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Reparametrize the curve with respect to arc length measured from the point wheret = 0 in the direction of increasing t. r(t) = (- 2+3t)i +(-1- 2t)j+ 4k 35 - 1 V13 a. r(s) = (-2 + b. r(s)=(-T13 35 25 V13 35 25 C. r(s) = (-2+ - 1 V13 d. r(s) = (-2 + 13 e. r(s) = (-2+V13s, – 1-/135,4) O c O a O d O b

Reparametrize the curve with respect to arc length measured from the point wheret = 0 in the direction of increasing t. r(t) = (- 2+3t)i +(-1- 2t)j+ 4k 35 - 1 V13 a. r(s) = (-2 + b. r(s)=(-T13 35 25 V13 35 25 C. r(s) = (-2+ - 1 V13 d. r(s) = (-2 + 13 e. r(s) = (-2+V13s, – 1-/135,4) O c O a O d O b

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Reparametrize the curve with respect to arc length measured from the point where \( t = 0 \) in the direction of increasing \( t \). **Given Function:** \[ \mathbf{r}(t) = (-2 + 3t)\mathbf{i} + (-1 - 2t)\mathbf{j} + 4\mathbf{k} \] **Options:** a. \[ \mathbf{r}(s) = \left\langle -2 + \frac{3s}{\sqrt{13}}, -1 - \frac{2s}{\sqrt{13}}, 0 \right\rangle \] b. \[ \mathbf{r}(s) = \left\langle -\frac{3s}{\sqrt{13}}, -\frac{2s}{\sqrt{13}}, 0 \right\rangle \] c. \[ \mathbf{r}(s) = \left\langle -2 + \frac{3s}{\sqrt{13}}, -1 - \frac{2s}{\sqrt{13}}, 4 \right\rangle \] d. \[ \mathbf{r}(s) = \left\langle -2 + \frac{s}{\sqrt{13}}, -1 - \frac{s}{\sqrt{13}}, 4 \right\rangle \] e. \[ \mathbf{r}(s) = \langle -2 + \sqrt{13}s, -1 - \sqrt{13}s, 4 \rangle \] **Answer Choices:** - o c - o a - o d - o b - o e
Transcribed Image Text:**Problem Statement:** Reparametrize the curve with respect to arc length measured from the point where \( t = 0 \) in the direction of increasing \( t \). **Given Function:** \[ \mathbf{r}(t) = (-2 + 3t)\mathbf{i} + (-1 - 2t)\mathbf{j} + 4\mathbf{k} \] **Options:** a. \[ \mathbf{r}(s) = \left\langle -2 + \frac{3s}{\sqrt{13}}, -1 - \frac{2s}{\sqrt{13}}, 0 \right\rangle \] b. \[ \mathbf{r}(s) = \left\langle -\frac{3s}{\sqrt{13}}, -\frac{2s}{\sqrt{13}}, 0 \right\rangle \] c. \[ \mathbf{r}(s) = \left\langle -2 + \frac{3s}{\sqrt{13}}, -1 - \frac{2s}{\sqrt{13}}, 4 \right\rangle \] d. \[ \mathbf{r}(s) = \left\langle -2 + \frac{s}{\sqrt{13}}, -1 - \frac{s}{\sqrt{13}}, 4 \right\rangle \] e. \[ \mathbf{r}(s) = \langle -2 + \sqrt{13}s, -1 - \sqrt{13}s, 4 \rangle \] **Answer Choices:** - o c - o a - o d - o b - o e
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