Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

1st Edition

ISBN: 9781680331165

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Houghton Mifflin Harcourt

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Question

Chapter 3.5, Problem 50E

To determine

To calculate: The length of the highway for which the cars are ale to receive the broadcast signal.

Expert Solution & Answer

Answer to Problem 50E

The required length of the highway is 56.9 miles.

Explanation of Solution

Given information:

The equation of the range of broadcast signal from a radio tower bounded by a circle: x2+y2=1620

The model equation of the straight highway: y=−13x+30

Formula used:

Distance formula:

The distance between two points (x1,y1) and (x2,y2) is (x1−x2)2+(y1−y2)2 .

Calculation:

The given equation of the range of broadcast signal from a radio tower bounded by a circle is x2+y2=1620 and the model equation of the straight highway is y=−13x+30 .

To find the length of the highway, solve the given equations using graph.

The graph of the given equations is shown below:

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 3.5, Problem 50E

From the graph, it is seen that the two equations intersect each other at the points (−18,36) and (36,18) .

To find the required length of the highway, use the distance formula (x12−x22)+(y12−y22) .

Substitute −18 for x1 , 36 for x2 , 36 for y1 and 18 for y2 in the above formula and simplify.

(x12−x22)+(y12−y22)=(−18−36)2+(36−18)2=(−54)2+(18)2=2916+324=56.9

Hence, the required length of the highway is 56.9 miles.

Chapter 3.5, Problem 49E

Chapter 3.5, Problem 51E

Chapter 3 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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