EXAMPLE 5 Use graphs of circles EARTHQUAKES The epicenter of an earthquake is the point on Earth's surface directly above the earthquake's origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Use the seismograph readings from locations A, B, and C to find the epicenter of an earthquake. • The epicenter is 7 miles away from A(-2, 2.5). • The epicenter is 4 miles away from B(4, 6). • The epicenter is 5 miles away from C(3, –2.5). Solution The set of all points equidistant from a given point is a circle, so the epicenter is located on each of the following circles. 8 OA with center (-2, 2.5) and radius 7 4 OB with center (4, 6) and radius 4 A OC with center (3, -2.5) and radius 5 -4 To find the epicenter, graph the circles on a graph where units are measured in miles. Find the point of intersection of all three circles. The epicenter is at about (5, 2). Guided Practice for Example #5 Why are three seismographs needed to locate an earthquake's epicenter? (Analyze Example #5 to help your thinking.)
EXAMPLE 5 Use graphs of circles EARTHQUAKES The epicenter of an earthquake is the point on Earth's surface directly above the earthquake's origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Use the seismograph readings from locations A, B, and C to find the epicenter of an earthquake. • The epicenter is 7 miles away from A(-2, 2.5). • The epicenter is 4 miles away from B(4, 6). • The epicenter is 5 miles away from C(3, –2.5). Solution The set of all points equidistant from a given point is a circle, so the epicenter is located on each of the following circles. 8 OA with center (-2, 2.5) and radius 7 4 OB with center (4, 6) and radius 4 A OC with center (3, -2.5) and radius 5 -4 To find the epicenter, graph the circles on a graph where units are measured in miles. Find the point of intersection of all three circles. The epicenter is at about (5, 2). Guided Practice for Example #5 Why are three seismographs needed to locate an earthquake's epicenter? (Analyze Example #5 to help your thinking.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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