Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 2.4, Problem 8E

(a)

To determine

To find: The slope of the secants PQ1 , PQ2 , PQ3 and PQ4 , arrange them in a table. Also, write the unit for the slope.

(a)

Expert Solution

Answer to Problem 8E

The units for the slope are m/sec and the slope of the secants is shown in below table:

Secant	Slope
PQ1	12 m/sec
PQ2	14 m/sec
PQ3	16 m/sec
PQ4	16 m/sec

Explanation of Solution

Given information: The below figure shows the distance-time graph for a wrench that fell from the top platform of a communication mast on the moon to the station roof 80 m below:

Calculus: Graphical, Numerical, Algebraic, Chapter 2.4, Problem 8E , additional homework tip 1

Calculation:

As shown in the graph the points are Q1(5,20) , Q2(7,38) , Q3(8.5,56) , Q4(9.5,72) and P(10,80).

The slope of the secant PQ1 can be calculated as:

m=y2−y1x2−x1=80−2010−5=605=12

So, the slope of the secant PQ1 is 12 m/sec.

The slope of the secant PQ2 can be calculated as:

m=y2−y1x2−x1=80−3810−7=423=14

So, the slope of the secant PQ2 is 14 m/sec.

The slope of the secant PQ3 can be calculated as:

m=y2−y1x2−x1=80−5610−8.5=241.5=16

So, the slope of the secant PQ3 is 16 m/sec.

The slope of the secant PQ4 can be calculated as:

m=y2−y1x2−x1=80−7210−9.5=80.5=16

So, the slope of the secant PQ4 is 16 m/sec.

Therefore, the following table shows the slope of the secant lines:

Secant	Slope
PQ1	12 m/sec
PQ2	14 m/sec
PQ3	16 m/sec
PQ4	16 m/sec

(b)

To determine

To find: The speed at the point P.

(b)

Expert Solution

Answer to Problem 8E

The speed at the point P is equal to 16 m/sec.

Explanation of Solution

Given information: The below figure shows the distance-time graph for a 1994 Ford Mustang Cobra accelerating from a standstill:

Calculus: Graphical, Numerical, Algebraic, Chapter 2.4, Problem 8E , additional homework tip 2

Calculation:

As calculated in part (a), the slope of the line joining the point nearest to the point P is equal to the speed at point P.

The point nearest to the point P is Q4 and the slope of the secant PQ4 is equal to 16 m/sec.

Therefore, the speed at the point P is equal to 16 m/sec.

Chapter 2.4, Problem 7E

Chapter 2.4, Problem 9E

Chapter 2 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 2.1 - Prob. 1QR Ch. 2.1 - Prob. 2QR Ch. 2.1 - Prob. 3QR Ch. 2.1 - Prob. 4QR Ch. 2.1 - Prob. 5QR Ch. 2.1 - Prob. 6QR Ch. 2.1 - Prob. 7QR Ch. 2.1 - Prob. 8QR Ch. 2.1 - Prob. 9QR Ch. 2.1 - Prob. 10QR

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The slope of the secants P Q 1 , P Q 2 , P Q 3 and P Q 4 , arrange them in a table. Also, write the unit for the slope.

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To find: The slope of the secants PQ1 , PQ2 , PQ3 and PQ4 , arrange them in a table. Also, write the unit for the slope.

Answer to Problem 8E

Explanation of Solution

To find: The speed at the point P.

Answer to Problem 8E

Explanation of Solution

Chapter 2 Solutions

Additional Math Textbook Solutions