Precalculus: Mathematics for Calculus - 6th Edition

6th Edition

ISBN: 9780840068071

Author: Stewart, James, Redlin, Lothar, Watson, Saleem

Publisher: Cengage Learning

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Question

Chapter 2.4, Problem 31E

To determine

To find the average speed of each winner.

Expert Solution

Answer to Problem 31E

The average speed of each of the winner is 10 m/sec .

Explanation of Solution

Given information:

The graph provided in the question shows the distance as a function of time for each of the three winners.

Calculation:

Since, each of the winner reached finished the race at the same time that is at t=10 sec.

So, the average speed of each of the winner must be same.

Therefore,

At t=0 sec, distance traveled=0 m.

At t=10 sec, distance traveled=100 m.

Average speed of each of the winner is obtained as:

distance traveledtime elapsed=100−010−0=10010=10 m/sec

Hence,

The average speed of each of the winner is 10 m/sec .

To determine

To explain the difference between the ways in which the three runners ran the race.

Expert Solution

Answer to Problem 31E

The differencebetween the ways in which the three runners ran the race is that the runner A ran the first half of the race with a higher speed that is 16 m/sec and in the next half, he slow down to 5 m/sec , runner C ran the first half of the race with a relatively lesser speed that is 5 m/sec and in the next half, he boast up to 16 m/sec , and runner B ran the whole race at an average speed of 10 m/sec .

Explanation of Solution

Given information:

The graph provided in the question shows the distance as a function of time for each of the three winners.

The graph showing the distance travelled by the runner at different time interval.

Since, each of the winner reached finished the race at the same time that is at Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.4, Problem 31E , additional homework tip 1

So, the average speed of each the winner must be same

Therefore

At, t-0 sec, Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.4, Problem 31E , additional homework tip 2 m.

At Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.4, Problem 31E , additional homework tip 3 sec, distance traveled-100 m.

Average speed of each of the winner is obtained as

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.4, Problem 31E , additional homework tip 4

Hence,

The average speed of each of the winner is 10m/sec.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.4, Problem 31E , additional homework tip 5

From the above graph, it can be observed that, distance travelled by A at t=5 sec is 80 m, distance travelled by B at t=5 sec is 50 m and distance travelled by C at t=5 sec is 20 m.

Time elapsed =5 sec

Average speed of runner A from 0 to 5 second is obtained as:

distance travelledtime elapsed=805=16 m/sec

Average speed of runner B from 0 to 5 second is obtained as:

distance travelledtime elapsed=505=10 m/sec

Average speed of runner C from 0 to 5 second is obtained as:

distance travelledtime elapsed=205=4 m/sec

Similarly,

Average speed of runner A from 5 to 10 second is obtained as:

distance travelledtime elapsed=100−805=205=5 m/sec

Average speed of runner B from 5 to 10 second is obtained as:

distance travelledtime elapsed=100−505=505=10 m/sec

Average speed of runner C from 5 to 10 second is obtained as:

distance travelledtime elapsed=100−205=805=16 m/sec

Hence,

It can be concluded easily that the differencebetween the ways in which the three runners ran the race is that the runner A ran the first half of the race with a higher speed that is 16 m/sec and in the next half, he slow down to 5 m/sec , runner C ran the first half of the race with a relatively lesser speed that is 5 m/sec and in the next half, he boast up to 16 m/sec , and runner B ran the whole race at an average speed of 10 m/sec .

Chapter 2.4, Problem 30E

Chapter 2.4, Problem 32E

Chapter 2 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 2.1 - Prob. 1E Ch. 2.1 - For a function f, the set of all possible inputs...Ch. 2.1 - (a) Which of the following functions have 5 in...Ch. 2.1 - A function is given algebraically by the formula...Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E

