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 10.6, Problem 40E

a.

To determine

A rectangular equation to model the shape of the paddle wheel.

a.

Expert Solution
Check Mark

Explanation of Solution

Given information:

A river boat paddle wheel has diameter of 12feet and at full speed makes one clockwise revolution in 2 seconds.

Calculations:

The shape of a river boat paddle wheel is a circle.

The rectangular equation of a circle is,

   (x−a) 2 + (y−b) 2 = r 2 Where,(a,b) shows the coordiantes of the center and r shows the radius.

Let the boat starts at origin, therefore

  (a,b)=(0,0)

Thus the equation becomes,

  x2+y2=r2

Diameter of the paddle wheel is 12feet

So radius of the paddle wheel is 122feet=6feet.

Thus the equation becomes,

  x2+y2=62

b.

To determine

The parametric equations describing the position of a point A on the paddlewheel for any given time t.

b.

Expert Solution
Check Mark

Explanation of Solution

Given information:

A river boat paddle wheel has diameter of 12feet and at full speed makes one clockwise revolution in 2 seconds.

Calculations:

The shape of a river boat paddle wheel is a circle.

The rectangular equation of a circle is,

   (x−a) 2 + (y−b) 2 = r 2 Where,(a,b) shows the coordiantes of the center and r shows the radius.

Let the boat starts at origin, therefore

  (a,b)=(0,0)

Thus the equation becomes,

  x2+y2=r2

Diameter of the paddle wheel is 12feet

So radius of the paddle wheel is 122feet=6feet.

Thus the equation becomes,

  x2+y2=62

Now the parametric equation of the circle is

  x2+y2=62let,x=6sint.y=6cost.Therefore,x2+y2 (6sint) 2 + (6cost) 2 = 6 2 ( (sint) 2 + (cost) 2 )=62 Thus LFS=RHS.

Thus the parametric equation of the point A is

  x=6sint.y=6cost.

c.

To determine

The position of a point A on the paddlewheel after one minute.

c.

Expert Solution
Check Mark

Explanation of Solution

Given information:

A river boat paddle wheel has diameter of 12feet and at full speed makes one clockwise revolution in 2 seconds.

Calculations:

Here,

At full speed the paddlewheel makes one clockwise revolution in 2 seconds.

Therefore in one minute it will make,

  602revolution=30revolution.

Therefore the paddlewheel will make 30 clockwise revolutions in one minute.

Therefore the position of the point A on the paddlewheel after one minute will be on the same position as in the stating time.

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Chapter 10.6, Problem 39E
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Chapter 10.6, Problem 41E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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