BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.8, Problem 56E
To determine

To calculate: The x- and y- intercepts for the equation x2+y3x2y2=64 and the graph of the equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 56E , additional homework tip  1

Expert Solution

Answer to Problem 56E

The x-intercepts are 8 and 8andy-intercept is 4 .

Explanation of Solution

Given information:

The equation x2+y3x2y2=64 and the graph of the equation is provided below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 56E , additional homework tip  2

Formula used:

The x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

The y-intercepts are the points on y-axis where the graph of the equation intersects the y-axis.

Calculation:

Consider the provided equation x2+y3x2y2=64 and the graph of the equation is sketched below,

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1.8, Problem 56E , additional homework tip  3

Observe from the graph that the curve intersects x-axis at two points 8 and 8 also y-axis at one point that is 4 .

Recall that the x-intercepts are the points on x-axis where the graph of the equation intersects the x-axis.

Substitute y=0 in the equation x2+y3x2y2=64 ,

  x2+03x2(0)2=64x2=64x=±8

Therefore, x-intercepts are 8 and 8.

Recall that the y-intercepts are the points on x-axis where the graph of the equation intersects the y-axis.

Substitute x=0 in the equation x2+y3x2y2=64 ,

  02+y3(0)2y2=64y3=64y=4

Therefore, y-intercept is 4 .

Thus, the x-intercepts are 8 and 8andy-intercept is 4 .

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