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So if g(2) = 5...Ch. 2.6 - If the rule of the function f is add one and the...Ch. 2.6 - We can express the functions in Exercise 3...Ch. 2.6 - Prob. 5E Ch. 2.6 - Prob. 6E Ch. 2.6 - Prob. 7E Ch. 2.6 - Prob. 8E Ch. 2.6 - Prob. 9E Ch. 2.6 - Prob. 10E Ch. 2.6 - Prob. 11E Ch. 2.6 - Prob. 12E Ch. 2.6 - Prob. 13E Ch. 2.6 - Prob. 14E Ch. 2.6 - Prob. 15E Ch. 2.6 - Prob. 16E Ch. 2.6 - Prob. 17E Ch. 2.6 - Prob. 18E Ch. 2.6 - Prob. 19E Ch. 2.6 - Prob. 20E Ch. 2.6 - Prob. 21E Ch. 2.6 - Prob. 22E Ch. 2.6 - Prob. 23E Ch. 2.6 - Prob. 24E Ch. 2.6 - Prob. 25E Ch. 2.6 - Prob. 26E Ch. 2.6 - Prob. 27E Ch. 2.6 - Prob. 28E Ch. 2.6 - Prob. 29E Ch. 2.6 - Prob. 30E Ch. 2.6 - Prob. 31E Ch. 2.6 - Prob. 32E Ch. 2.6 - Prob. 33E Ch. 2.6 - Prob. 34E Ch. 2.6 - Prob. 35E Ch. 2.6 - Prob. 36E Ch. 2.6 - Prob. 37E Ch. 2.6 - Prob. 38E Ch. 2.6 - Prob. 39E Ch. 2.6 - Prob. 40E Ch. 2.6 - Prob. 41E Ch. 2.6 - Prob. 42E Ch. 2.6 - Prob. 43E Ch. 2.6 - Prob. 44E Ch. 2.6 - Prob. 45E Ch. 2.6 - Prob. 46E Ch. 2.6 - Prob. 47E Ch. 2.6 - Prob. 48E Ch. 2.6 - Prob. 49E Ch. 2.6 - Prob. 50E Ch. 2.6 - Prob. 51E Ch. 2.6 - Prob. 52E Ch. 2.6 - Prob. 53E Ch. 2.6 - Prob. 54E Ch. 2.6 - Prob. 55E Ch. 2.6 - Prob. 56E Ch. 2.6 - Prob. 57E Ch. 2.6 - Prob. 58E Ch. 2.6 - Prob. 59E Ch. 2.6 - Revenue, Cost, and Profit A print shop makes...Ch. 2.6 - Area of a Ripple A stone is dropped in a lake,...Ch. 2.6 - Inflating a Balloon A spherical balloon is being...Ch. 2.6 - Area of a Balloon A spherical weather balloon is...Ch. 2.6 - Multiple Discounts You have a 50 coupon from the...Ch. 2.6 - Multiple Discounts An appliance dealer advertises...Ch. 2.6 - Airplane Trajectory An airplane is flying at a...Ch. 2.6 - Prob. 67E Ch. 2.6 - Prob. 68E Ch. 2.6 - Prob. 69E Ch. 2.6 - Prob. 70E Ch. 2.7 - A function f is one-to-one if different inputs...Ch. 2.7 - (a) For a function to have an inverse, it must be...Ch. 2.7 - A function f has the following verbal description:...Ch. 2.7 - True or false? (a) If f has an inverse, then f1(x)...Ch. 2.7 - Prob. 5E Ch. 2.7 - Prob. 6E Ch. 2.7 - Prob. 7E Ch. 2.7 - Prob. 8E Ch. 2.7 - Prob. 9E Ch. 2.7 - Prob. 10E Ch. 2.7 - Prob. 11E Ch. 2.7 - Prob. 12E Ch. 2.7 - Prob. 13E Ch. 2.7 - Prob. 14E Ch. 2.7 - Prob. 15E Ch. 2.7 - Prob. 16E Ch. 2.7 - Prob. 17E Ch. 2.7 - Prob. 18E Ch. 2.7 - Prob. 19E Ch. 2.7 - Prob. 20E Ch. 2.7 - Prob. 21E Ch. 2.7 - Prob. 22E Ch. 2.7 - Prob. 23E Ch. 2.7 - Prob. 24E Ch. 2.7 - Prob. 25E Ch. 2.7 - Prob. 26E Ch. 2.7 - Prob. 27E Ch. 2.7 - Prob. 28E Ch. 2.7 - Prob. 29E Ch. 2.7 - Prob. 30E Ch. 2.7 - Prob. 31E Ch. 2.7 - Prob. 32E Ch. 2.7 - Prob. 33E Ch. 2.7 - Prob. 34E Ch. 2.7 - Prob. 35E Ch. 2.7 - Prob. 36E Ch. 2.7 - Prob. 37E Ch. 2.7 - Prob. 38E Ch. 2.7 - Prob. 39E Ch. 2.7 - Prob. 40E Ch. 2.7 - Prob. 41E Ch. 2.7 - Prob. 42E Ch. 2.7 - Prob. 43E Ch. 2.7 - Prob. 44E Ch. 2.7 - Prob. 45E Ch. 2.7 - Prob. 46E Ch. 2.7 - Prob. 47E Ch. 2.7 - Prob. 48E Ch. 2.7 - Prob. 49E Ch. 2.7 - Prob. 50E Ch. 2.7 - Prob. 51E Ch. 2.7 - Prob. 52E Ch. 2.7 - Prob. 53E Ch. 2.7 - Prob. 54E Ch. 2.7 - Prob. 55E Ch. 2.7 - Prob. 56E Ch. 2.7 - Prob. 57E Ch. 2.7 - Prob. 58E Ch. 2.7 - Prob. 59E Ch. 2.7 - Prob. 