EBK MATHEMATICAL APPLICATIONS FOR THE M
11th Edition
ISBN: 9780100546233
Author: Reynolds
Publisher: YUZU
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Chapter 11.4, Problem 27E
To determine
To calculate: The percent rate of change of resistance of a claw weight in terms of the percent rate of change of the body weight for fiddler crabs if the allometric relationship between the weight
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7. [10 marks]
Let G
=
(V,E) be a 3-connected graph. We prove that for every x, y, z Є V, there is a
cycle in G on which x, y, and z all lie.
(a) First prove that there are two internally disjoint xy-paths Po and P₁.
(b) If z is on either Po or P₁, then combining Po and P₁ produces a cycle on which
x, y, and z all lie. So assume that z is not on Po and not on P₁. Now prove that
there are three paths Qo, Q1, and Q2 such that:
⚫each Qi starts at z;
• each Qi ends at a vertex w; that is on Po or on P₁, where wo, w₁, and w₂ are
distinct;
the paths Qo, Q1, Q2 are disjoint from each other (except at the start vertex
2) and are disjoint from the paths Po and P₁ (except at the end vertices wo,
W1, and w₂).
(c) Use paths Po, P₁, Qo, Q1, and Q2 to prove that there is a cycle on which x, y, and
z all lie. (To do this, notice that two of the w; must be on the same Pj.)
6. [10 marks]
Let T be a tree with n ≥ 2 vertices and leaves. Let BL(T) denote the block graph of
T.
(a) How many vertices does BL(T) have?
(b) How many edges does BL(T) have?
Prove that your answers are correct.
4. [10 marks]
Find both a matching of maximum size and a vertex cover of minimum size in
the following bipartite graph. Prove that your answer is correct.
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Chapter 11 Solutions
EBK MATHEMATICAL APPLICATIONS FOR THE M
Ch. 11.1 - 1.
Ch. 11.1 - 2. If
Ch. 11.1 - Prob. 3CPCh. 11.1 - 4. Find .
Ch. 11.1 - Prob. 1ECh. 11.1 - Prob. 2ECh. 11.1 - Prob. 3ECh. 11.1 - Prob. 4ECh. 11.1 - Prob. 5ECh. 11.1 - Find the derivatives of the functions in Problems...
Ch. 11.1 - Find the derivatives of the functions in Problems...Ch. 11.1 - Find the derivatives of the functions in Problems...Ch. 11.1 - Find the derivatives of the functions in Problems...Ch. 11.1 - Find the derivatives of the functions in Problems...Ch. 11.1 - 11. Find .
Ch. 11.1 - Prob. 12ECh. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - In each of Problems 13-18, find the derivative of...Ch. 11.1 - 19. Find .
Ch. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - 24. Find
Ch. 11.1 - In Problems 25-38, find y'.
Ch. 11.1 - In Problems 25-38, find y'.
26.
Ch. 11.1 - In Problems 25-38, find y'.
27.
Ch. 11.1 - Prob. 28ECh. 11.1 - In Problems 25-38, find y'.
29.
Ch. 11.1 - Prob. 30ECh. 11.1 - In Problems 25-38, find y'.
31.
Ch. 11.1 - Prob. 32ECh. 11.1 - In Problems 25-38, find y'.
33.
Ch. 11.1 - Prob. 34ECh. 11.1 - Prob. 35ECh. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - 43. Marginal cost Suppose that the total cost (in...Ch. 11.1 - 44. Investment If money is invested at the...Ch. 11.1 - 45. Marginal revenue The total revenue, in...Ch. 11.1 - 46. Supply Suppose that the supply of x units of a...Ch. 11.1 - 47. Demand The demand function for a product is...Ch. 11.1 - Prob. 48ECh. 11.1 - Prob. 49ECh. 11.1 - Prob. 50ECh. 11.1 - Prob. 51ECh. 11.1 - 52. Women in the workforce From 1950 and projected...Ch. 11.2 - 1. If , find y’.
Ch. 11.2 - 2. If , find y’.
