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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Question
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Chapter 5.3, Problem 49E

(a)

To determine

How far above the ground will Domingo be when his seat reaches the top, if the radius of the Ferris wheel is 36 feet?

(a)

Expert Solution
Check Mark

Answer to Problem 49E

   76 feet off the ground

Explanation of Solution

Given information: Entertainment: Domingo decides to ride the Ferris wheel at the local carnival. When he gets into the seat that is at the bottom of the Ferris wheel, he is 4 feet above the ground.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.3, Problem 49E , additional homework tip 1

Calculation:

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.3, Problem 49E , additional homework tip 2

He will be two radii and four feet or,

   76 feet off the ground

(b)

To determine

How far above the ground is Domingo when the Ferris wheel stops, if the Ferris wheel rotates 300∘ counterclockwise and stops to let another passenger on the ride?

(b)

Expert Solution
Check Mark

Answer to Problem 49E

  22 feet off the ground

Explanation of Solution

Given information: Entertainment: Domingo decides to ride the Ferris wheel at the local carnival. When he gets into the seat that is at the bottom of the Ferris wheel, he is 4 feet above the ground.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.3, Problem 49E , additional homework tip 3

Calculation:

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.3, Problem 49E , additional homework tip 4

Study the sketch for a minute. After a 300∘ counterclockwise rotation he will be 30∘ below the x-axis. We need to find the opposite side of the triangle drawn. This will be how far in elevation he is below the x-axis which is 4 feet plus the radius above the ground

4 + 36 = 40

If we subtract the length of this opposite side from 40, it will give us his height above ground.

For a 30-60-90 triangle, the short side is always half the hypotenuse. The hypotenuse is a radius so it is 36 feet so the short side is 18 feet. So he is 18 feet below the x-axis which was 40 feet.

So he is 22 feet above the ground.

(c)

To determine

How far above the ground is Domingo when the Ferris wheel rotates 300∘ , if the radius of the Ferris wheel is only 30 feet?

(c)

Expert Solution
Check Mark

Answer to Problem 49E

  19 feet off the ground

Explanation of Solution

Given information: Entertainment: Domingo decides to ride the Ferris wheel at the local carnival. When he gets into the seat that is at the bottom of the Ferris wheel, he is 4 feet above the ground.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.3, Problem 49E , additional homework tip 5

Calculation:

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.3, Problem 49E , additional homework tip 6

Study the sketch for a minute. After a 300∘ counterclockwise rotation he will be 30∘ below the x-axis. We need to find the opposite side of the triangle drawn. This will be how far in elevation he is below the x-axis which is 4 feet plus the radius above the ground

4 + 33 = 34

If we subtract the length of this opposite side from 34, it will give us his height above ground.

For a 30-60-90 triangle, the short side is always half the hypotenuse. The hypotenuse is a radius so it is 30 feet so the short side is 15 feet. So he is 15 feet below the x-axis which was 34 feet.

So he is 19 feet above the ground.

(d)

To determine

To write:An expression for the distance from the ground to Domingo after the Ferris wheel rotates 300∘ , if the radius of the Ferris wheel is r.

(d)

Expert Solution
Check Mark

Answer to Problem 49E

  distance above ground=8+r2

Explanation of Solution

Given information: Entertainment: Domingo decides to ride the Ferris wheel at the local carnival. When he gets into the seat that is at the bottom of the Ferris wheel, he is 4 feet above the ground.

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.3, Problem 49E , additional homework tip 7

Calculation:

  Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.3, Problem 49E , additional homework tip 8

Study the sketch for a minute. After a 300∘ counterclockwise rotation he will be 30∘ below the x-axis. We need to find the opposite side of the triangle drawn. This will be how far in elevation he is below the x-axis which is 4 feet plus the radius above the ground

4 + r

If we subtract the length of this opposite side from 4 + r, it will give us his height above ground.

For a 30-60-90 triangle, the short side is always half the hypotenuse. The hypotenuse is a radius so it is r feet so the short side is r2 feet. So he is r2 feet below the x-axis which was 4 + r feet.

So he is 4+r−r2 feet above the ground.

  distance above ground=8+r2

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Chapter 5.3, Problem 48E
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Chapter 5.3, Problem 50E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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