EBK MATHEMATICS FOR MACHINE TECHNOLOGY
7th Edition
ISBN: 9780100548169
Author: SMITH
Publisher: YUZU
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Chapter 21, Problem 4A
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(^)
k
Recall that for numbers 0 ≤ k ≤ n the binomial coefficient (^) is defined as
n!
k! (n−k)!
Question 1.
(1) Prove the following identity: (22) + (1121) = (n+1).
(2) Use the identity above to prove the binomial theorem by induction. That
is, prove that for any a, b = R,
n
(a + b)" = Σ (^)
an-
n-kyk.
k=0
n
Recall that Σ0 x is short hand notation for the expression x0+x1+
+xn-
(3) Fix x = R, x > 0. Prove Bernoulli's inequality: (1+x)" ≥1+nx, by using
the binomial theorem.
-
Question 2. Prove that ||x| - |y|| ≤ |x − y| for any real numbers x, y.
Question 3. Assume (In) nEN is a sequence which is unbounded above. That is,
the set {xn|nЄN} is unbounded above. Prove that there are natural numbers
N] k for all k Є N.
be natural numbers (nk Є N). Prove that
not use ai please
3) Let G be the group generated by elements a and b satisfying the relations a² = 63,
66 = 1, and a ¹ba = b¹. Which of the following is equivalent to the element
z = a a-2ba3b3?
A) b-2a-1
B) ab²
C) ab
D) ba
E) b²a
Chapter 21 Solutions
EBK MATHEMATICS FOR MACHINE TECHNOLOGY
Ch. 21 - Express 5.037 as a percent.Ch. 21 - Prob. 2ACh. 21 - Prob. 3ACh. 21 - Raise (21.54.3)3 to the indicated power.Ch. 21 - The length, L, of the standard 82° included angle...Ch. 21 - Write the number 107.2004 as words.Ch. 21 - Prob. 7ACh. 21 - Prob. 8ACh. 21 - Find each percentage. Round the answers to 2...Ch. 21 - Prob. 10A
Ch. 21 - Prob. 11ACh. 21 - Prob. 12ACh. 21 - Prob. 13ACh. 21 - Prob. 14ACh. 21 - Prob. 15ACh. 21 - Prob. 16ACh. 21 - Prob. 17ACh. 21 - Prob. 18ACh. 21 - Prob. 19ACh. 21 - Prob. 20ACh. 21 - Prob. 21ACh. 21 - Prob. 22ACh. 21 - Prob. 23ACh. 21 - Prob. 24ACh. 21 - Find each percentage. Round the answers to 2...Ch. 21 - Prob. 26ACh. 21 - Prob. 27ACh. 21 - Find each percent (rate). Round the answers to 2...Ch. 21 - Prob. 29ACh. 21 - Prob. 30ACh. 21 - Prob. 31ACh. 21 - Prob. 32ACh. 21 - Prob. 33ACh. 21 - Prob. 34ACh. 21 - Prob. 35ACh. 21 - Prob. 36ACh. 21 - Prob. 37ACh. 21 - Prob. 38ACh. 21 - Prob. 39ACh. 21 - Prob. 40ACh. 21 - Prob. 41ACh. 21 - Prob. 42ACh. 21 - Prob. 43ACh. 21 - Prob. 44ACh. 21 - Prob. 45ACh. 21 - Prob. 46ACh. 21 - Prob. 47ACh. 21 - Prob. 48ACh. 21 - Prob. 49ACh. 21 - Prob. 50ACh. 21 - Find each base. Round the answers to 2 decimal...Ch. 21 - Prob. 52ACh. 21 - Prob. 53ACh. 21 - Prob. 54ACh. 21 - Prob. 55ACh. 21 - Prob. 56ACh. 21 - Prob. 57ACh. 21 - Prob. 58ACh. 21 - Prob. 59ACh. 21 - Prob. 60ACh. 21 - Prob. 61ACh. 21 - Prob. 62ACh. 21 - Prob. 63ACh. 21 - Prob. 64ACh. 21 - Prob. 65ACh. 21 - Prob. 66ACh. 21 - Prob. 67ACh. 21 - Prob. 68ACh. 21 - Prob. 69ACh. 21 - Prob. 70ACh. 21 - Prob. 71ACh. 21 - Prob. 72ACh. 21 - Prob. 73ACh. 21 - Prob. 74ACh. 21 - Prob. 75ACh. 21 - Prob. 76ACh. 21 - Prob. 77ACh. 21 - Prob. 78A
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