a. Answer t 0 1 2 3 4 x 0 1 2 3 2 y 2 1 0 − 1 − 2 Explanation Given: The parametric equations x = t and y = 2 − t . Calculation: When t = 0 , x = 0 = 0 , y = 2 − 0 = 2 . When t = 1 , x = 1 = 1 , y = 2 − 1 = 1 . When t = 2 , x = 2 , y = 2 − 2 = 0 . When t = 3 , x = 3 , y = 2 − 3 = − 1 . When t = 4 , x = 4 = 2 , y = 2 − 4 = − 2 . So, the table becomes as shown below. t 0 1 2 3 4 x 0 1 2 3 2 y 2 1 0 − 1 − 2 b. To determine To plot the points ( x , y ) generated in part (a) and graph the parametric equation. Also, describe the orientation of the curve. Explanation Given: The parametric equations x = t and y = 2 − t . Plot: From part (a), the table is given below. t 0 1 2 3 4 x 0 1 2 3 2 y 2 1 0 − 1 − 2 The points become ( 0 , 2 ) , ( 1 , 1 ) , ( 2 , 0 ) , ( 3 , − 1 ) , ( 2 , − 2 ) . Now, plot these points on the coordinate axes as shown below. Now, join the points to graph the parametric equations. The curve is moving towards negative infinity as the value of x increases. c. To determine To graph the parametric equations by using graphing utility. Explanation Given: The parametric equations x = t and y = 2 − t . Graph: The graph of the parametric equations using graphing utility can be given as shown below. The curve is moving towards negative infinity as the value of x increases. d. To determine To find the rectangular equation by eliminating the parameter t . Then, sketch its graph and describe how the graph differs from the graphs in part (b) and (c). Answer y = 2 − x 2 , x ≥ 0 Explanation Given: The parametric equations x = t and y = 2 − t . Calculation: x = t ⇒ t = x 2 . Then, y = 2 − t ⇒ y = 2 − x 2 . So, the rectangular equation for the given parametric equations is y = 2 − x 2 , x ≥ 0 . The graph of this equation can be given as shown below. The curve is moving towards negative infinity as the value of x increases. The graph is same as obtained in part (b) and (c).

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 9.4, Problem 9E

To determine

To create a table of $x−$ and $y−$ values using the $t=0,1,2,3,4$ for the given parametric equations.

Expert Solution

Answer to Problem 9E

$t01234x01232y210−1−2$

Explanation of Solution

Given: The parametric equations $x=t$ and $y=2−t$ .

Calculation:

When $t=0$ , $x=0=0,y=2−0=2$ .

When $t=1$ , $x=1=1,y=2−1=1$ .

When $t=2$ , $x=2,y=2−2=0$ .

When $t=3$ , $x=3,y=2−3=−1$ .

When $t=4$ , $x=4=2,y=2−4=−2$ .

So, the table becomes as shown below.

$t01234x01232y210−1−2$

To determine

To plot the points $(x,y)$ generated in part (a) and graph the parametric equation. Also, describe the orientation of the curve.

Expert Solution

Explanation of Solution

Given: The parametric equations $x=t$ and $y=2−t$ .

Plot:

From part (a), the table is given below.

$t01234x01232y210−1−2$

The points become $(0,2),(1,1),(2,0),(3,−1),(2,−2)$ .

Now, plot these points on the coordinate axes as shown below.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 9.4, Problem 9E , additional homework tip 1

Now, join the points to graph the parametric equations.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 9.4, Problem 9E , additional homework tip 2

The curve is moving towards negative infinity as the value of x increases.

To determine

To graph the parametric equations by using graphing utility.

Expert Solution

Explanation of Solution

Given: The parametric equations $x=t$ and $y=2−t$ .

Graph:

The graph of the parametric equations using graphing utility can be given as shown below.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 9.4, Problem 9E , additional homework tip 3

The curve is moving towards negative infinity as the value of x increases.

To determine

To find the rectangular equation by eliminating the parameter $t$ . Then, sketch its graph and describe how the graph differs from the graphs in part (b) and (c).

Expert Solution

Answer to Problem 9E

$y=2−x2,x≥0$

Explanation of Solution

Given: The parametric equations $x=t$ and $y=2−t$ .

Calculation:

$x=t⇒t=x2$ .

Then, $y=2−t⇒y=2−x2$ .

So, the rectangular equation for the given parametric equations is $y=2−x2,x≥0$ .

The graph of this equation can be given as shown below.

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 9.4, Problem 9E , additional homework tip 4

The curve is moving towards negative infinity as the value of x increases.

The graph is same as obtained in part (b) and (c).

Chapter 9.4, Problem 8E

Chapter 9.4, Problem 10E

Chapter 9 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

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To create a table of x − and y − values using the t = 0 , 1 , 2 , 3 , 4 for the given parametric equations.

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Answer to Problem 9E

Explanation of Solution

To plot the points (x,y)<m:math><m:mrow><m:mrow><m:mo>(</m:mo><m:mrow><m:mi>x</m:mi><m:mo>,</m:mo><m:mi>y</m:mi></m:mrow><m:mo>)</m:mo></m:mrow></m:mrow></m:math> generated in part (a) and graph the parametric equation. Also, describe the orientation of the curve.

Explanation of Solution

To graph the parametric equations by using graphing utility.

Explanation of Solution

To find the rectangular equation by eliminating the parameter t<m:math><m:mi>t</m:mi></m:math> . Then, sketch its graph and describe how the graph differs from the graphs in part (b) and (c).

Answer to Problem 9E

Explanation of Solution

Chapter 9 Solutions

To plot the points $(x,y)$ generated in part (a) and graph the parametric equation. Also, describe the orientation of the curve.

To find the rectangular equation by eliminating the parameter $t$ . Then, sketch its graph and describe how the graph differs from the graphs in part (b) and (c).