### Problem Statement: Find the speed over the path **r(t) = ⟨cosh(t), cosh(t), 9t⟩** at **t = 2**. *(Use decimal notation. Give your answer to four decimal places.)* ### Provided Answer: \( v(2) \approx 9.0001 \) ### Result: - **Status: Incorrect** ### Explanation: In attempting this problem, ensure that you calculate the speed correctly using the given path equation. The speed \( v(t) \) of a particle at time \( t \) for the path **r(t)** is given by the magnitude of the velocity vector **r'(t)**. The velocity vector **r'(t)** is the derivative of the path equation **r(t)** with respect to **t**. Calculate this by finding the derivatives of each component of **r(t)**, and then use the following formula to find the magnitude: \[ v(t) = \sqrt{(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2} \] Then, substitute **t = 2** into the resulting expression to find \( v(2) \) and ensure to round to four decimal places as instructed.
### Problem Statement: Find the speed over the path **r(t) = ⟨cosh(t), cosh(t), 9t⟩** at **t = 2**. *(Use decimal notation. Give your answer to four decimal places.)* ### Provided Answer: \( v(2) \approx 9.0001 \) ### Result: - **Status: Incorrect** ### Explanation: In attempting this problem, ensure that you calculate the speed correctly using the given path equation. The speed \( v(t) \) of a particle at time \( t \) for the path **r(t)** is given by the magnitude of the velocity vector **r'(t)**. The velocity vector **r'(t)** is the derivative of the path equation **r(t)** with respect to **t**. Calculate this by finding the derivatives of each component of **r(t)**, and then use the following formula to find the magnitude: \[ v(t) = \sqrt{(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2} \] Then, substitute **t = 2** into the resulting expression to find \( v(2) \) and ensure to round to four decimal places as instructed.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help because I gott this answer wrong
![### Problem Statement:
Find the speed over the path **r(t) = ⟨cosh(t), cosh(t), 9t⟩** at **t = 2**.
*(Use decimal notation. Give your answer to four decimal places.)*
### Provided Answer:
\( v(2) \approx 9.0001 \)
### Result:
- **Status: Incorrect**
### Explanation:
In attempting this problem, ensure that you calculate the speed correctly using the given path equation. The speed \( v(t) \) of a particle at time \( t \) for the path **r(t)** is given by the magnitude of the velocity vector **r'(t)**.
The velocity vector **r'(t)** is the derivative of the path equation **r(t)** with respect to **t**. Calculate this by finding the derivatives of each component of **r(t)**, and then use the following formula to find the magnitude:
\[ v(t) = \sqrt{(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2} \]
Then, substitute **t = 2** into the resulting expression to find \( v(2) \) and ensure to round to four decimal places as instructed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe815a6c0-dcfd-4fc5-aa4e-03e2f1f5f601%2F834f92c5-9d06-40af-afec-307c523ee648%2F2ji1w3l_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Find the speed over the path **r(t) = ⟨cosh(t), cosh(t), 9t⟩** at **t = 2**.
*(Use decimal notation. Give your answer to four decimal places.)*
### Provided Answer:
\( v(2) \approx 9.0001 \)
### Result:
- **Status: Incorrect**
### Explanation:
In attempting this problem, ensure that you calculate the speed correctly using the given path equation. The speed \( v(t) \) of a particle at time \( t \) for the path **r(t)** is given by the magnitude of the velocity vector **r'(t)**.
The velocity vector **r'(t)** is the derivative of the path equation **r(t)** with respect to **t**. Calculate this by finding the derivatives of each component of **r(t)**, and then use the following formula to find the magnitude:
\[ v(t) = \sqrt{(dx/dt)^2 + (dy/dt)^2 + (dz/dt)^2} \]
Then, substitute **t = 2** into the resulting expression to find \( v(2) \) and ensure to round to four decimal places as instructed.
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