even and where it is odd. When it is even, note that (k + 1)=2 is an integer.
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Mathematics, 21.06.2019 15:00
Abcd is a parallelogram. the diagram is not drawn to scale. if m
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Mathematics, 21.06.2019 19:00
The weight of an object in the water is 7% of its weight out of the water. what is the weight of a 652g object in the water?
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Mathematics, 21.06.2019 19:50
Prove (a) cosh2(x) β sinh2(x) = 1 and (b) 1 β tanh 2(x) = sech 2(x). solution (a) cosh2(x) β sinh2(x) = ex + eβx 2 2 β 2 = e2x + 2 + eβ2x 4 β = 4 = . (b) we start with the identity proved in part (a): cosh2(x) β sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 β sinh2(x) cosh2(x) = 1 or 1 β tanh 2(x) = .
Answers: 3
Mathematics, 22.06.2019 00:30
Astudent was asked to find the square of 7x+3. the student quickly wrote (7x+3)^3= 49x^2+9. identify the student's error and provide the correct answer.
Answers: 3
Strong Induction (11 points) (1) (6 points) Let P(n) be the statement that a postage of n cents can...
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