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Exercise. A curve C is described by the vector-valued function p(t) = (t, 4 – 21,² +2). Exercise. Find all t-values where p and p' are orthogonal. List your answers in order from least to greatest: t = ?, t= t =

Exercise. A curve C is described by the vector-valued function p(t) = (t, 4 – 21,² +2). Exercise. Find all t-values where p and p' are orthogonal. List your answers in order from least to greatest: t = ?, t= t =

Advanced Engineering Mathematics
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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1. Exercise. A curve C is described by the vector-valued function p(t) = (t²,4 – 2t², t² + 2). Exercise. Find all t-values where p and p' are orthogonal. List your answers in order from least to greatest: t = ? t = ? t = 2. Exercise. Let C be a curve drawn by: p(t) = (2 cos(t), –2 sin(t)) Find the length of the curve drawn by p as t runs from 0 to T: length = 3. Exercise. The starting position of a particle is given by Р(0) — (5, —2) Suppose the initial velocity is given by v(0) = (1,2) and the acceleration is given by a(t) = (2,3). Find: • The velocity function: v(t) = • The speed function: s(t) = • The position function: p(t) = 4. Exercise. The position vector for a particle is described by the vector-valued function: t r(t) = 4' for t > 0. Find (positive) a so the curve uses arc length as a parameter. a =
Transcribed Image Text:1. Exercise. A curve C is described by the vector-valued function p(t) = (t²,4 – 2t², t² + 2). Exercise. Find all t-values where p and p' are orthogonal. List your answers in order from least to greatest: t = ? t = ? t = 2. Exercise. Let C be a curve drawn by: p(t) = (2 cos(t), –2 sin(t)) Find the length of the curve drawn by p as t runs from 0 to T: length = 3. Exercise. The starting position of a particle is given by Р(0) — (5, —2) Suppose the initial velocity is given by v(0) = (1,2) and the acceleration is given by a(t) = (2,3). Find: • The velocity function: v(t) = • The speed function: s(t) = • The position function: p(t) = 4. Exercise. The position vector for a particle is described by the vector-valued function: t r(t) = 4' for t > 0. Find (positive) a so the curve uses arc length as a parameter. a =
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