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 10.6, Problem 40E
a.
To determine
A rectangular equation to model the shape of the paddle wheel.
a.
Expert Solution
Explanation of Solution
Given information:
A river boat paddle wheel has diameter of
Calculations:
The shape of a river boat paddle wheel is a circle.
The rectangular equation of a circle is,
Let the boat starts at origin, therefore
Thus the equation becomes,
Diameter of the paddle wheel is
So radius of the paddle wheel is
Thus the equation becomes,
b.
To determine
The parametric equations describing the position of a point A on the paddlewheel for any given time t.
b.
Expert Solution
Explanation of Solution
Given information:
A river boat paddle wheel has diameter of
Calculations:
The shape of a river boat paddle wheel is a circle.
The rectangular equation of a circle is,
Let the boat starts at origin, therefore
Thus the equation becomes,
Diameter of the paddle wheel is
So radius of the paddle wheel is
Thus the equation becomes,
Now the parametric equation of the circle is
Thus the parametric equation of the point A is
c.
To determine
The position of a point A on the paddlewheel after one minute.
c.
Expert Solution
Explanation of Solution
Given information:
A river boat paddle wheel has diameter of
Calculations:
Here,
At full speed the paddlewheel makes one clockwise revolution in 2 seconds.
Therefore in one minute it will make,
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.
Chapter 10 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Ch. 10.1 - Prob. 1CFUCh. 10.1 - Prob. 2CFUCh. 10.1 - Prob. 3CFUCh. 10.1 - Prob. 4CFUCh. 10.1 - Prob. 5CFUCh. 10.1 - Prob. 6CFUCh. 10.1 - Prob. 7CFUCh. 10.1 - Prob. 8CFUCh. 10.1 - Prob. 9CFUCh. 10.1 - Prob. 10CFU
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