(sin(t), cos(2), 8t) intersects the z-axis, and if it does, determine where. (Use symbolic notation and fractions where needed. Give your answer as the coordinates of a point in the form (*,*,*). Enter NO SOLUTION if the curve does not intersect the z-axis. Give your answer for 32 ≤ z ≤ 48.) Determine whether the space curve given by r(t) point coordinates: =
(sin(t), cos(2), 8t) intersects the z-axis, and if it does, determine where. (Use symbolic notation and fractions where needed. Give your answer as the coordinates of a point in the form (*,*,*). Enter NO SOLUTION if the curve does not intersect the z-axis. Give your answer for 32 ≤ z ≤ 48.) Determine whether the space curve given by r(t) point coordinates: =
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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![**Problem Statement:**
Determine whether the space curve given by \( \mathbf{r}(t) = \langle \sin(t), \cos\left(\frac{1}{2}\right), 8t \rangle \) intersects the z-axis, and if it does, determine where.
(Use symbolic notation and fractions where needed. Give your answer as the coordinates of a point in the form \((*,*,*)\). Enter NO SOLUTION if the curve does not intersect the z-axis. Give your answer for \(32\pi \leq z \leq 48\pi\).)
**Answer Box:**
point coordinates: [ __________________ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd370dc10-a80b-4ff7-aff7-eb45807dd9a9%2F8340763a-72f8-47da-92a4-d4f8fa0a1f66%2Fhzsv6q_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine whether the space curve given by \( \mathbf{r}(t) = \langle \sin(t), \cos\left(\frac{1}{2}\right), 8t \rangle \) intersects the z-axis, and if it does, determine where.
(Use symbolic notation and fractions where needed. Give your answer as the coordinates of a point in the form \((*,*,*)\). Enter NO SOLUTION if the curve does not intersect the z-axis. Give your answer for \(32\pi \leq z \leq 48\pi\).)
**Answer Box:**
point coordinates: [ __________________ ]
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