60E Ch. 2.7 - Prob. 61E Ch. 2.7 - Prob. 62E Ch. 2.7 - Prob. 63E Ch. 2.7 - Prob. 64E Ch. 2.7 - Prob. 65E Ch. 2.7 - Prob. 66E Ch. 2.7 - Prob. 67E Ch. 2.7 - Prob. 68E Ch. 2.7 - Prob. 69E Ch. 2.7 - Prob. 70E Ch. 2.7 - Prob. 71E Ch. 2.7 - Prob. 72E Ch. 2.7 - Prob. 73E Ch. 2.7 - Prob. 74E Ch. 2.7 - Prob. 75E Ch. 2.7 - Prob. 76E Ch. 2.7 - Prob. 77E Ch. 2.7 - Prob. 78E Ch. 2.7 - Prob. 79E Ch. 2.7 - Prob. 80E Ch. 2.7 - Fee for Service For his services, a private...Ch. 2.7 - Prob. 82E Ch. 2.7 - Prob. 83E Ch. 2.7 - Prob. 84E Ch. 2.7 - Prob. 85E Ch. 2.7 - Prob. 86E Ch. 2.7 - Income Tax In a certain country the tax on incomes...Ch. 2.7 - Prob. 88E Ch. 2.7 - Prob. 89E Ch. 2.7 - Prob. 90E Ch. 2.7 - Prob. 91E Ch. 2.7 - Prob. 92E Ch. 2.7 - Prob. 93E Ch. 2 - Prob. 1RCC Ch. 2 - Prob. 2RCC Ch. 2 - Prob. 3RCC Ch. 2 - Prob. 4RCC Ch. 2 - Prob. 5RCC Ch. 2 - Prob. 6RCC Ch. 2 - Prob. 7RCC Ch. 2 - Prob. 8RCC Ch. 2 - Prob. 9RCC Ch. 2 - Prob. 10RCC Ch. 2 - Prob. 11RCC Ch. 2 - Prob. 12RCC Ch. 2 - Prob. 1RE Ch. 2 - Prob. 2RE Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - Prob. 68RE Ch. 2 - Prob. 69RE Ch. 2 - Prob. 70RE Ch. 2 - Prob. 71RE Ch. 2 - Prob. 72RE Ch. 2 - Prob. 73RE Ch. 2 - Prob. 74RE Ch. 2 - Prob. 75RE Ch. 2 - Prob. 76RE Ch. 2 - Prob. 77RE Ch. 2 - Prob. 78RE Ch. 2 - Prob. 79RE Ch. 2 - Prob. 80RE Ch. 2 - Prob. 81RE Ch. 2 - Prob. 82RE Ch. 2 - Prob. 83RE Ch. 2 - Prob. 84RE Ch. 2 - Prob. 85RE Ch. 2 - Prob. 86RE Ch. 2 - Prob. 87RE Ch. 2 - Prob. 88RE Ch. 2 - Prob. 89RE Ch. 2 - Prob. 90RE Ch. 2 - Prob. 91RE Ch. 2 - Prob. 92RE Ch. 2 - Prob. 1T Ch. 2 - Prob. 2T Ch. 2 - A function f has the following verbal description:...Ch. 2 - A school fund-raising group sells chocolate bars...Ch. 2 - Prob. 5T Ch. 2 - Prob. 6T Ch. 2 - Prob. 7T Ch. 2 - Prob. 8T Ch. 2 - Prob. 9T Ch. 2 - Prob. 10T Ch. 2 - Prob. 11T Ch. 2 - Prob. 12T Ch. 2 - Prob. 1P Ch. 2 - Prob. 2P Ch. 2 - Prob. 3P Ch. 2 - Prob. 4P Ch. 2 - Prob. 5P Ch. 2 - Prob. 6P Ch. 2 - Prob. 7P Ch. 2 - Prob. 8P Ch. 2 - Prob. 9P Ch. 2 - Prob. 10P Ch. 2 - Prob. 11P Ch. 2 - Length A woman 5 ft tall is standing near a street...Ch. 2 - Distance Two ships leave port at the same time....Ch. 2 - Prob. 14P Ch. 2 - Area An isosceles triangle has a perimeter of 8...Ch. 2 - Prob. 16P Ch. 2 - Area A rectangle is inscribed in a semicircle of...Ch. 2 - Height The volume of a cone is 100 in3. Find a...Ch. 2 - Prob. 19P Ch. 2 - Minimizing a Sum Find two positive numbers whose...Ch. 2 - Prob. 21P Ch. 2 - Dividing a Pen A rancher with 750 ft of fencing...Ch. 2 - Fencing a Garden Plot A property owner wants to...Ch. 2 - Maximizing Area A wire 10 cm long is cut into two...Ch. 2 - Light from a Window A Norman window has the shape...Ch. 2 - Volume of a Box A box with an open top is to be...Ch. 2 - Area of a Box An open box with a square base is to...Ch. 2 - Inscribed Rectangle Find the dimensions that give...Ch. 2 - Minimizing Costs A rancher wants to build a...Ch. 2 - Minimizing Time A man stands at a point A on the...Ch. 2 - Bird Flight A bird is released from point A on an...Ch. 2 - Area of a Kite A kite frame is to be made from six...

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