Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 10.8, Problem 40E

a.

To determine

Write the second degree system of equations.

a.

Expert Solution
Check Mark

Answer to Problem 40E

  x2+y2=2500x2+(y−30)2=1600(x−35)2+(y−18)2=169

Explanation of Solution

Given information:

Seismograph reading indicate that the epicenter of the earthquake is 50 km from the first station, 40 km from the second station 13 km from the third station. First station is at origin, the second at (0,30) and third station at (35,18)

Calculation:

Consider (x,y) be the epicenter of the map, First station is at origin (0,0) , 50 km from the epicenter,

The equation will be,

  (x−0)2+(y−0)2=50x2+y2=502x2+y2=2500

This is equation of circle at (0,0) origin and radius 50 .

Now, second station is at (0,30) , 40 km from the epicenter

The equation will be,

  (x−0)2+(y−30)2=40x2+(y−30)2=402x2+(y−30)2=1600

This is equation of circle at (0,30) and radius 40 .

Now, third station is at (35,18) , 13 km from the epicenter

The equation will be,

  (x−35)2+(y−18)2=13(x−35)2+(y−18)2=169

This is equation of circle at (35,18) and radius 13 .

Hence, the systems of second degree equations are,

  x2+y2=2500x2+(y−30)2=1600(x−35)2+(y−18)2=169

b.

To determine

Graph the system of equations.

b.

Expert Solution
Check Mark

Answer to Problem 40E

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.8, Problem 40E , additional homework tip 1

Explanation of Solution

Given information:

Seismograph reading indicates that the epicenter of the earthquake is 50 km from the first station, 40 km from the second station 13 km from the third station. First station is at origin, the second at (0,30) and third station at (35,18)

Calculation:

Graph the system of equations,

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.8, Problem 40E , additional homework tip 2

c.

To determine

Find the location of epicenter by solving the equations.

c.

Expert Solution
Check Mark

Answer to Problem 40E

  (40,30)

Explanation of Solution

Given information:

Seismograph reading indicates that the epicenter of the earthquake is 50 km from the first station, 40 km from the second station 13 km from the third station. First station is at origin, the second at (0,30) and third station at (35,18)

Calculation:

Consider equation,

  x2+y2=2500x2+(y−30)2=1600(x−35)2+(y−18)2=169

Now solve the equations,

  x2+y2=2500x2=2500−y2put  x2=2500−y2  in  x2+(y−30)2=1600(2500−y2)+(y−30)2=16002500−y2+y2−60y+900=16002500−60y+900=160060y=1800y=30so  x2=2500−y2  will  bex2=2500−302x2=2500−900x2=1600x=±40

The solution from two equations is (40,30)  and (−40,30)

  put  (40,30)  in  (x−35)2+(y−18)2=169(40−35)2+(30−18)2=16925+144=169169=169LHS=RHSsatisfy  the  equationput  (−40,30)  in  (x−35)2+(y−18)2=169(−40−35)2+(30−18)2=169−752+122=1695625+144=169LHS=RHSDoes  not  satisfy,The  epicenter is  (40,30)

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Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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