Suppose you are given the points P = (4,3) and Q = (-1,5). (a) Find parametric equations r(t) and y(t) such that the set of points (z(t), y(t)) form the line segment from P to Q, and P = (x(0), y(0)) and Q = (z(1), y(1)). (b) How would your answer to (1) change if instead you wanted P = (x(0), y(0)) and Q = (z(2), y(2))? What about P = (x(-1), y(-1)) and Q = (x(0), y(0))? (c) Describe what happens if you instead replace t with t2 in your equations from (1), in terms of the way the path is traced. Please use complete sentences. (d) Describe what happens if you instead replace t with 1-t in your equations from (1), in terms of the way the path is traced. Please use complete sentences.
Suppose you are given the points P = (4,3) and Q = (-1,5). (a) Find parametric equations r(t) and y(t) such that the set of points (z(t), y(t)) form the line segment from P to Q, and P = (x(0), y(0)) and Q = (z(1), y(1)). (b) How would your answer to (1) change if instead you wanted P = (x(0), y(0)) and Q = (z(2), y(2))? What about P = (x(-1), y(-1)) and Q = (x(0), y(0))? (c) Describe what happens if you instead replace t with t2 in your equations from (1), in terms of the way the path is traced. Please use complete sentences. (d) Describe what happens if you instead replace t with 1-t in your equations from (1), in terms of the way the path is traced. Please use complete sentences.
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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Transcribed Image Text:(1) Suppose you are given the points P = (4,3) and Q = (-1,5).
(a) Find parametric equations r(t) and y(t) such that the set of points (x(t), y(t))
form the line segment from P to Q, and P = (x(0), y(0)) and Q = (z(1), y(1)).
(b) How would your answer to (1) change if instead you wanted P
and Q = (x(2), y(2))? What about P = (x(-1), y(-1)) and Q = (x(0), y(0))?
(z (0), y(0))
=
(c) Describe what happens if you instead replace t with t2 in your equations from
(1), in terms of the way the path is traced. Please use complete sentences.
(d) Describe what happens if you instead replace t with 1-t in your equations from
(1), in terms of the way the path is traced. Please use complete sentences.
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