(a) Answer The graph is an ellipse. Explanation Given: x 2 81 + y 2 36 = 1. Concept used: The graph of the equation can plot using Desmos graphing calculator. Calculation: Consider the cam in a punch press shaped like an ellipse, with the equation: x 2 81 + y 2 36 = 1. The camshaft goes through the focus on the positive axis. To graph the model of the cam as: Hence, the graph is an ellipse. (b) To determine To find: Theequation of the model when the camshaft is at the origin. Answer The equation of the translates the model is ( x − 45 ) 2 81 + y 2 36 = 1. Explanation Given: x 2 81 + y 2 36 = 1. Concept used: The equation of ellipse: x 2 a 2 + y 2 b 2 = 1. Calculation: the same picture in the other graphing calculator is: Hence, The equation of the translates the model is ( x − 45 ) 2 81 + y 2 36 = 1. (c) To determine To find: the equation of the model in part b when the cam is rotated to an upright position. Answer ( x − 45 ) 2 81 + y 2 36 = 1. Explanation Given: x 2 81 + y 2 36 = 1. Concept used: The equation of ellipse: x 2 a 2 + y 2 b 2 = 1. Calculation: The equation that translated the model so, that the cam shaft is at origin is: ( x − 45 ) 2 81 + y 2 36 = 1. Hence, the equation is ( x − 45 ) 2 81 + y 2 36 = 1.

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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Concept explainers

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 10.7, Problem 48E

(a)

To determine

To graph: the model of the given cam.

(a)

Expert Solution

Answer to Problem 48E

The graph is an ellipse.

Explanation of Solution

Given:

x281+y236=1.

Concept used:

The graph of the equation can plot using Desmos graphing calculator.

Calculation:

Consider the cam in a punch press shaped like an ellipse, with the equation:

x281+y236=1.

The camshaft goes through the focus on the positive axis.

To graph the model of the cam as:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.7, Problem 48E , additional homework tip 1

Hence, the graph is an ellipse.

(b)

To determine

To find: Theequation of the model when the camshaft is at the origin.

(b)

Expert Solution

Answer to Problem 48E

The equation of the translates the model is (x−45)281+y236=1.

Explanation of Solution

Given:

x281+y236=1.

Concept used:

The equation of ellipse:

x2a2+y2b2=1.

Calculation:

the same picture in the other graphing calculator is:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 10.7, Problem 48E , additional homework tip 2

Hence, The equation of the translates the model is (x−45)281+y236=1.

(c)

To determine

To find:the equation of the model in part b when the cam is rotated to an upright position.

(c)

Expert Solution

Answer to Problem 48E

(x−45)281+y236=1.

Explanation of Solution

Given:

x281+y236=1.

Concept used:

The equation of ellipse:

x2a2+y2b2=1.

Calculation:

The equation that translated the model so, that the cam shaft is at origin is:

(x−45)281+y236=1.

Hence, the equation is (x−45)281+y236=1.

Chapter 10.7, Problem 47E

Chapter 10.7, Problem 49E

Chapter 10 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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