Ch. 11.2 - Prob. 3CPCh. 11.2 - 4. If the sales of a product are given by , where...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Prob. 3ECh. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Prob. 9ECh. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Prob. 27ECh. 11.2 - Prob. 28ECh. 11.2 - Find the derivatives of the functions in Problems...Ch. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.2 - Prob. 36ECh. 11.2 - Prob. 37ECh. 11.2 - Prob. 38ECh. 11.2 - In Problems 39-42, find any relative maxima and...Ch. 11.2 - Prob. 40ECh. 11.2 - Prob. 41ECh. 11.2 - Prob. 42ECh. 11.2 - 43. Future value If $P is invested for n years at...Ch. 11.2 - 44. Future value The future value that accrues...Ch. 11.2 - 45. Sales decay After the end of an advertising...Ch. 11.2 - Prob. 46ECh. 11.2 - 47. Marginal cost Suppose that the total cost in...Ch. 11.2 - 48. Marginal revenue Suppose that the revenue in...Ch. 11.2 - 49. Drugs in a bloodstream The percent...Ch. 11.2 - 50. Radioactive decay The amount of the...Ch. 11.2 - 51. Pollution Pollution levels in Lake Sagamore...Ch. 11.2 - Prob. 52ECh. 11.2 - Prob. 55ECh. 11.2 - Prob. 56ECh. 11.2 - 58. Blood pressure Medical research has shown...Ch. 11.2 - Prob. 59ECh. 11.2 - Prob. 60ECh. 11.2 - Prob. 61ECh. 11.2 - 62. Carbon dioxide emissions Using U.S. Department...Ch. 11.2 - Prob. 66ECh. 11.3 - Find the following:
(b) (c)
Ch. 11.3 - Prob. 2CPCh. 11.3 - In Problems 1-6, find dy/dx at the given point...Ch. 11.3 - In Problems 1-6, find at the given point without...Ch. 11.3 - In Problems 1-6, find dy/dx at the given point...Ch. 11.3 - In Problems 1-6, find at the given point without...Ch. 11.3 - In Problems 1-6, find at the given point without...Ch. 11.3 - In Problems 1-6, find at the given point without...Ch. 11.3 - Find dy/dx for the functions in Problems 7-10.
7....Ch. 11.3 - Find for the functions in Problems 7-10.
8.
Ch. 11.3 - Find for the functions in Problems 7-10.
9.
Ch. 11.3 - Find for the functions in Problems 7-10.
10.
Ch. 11.3 - 11.
Ch. 11.3 - 12.
Ch. 11.3 - 13.
Ch. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - 16.
Ch. 11.3 - 17.
Ch. 11.3 - 18. If find .
Ch. 11.3 - 19.
Ch. 11.3 - Prob. 20ECh. 11.3 - Prob. 21ECh. 11.3 - Prob. 22ECh. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Prob. 25ECh. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.3 - Prob. 32ECh. 11.3 - Prob. 33ECh. 11.3 - 34. If ln find .
Ch. 11.3 - Prob. 35ECh. 11.3 - Prob. 36ECh. 11.3 - 35.
Ch. 11.3 - Prob. 38ECh. 11.3 - 37.
Ch. 11.3 - Prob. 40ECh. 11.3 - Prob. 41ECh. 11.3 - Prob. 42ECh. 11.3 - Prob. 43ECh. 11.3 - Prob. 44ECh. 11.3 - Prob. 45ECh. 11.3 - Prob. 46ECh. 11.3 - Prob. 47ECh. 11.3 - Prob. 48ECh. 11.3 - Prob. 49ECh. 11.3 - Prob. 50ECh. 11.3 - Prob. 51ECh. 11.3 - Prob. 52ECh. 11.3 - Prob. 53ECh. 11.3 - Prob. 54ECh. 11.3 - 55. Advertising and sales Suppose that a company’s...Ch. 11.3 - Prob. 56ECh. 11.3 - 57. Production Suppose that a company can produce...Ch. 11.3 - Prob. 58ECh. 11.3 - 59. Demand If the demand function for q units of a...Ch. 11.3 - Prob. 60ECh. 11.3 - Prob. 61ECh. 11.3 - Prob. 62ECh. 11.3 - Prob. 63ECh. 11.4 - 1. If V represents volume, write a mathematical...Ch. 11.4 - Prob. 2CPCh. 11.4 - 3. True or false: In solving a related-rates...Ch. 11.4 - Prob. 1ECh. 11.4 - In Problems 1-4, find using the given values.
