For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on the given interval. r(t) = (3t³, -t³, 5t³), for 0≤t≤7 The speed associated with the trajectory is. (Type an exact answer, using radicals as needed.)
For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on the given interval. r(t) = (3t³, -t³, 5t³), for 0≤t≤7 The speed associated with the trajectory is. (Type an exact answer, using radicals as needed.)
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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![For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on the given interval.
\( \mathbf{r}(t) = \langle 3t^3, -t^3, 5t^3 \rangle \), for \( 0 \leq t \leq 7 \)
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The speed associated with the trajectory is [ ].
(Type an exact answer, using radicals as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c944127-f965-40a6-9c0b-c6a92e7a1d8e%2F1922d6b3-2f4e-450a-a5c4-9d2e235dea5c%2Fioqe6di_processed.png&w=3840&q=75)
Transcribed Image Text:For the following trajectory, find the speed associated with the trajectory and then find the length of the trajectory on the given interval.
\( \mathbf{r}(t) = \langle 3t^3, -t^3, 5t^3 \rangle \), for \( 0 \leq t \leq 7 \)
---
The speed associated with the trajectory is [ ].
(Type an exact answer, using radicals as needed.)
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