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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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Question

Chapter 10.6, Problem 43E

To determine

A rectangular equation to model the shape of the clock.

Expert Solution

Explanation of Solution

Given information:

The radius of the clock is 6 inches.

Calculations:

The shape of a clock 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 clock starts at origin, therefore

(a,b)=(0,0)

Thus the equation becomes,

x2+y2=r2

The radius of the clock is 6 inches. .

Thus the equation becomes,

x2+y2=62

To determine

The parametric equations describing the motion of the tip as it moves from 12 o’clock noon to 12 o’clock noon.

Expert Solution

Explanation of Solution

Given information:

The radius of the clock is 6 inches.

Calculations:

The shape of a clock 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 clock starts at origin, therefore

(a,b)=(0,0)

Thus the equation becomes,

x2+y2=r2

The radius of the clock is 6 inches. .

Thus the equation becomes,

x2+y2=62

Now the parametric equation of the circle is

let,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 tip of the point is

x=6sint.y=6cost0≤t≤4π

To determine

The graph of the motion of the clock.

Expert Solution

Explanation of Solution

The shape of a clock 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 clock starts at origin, therefore

(a,b)=(0,0)

Thus the equation becomes,

x2+y2=r2

The radius of the clock is 6 inches. .

Thus the equation becomes,

x2+y2=62

Now the parametric equation of the circle is

let,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 tip of the point is

x=6sint.y=6cost0≤t≤4π

The graph of the equation is shown below.

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.6, Problem 43E

Chapter 10.6, Problem 42E

Chapter 10.6, Problem 44E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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