2....Ch. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Prob. 11ECh. 11.4 - Prob. 12ECh. 11.4 - 13. The radius of a circle is increasing at a rate...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - 17. Profit Suppose that the daily profit (in...Ch. 11.4 - 18. Profit Suppose that the monthly revenue and...Ch. 11.4 - Prob. 19ECh. 11.4 - Supply The supply function for a product is given...Ch. 11.4 - Prob. 21ECh. 11.4 - Prob. 22ECh. 11.4 - Tumor growth For Problems 23 and 24, suppose that...Ch. 11.4 - Tumor growth For Problems 23 and 24, suppose that...Ch. 11.4 - 25. Allomelric relationships—fish For many species...Ch. 11.4 - Prob. 26ECh. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - 30. Water purification Assume that water is being...Ch. 11.4 - Prob. 31ECh. 11.4 - 32. Boat docking Suppose that a boat is being...Ch. 11.4 - 33. Ladder safety A 30-ft ladder is leaning...Ch. 11.4 - 34. Flight A kite is 30 ft high and is moving...Ch. 11.4 - 35. Flight A plane is flying at a constant...Ch. 11.4 - 36. Distance Two boats leave the same port at the...Ch. 11.4 - 37. Distance Two cars are approaching an...Ch. 11.4 - 38. Water depth Water is flowing into a barrel in...Ch. 11.4 - Prob. 39ECh. 11.5 - 1. Write the formula for point elasticity, .
Ch. 11.5 - 2. (a) If , the demand is called _______.
(b) If...Ch. 11.5 - Prob. 3CPCh. 11.5 - Prob. 4CPCh. 11.5 - Prob. 1ECh. 11.5 - Prob. 2ECh. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - Prob. 7ECh. 11.5 - In Problems 1 -8, p is in dollars and q is the...Ch. 11.5 - 9. Suppose the demand function for a product is...Ch. 11.5 - 10. Suppose the weekly demand function for a...Ch. 11.5 - In Problems 11 and 12, the demand functions for...Ch. 11.5 - In Problems 11 and 12, the demand functions for...Ch. 11.5 - Prob. 15ECh. 11.5 - Prob. 16ECh. 11.5 - Prob. 17ECh. 11.5 - Prob. 18ECh. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - Prob. 22ECh. 11.5 - In Problems 15-24, p is the price per unit in...Ch. 11.5 - Prob. 24ECh. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - In Problems 1-12, find the derivative of each...Ch. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Prob. 14RECh. 11 - Prob. 15RECh. 11 - Prob. 16RECh. 11 - Prob. 17RECh. 11 - Prob. 18RECh. 11 - In Problems 15-20, find the indicated...Ch. 11 - Prob. 20RECh. 11 - Prob. 21RECh. 11 - Prob. 22RECh. 11 - Prob. 23RECh. 11 - Prob. 24RECh. 11 - Prob. 25RECh. 11 - Prob. 26RECh. 11 - Prob. 27RECh. 11 - Prob. 28RECh. 11 - 29. Radioactive decay A breeder reactor converts...Ch. 11 - Prob. 30RECh. 11 - Prob. 31RECh. 11 - Prob. 32RECh. 11 - Prob. 33RECh. 11 - Prob. 34RECh. 11 - Prob. 38RECh. 11 - Prob. 39RECh. 11 - 37. Elasticity Suppose the weekly demand function...Ch. 11 - Prob. 41RECh. 11 - Prob. 35RECh. 11 - Prob. 36RECh. 11 - Prob. 37RECh. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - Prob. 2TCh. 11 - Prob. 3TCh. 11 - Prob. 4TCh. 11 - Prob. 5TCh. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - In Problems 1-8, find the derivative of each...Ch. 11 - Prob. 9TCh. 11 - Prob. 10TCh. 11 - Prob. 11TCh. 11 - 12. Suppose the weekly revenue and weekly cost...Ch. 11 - Prob. 13TCh. 11 - Prob. 14TCh. 11 - Prob. 15TCh. 11 - Prob. 16TCh. 11 - Prob. 17TCh. 11 - Prob. 19T
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