Answered: b) Suppose that w = x2 + y² - z2 and_x… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.4: Multiple-angle Formulas

Problem 54E

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Question

2. please answer letters B and C. thank you

2) Find the following:
b) Suppose that w = x² + y² - z² and x = p sin cos 0, y = p sin o sin 0, z = p cos
дw
дw
find
and
using the Chain rule.
ap
20
c) Find
дz
əx
дz
Əy
and of ye* 5 sin 3z
=
3z.

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Show that cos jx is orthogonal to cos kx in C [ -π,π] for j ≠k,j, k >=1
a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.
Suppose that the position of one particle at time t is given by x1 = 3 sin(t), y1 = 2 cos(t), 0 ≤ t ≤ 2? and the position of a second particle is given by x2 = −3 + cos(t), y2 = 1 + sin(t), 0 ≤ t ≤ 2?. (a) Graph the paths of both particles. How many points of intersection are there? __ points of intersection (b) Are any of these points of intersection collision points? That is, are the particles ever at the same place at the same time? If so, find the collision points. (Enter your answers as a comma-separated list of ordered pairs of the form (x, y). If there are no collision points, enter DNE.) (x, y) =__ (c) Describe what happens if the path of the second particle is given by x2 = 3 + cos(t), y2 = 1 + sin(t), 0 ≤ t ≤ 2?. The circle is centered at (x, y) = __ There are _ intersection point(s), and there are _ collision point(s).
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