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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Question

Chapter 10.4, Problem 14CFU

(a)

To determine

To write: The equation of the hyperbola centered the origin on which the plane is located.

(a)

Expert Solution

Answer to Problem 14CFU

x2625−y21875=1

Explanation of Solution

Given information: Aviation: Airplanes are equipped with signal devices to alert rescuers to their position. Suppose a downed plane sends out radio pulses that are detected by two receiving stations A and B . the stations are located 130 miles apart along a stretch of I-40 with A due west of B . the two stations are able to determine that the plane is 50 miles farther from station B than from station A .

Calculation:

Sketching out a drawing, the important piece of information is not only that the stations (foci) are 130 miles apart ( c = 65), but that the distance to the ship is 50 more for station B .

The difference between the distance from A to the plane and B to the ship is 50.

So,

50=2aa=25

Centered at the origin gives us:

x2625−y2b2=1

Since: a2+b2=c2→b2=502−252=1875

This gives us finally:

x2625−y21875=1

(b)

To determine

To graph: The equation, indicating on which branch of the hyperbola the plane is located.

(b)

Expert Solution

Answer to Problem 14CFU

The graph

Explanation of Solution

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.4, Problem 14CFU , additional homework tip 1

(c)

To determine

To find: The exact coordinates of its position, if the pilot estimates that the plane is 6 miles from I-40.

(c)

Expert Solution

Answer to Problem 14CFU

Plane’s coordinates: (−713,6)

Explanation of Solution

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.4, Problem 14CFU , additional homework tip 2

If the plane is 6 miles from the axis (I-40), then y = 6 at that point.

Plug in 6 for y and solve for x .

x2625−361875=1

x2625=637625→x2=637→x=±713

Since we are in quadrant 2, we’ll keep the negative.

Plane’s coordinates: (−713,6)

Chapter 10.4, Problem 13CFU

Chapter 10.4, Problem 15E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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