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