EBK ALGEBRA 2
EBK ALGEBRA 2
11th Edition
ISBN: 9780544714304
Author: Larson
Publisher: HMH PUB
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Expert Solution & Answer
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Chapter 3, Problem 1TP
Solution

(a)

The inverse model that gives the speed of the car as a function of its kinetic energy.

  s=E625

Given:

The kinetic energy (in joules) of a 1250-kilogram compact car is given by the equation E=625s2 where s is the speed of the car in meters per second.

Concept used:

  • The graph of the function y=fx and its inverse f1x are symmetric to the line y=x .
  • For any point a,b on the graph of fx , the corresponding point on the graph of inverse function f1x is b,a .
  • If a function is one-to-one, then it has an inverse.

Calculation:

In order to find the inverse of the given function E=625s2 , first switch E and s and then solve for E again as shown below

  E=625s2E625=s2s2=E625s=E625

Thus, the inverse function is s=E625 .

(b)

The speed of the car if its kinetic energy is 120000 joules.

  66.1 kilometers per hour

Given:

The inverse model that gives the speed of car as a function of its kinetic energy is s=E625 .

Concept used:

  • The graph of the function y=fx and its inverse f1x are symmetric to the line y=x .
  • For any point a,b on the graph of fx , the corresponding point on the graph of inverse function f1x is b,a .
  • If a function is one-to-one, then it has an inverse.

Calculation:

In order to find the speed of the car, substitute E=120000 into above inverse function and simplify further as shown below

  s=E625s=120000625s=192s13.86 meters per second

In order to find the speed in kilometers per hour, multiply by the conversion factor 1 meter per second=3.6 kilometer per hour and solve further as shown below

  s=13.86 meters per seconds=13.86×3.6 kilometers per hours66.1 kilometers per hour

Thus, the speed of the car is about 66.1 kilometers per hour .

(c)

If the kinetic energy doubles, will the speed double?

  No

Given:

The kinetic energy (in joules) of a 1250-kilogram compact car is given by the equation E=625s2 where s is the speed of the car in meters per second.

Concept used:

  • The graph of the function y=fx and its inverse f1x are symmetric to the line y=x .
  • For any point a,b on the graph of fx , the corresponding point on the graph of inverse function f1x is b,a .
  • If a function is one-to-one, then it has an inverse.

Calculation:

Since E and s are not directly proportional, on doubling the kinetic energy will increase the speed by a factor of 2 times.

Chapter 3 Solutions

EBK ALGEBRA 2

Ch. 3.1 - Prob. 11GPCh. 3.1 - Prob. 12GPCh. 3.1 - Prob. 13GPCh. 3.1 - Prob. 14GPCh. 3.1 - Prob. 15GPCh. 3.1 - Prob. 16GPCh. 3.1 - Prob. 17GPCh. 3.1 - Prob. 18GPCh. 3.1 - Prob. 19GPCh. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - 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