Answer all the boxes and highlight the answers no ai response or ai generator sec 4.10: Problem 5We wish to solve11u = Upp +UT+= 0rr2in polar coordinates for the region 1 < r < 5. (It is the region between the circles of radius 1and 5.) As the boundary conditions Suppose that u=9 if r = 1, and u=6 if r = 5.To solve this problem assume that u does not depend on 0, that is, u is a function of ralone. Write down the Laplacian in this case and solve.u =help (formulas)

Solution:The problem involves solving the Laplace equation in polar coordinates for u(r) in the…

Answered: sec 4.10: Problem 5 We wish to solve 1…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question 11
Find B and T for the space curve below. r(t) = (6 sin 4t)i + (6 cos 4t)j + 7tk T = 24 cos 4t 25 54¹) ₁- (24 24 sin 4t 25 N = ( sin 4t)i - (cos 4t)j B 11 K = 7 25 96 625 7 41] ₁ + (・ ( - 12/15 cos 4t 7 ²9₁ + 2/5 ² -k 24 141] ₁ + (−265) K sin 4t T= (Type an integer or a simplified fraction.)
8.) Represent the line Segment from P to Q by a vedor Valued function (P correspands to t=0 Q Corresponds to T=1 ) P(-3,9,-9), Q(-1,7,5) IT 20 nic (1) r(t) = %3D line Segment from P to Q by Set of parametric equations ( Enter Comma-Separated list ) t.
3 Just as in 4| from last HW set, consider the polar coordinate chart for R2: V: (0, 00) × (0, 27) → R²; (r, 0) → (r cos 0, r sin 0). Write {dr (a), do(a)} in terms of {dx(a), dy(a)}. Suppose that a cotangent vector p e TÄR² is written as (a) (b) p = Pxdx(a) + pydy(a) = prdr (a) + pod0(a). Find (px, Py) in terms of (pr. pe) using the result from (a). (с. * Find an expression for the cotangent lift T *V-(r, 0, pr, Pe). Consider a Hamiltonian L: T*R? → R that can be written in the Cartesian coordinates as (d) m k Н(х, у, рх. Ру) :%3D (p + p3)+ 2 x² + y² with some constants m,k > 0. Find an expression for the Hamiltonian in terms of the polar coordinates (r, 0) and their associated momentum components (pr, pe) by computing H oT*¥-(r, 0, pr. pe).
Show that the path given by r(t) = (cos t,cos(2t), sint) intersects the xy-plane infinitely many times, but the underlying space curve intersects the xy-plane only twice.
Question 12
Question 9
Convert to polar coordinates and evaluate
1szs 9-x² - y² and x' +y <1 Sketch the surface H.
Question 10
Question 8
1. Find a parametrization of the line segment L from -2 to -2 + 2i. 2. Find the image of L under the mapping w = -iz?. 3. Draw L and its image. q3-123191.pdf

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