We need to determine which of the following curves pass through the point ( 1 , 4 ) .

Question

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Answer 1

Question

Chapter 12, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

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Answer 2

Question

Chapter 12, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

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Answer 3

Question

Chapter 12, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

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Answer 4

Question

Chapter 12, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

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Answer 5

Chapter 12, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Answer 6

Chapter 12, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Answer 7

Chapter 12, Problem 1CRE

To determine

We need to determine which of the following curves pass through the point $(1, 4)$ .

Answer 8

Expert Solution & Answer

Answer to Problem 1CRE

Solution:

The curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Given:

a. $c (t) = (t^{2}, t + 3)$

b. $c (t) = (t^{2}, t - 3)$ .

c. $c (t) = (t^{2}, 3 - t)$

d. $c (t) = (t - 3, t^{2})$

Calculation:

Assume $t = - 1, 1, 4$ , then

a. $c (- 1) = (1, 2) c (1) = (1, 4) c (4) = (16, 7)$

b. $c (- 1) = (1, - 4) c (1) = (1, - 2) c (4) = (16, 1)$

c. $c (- 1) = (1, 4) c (1) = (1, 2) c (4) = (16, - 1)$

d. $c (- 1) = (- 4, 1) c (1) = (- 2, 1) c (4) = (1, 16)$

Thus, we can see that the curves given at (a) and (c) pass through the point $(1, 4)$ .

Conclusion:

Hence, the curves $c (t) = (t^{2}, t + 3)$ and $c (t) = (t^{2}, 3 - t)$ pass through the point $(1, 4)$ .

Answer 12

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

We need to determine which of the following curves pass through the point ( 1 , 4 ) .

Videos

We need to determine which of the following curves pass through the point $(1, 4)$ .

Answer to Problem 1CRE

Explanation of Solution

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Chapter 12 Solutions

We need to determine which of the following curves pass through the point ( 1 , 4 ) .

Videos

We need to determine which of the following curves pass through the point (1,4).

Answer to Problem 1CRE

Explanation of Solution

Want to see more full solutions like this?

Chapter 12 Solutions

We need to determine which of the following curves pass through the point $(1, 4)$ .