Contemporary Abstract Algebra
9th Edition
ISBN: 9781305657960
Author: Joseph Gallian
Publisher: Cengage Learning
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Chapter 5, Problem 16E
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For the following exercise, find the domain and range of the function below using interval notation.
10+
9
8
7
6
5
4
3
2
1
10 -9 -8 -7 -6 -5 -4 -3 -2 -1
2 34
5
6 7 8 9 10
-1
-2
Domain:
Range:
-4
-5
-6
-7-
67% 9
-8
-9
-10-
1. Given that h(t) = -5t + 3 t². A tangent line H to the function h(t) passes through
the point (-7, B).
a. Determine the value of ẞ.
b. Derive an expression to represent the gradient of the tangent line H that is
passing through the point (-7. B).
c. Hence, derive the straight-line equation of the tangent line H
2. The function p(q) has factors of (q − 3) (2q + 5) (q) for the interval -3≤ q≤ 4.
a. Derive an expression for the function p(q).
b. Determine the stationary point(s) of the function p(q)
c. Classify the stationary point(s) from part b. above.
d. Identify the local maximum of the function p(q).
e. Identify the global minimum for the function p(q).
3. Given that m(q)
=
-3e-24-169 +9
(-39-7)(-In (30-755
a. State all the possible rules that should be used to differentiate the function
m(q). Next to the rule that has been stated, write the expression(s) of the
function m(q) for which that rule will be applied.
b. Determine the derivative of m(q)
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Chapter 5 Solutions
Contemporary Abstract Algebra
Ch. 5 - Let [123456213546]and=[123456612435] . Compute...Ch. 5 - Let [1234567823451786]and=[1234567813876524] ....Ch. 5 - Write each of the following permutations as a...Ch. 5 - Find the order of each of the following...Ch. 5 - What is the order of each of the following...Ch. 5 - What is the order of each of the following...Ch. 5 - What is the order of the product of a pair of...Ch. 5 - Determine whether the following permutations are...Ch. 5 - What are the possible orders for the elements of...Ch. 5 - Show that A8 contains an element of order 15.
Ch. 5 - Find an element in A12 of order 30.Ch. 5 - Show that a function from a finite set S to itself...Ch. 5 - Prob. 13ECh. 5 - Suppose that is a 6-cycle and is a 5-cycle....Ch. 5 - Prob. 15ECh. 5 - If is even, prove that 1 is even. If is odd,...Ch. 5 - Prob. 17ECh. 5 - In Sn , let be an r-cycle, an s-cycle, and a...Ch. 5 - Let and belong to Sn . Prove that is even if...Ch. 5 - Associate an even permutation with the number +1...Ch. 5 - Complete the following statement: A product of...Ch. 5 - What cycle is (a1a2an)1 ?Ch. 5 - Show that if H is a subgroup of Sn , then either...Ch. 5 - Suppose that H is a subgroup of Sn of odd order....Ch. 5 - Give two reasons why the set of odd permutations...Ch. 5 - Let and belong to Sn . Prove that 11 is an...Ch. 5 - Prob. 27ECh. 5 - How many elements of order 5 are in S7 ?Ch. 5 - Prob. 29ECh. 5 - Prove that (1234) is not the product of 3-cycles....Ch. 5 - Let S7 and suppose 4=(2143567) . Find . What are...Ch. 5 - My mind rebels at stagnation. Give me problems,...Ch. 5 - Let (a1a2a3a4)and(a5a6) be disjoint cycles in S10...Ch. 5 - If and are distinct 2-cycles, what are the...Ch. 5 - Prob. 35ECh. 5 - Let =(1,3,5,7,9,8,6)(2,4,10) . What is the...Ch. 5 - Prob. 37ECh. 5 - Let H=S5(1)=1and(3)=3 . Prove that H is a...Ch. 5 - In S4 , find a cyclic subgroup of order 4 and a...Ch. 5 - In S3 , find elements and such that...Ch. 5 - Find group elements and in S5 such that...Ch. 5 - Represent the symmetry group of an equilateral...Ch. 5 - Prove that Sn is non-Abelian for all n3 .Ch. 5 - Prove that An is non-Abelian for all n4 .Ch. 5 - For n3 , let H=bSn(1)=1 or 2 and (2)=1or2 .Prove...Ch. 5 - Show that in S7 , the equation x2=(1234) has no...Ch. 5 - If (ab) and (cd) are distinct 2-cycles in Sn ,...Ch. 5 - Let and belong to Sn . Prove that 1 and are...Ch. 5 - Viewing the members of D4 as a group of...Ch. 5 - Viewing the members of D5 as a group of...Ch. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Show that A5 has 24 elements of order 5, 20...Ch. 5 - Find a cyclic subgroup of A8 that has order 4....Ch. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Show that every element in An for n3 can be...Ch. 5 - Show that for n3,Z(Sn)=[] .Ch. 5 - Prob. 59ECh. 5 - Use the Verhoeff check-digit scheme based on D5 to...Ch. 5 - Prob. 61ECh. 5 - (Indiana College Mathematics Competition) A...Ch. 5 - Prob. 63ECh. 5 - Find five subgroups of S5 of order 24.Ch. 5 - Why does the fact that the orders of the elements...Ch. 5 - Let a belong to Sn . Prove that divides n!Ch. 5 - Encrypt the message ATTACK POSTPONED using the...Ch. 5 - The message VAADENWCNHREDEYA was encrypted using...
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- So confused. Step by step instructions pleasearrow_forwardIn simplest terms, Sketch the graph of the parabola. Then, determine its equation. opens downward, vertex is (- 4, 7), passes through point (0, - 39)arrow_forwardIn simplest way, For each quadratic relation, find the zeros and the maximum or minimum. a) y = x 2 + 16 x + 39 b) y = 5 x2 - 50 x - 120arrow_forward
- In simplest terms and step by step Write each quadratic relation in standard form, then fi nd the zeros. y = - 4( x + 6)2 + 36arrow_forwardIn simplest terms and step by step For each quadratic relation, find the zeros and the maximum or minimum. 1) y = - 2 x2 - 28 x + 64 2) y = 6 x2 + 36 x - 42arrow_forwardWrite each relation in standard form a)y = 5(x + 10)2 + 7 b)y = 9(x - 8)2 - 4arrow_forward
- In simplest form and step by step Write the quadratic relation in standard form, then fi nd the zeros. y = 3(x - 1)2 - 147arrow_forwardStep by step instructions The path of a soccer ball can be modelled by the relation h = - 0.1 d 2 + 0.5 d + 0.6, where h is the ball’s height and d is the horizontal distance from the kicker. a) Find the zeros of the relation.arrow_forwardIn simplest terms and step by step how do you find the zeros of y = 6x2 + 24x - 192arrow_forward
- Step by step Find the zeros of each quadratic relation. a) y = x2 - 16xarrow_forwardIn simplest step by step terms, how do you find the zeros of y = x2 - 16arrow_forwardIn simplest terms, Describe the shape and position of the parabola relative to the graph of y = x 2 y = - 80( x + 9) 2 + 10.8arrow_forward
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