(c) Compute the distance in AU between the points (x,0) = (1.24,0) and (1.24, 7)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.5: Polar Coordinates
Problem 97E
Related questions
Question
Do part c of this problem
!["Prolate spheroidal coordinates" are a set of coordinates for flat three dimensional Euclidean space. They
are:
I = Rsinh x sin 0 cos ,
y = Rsinh x sin 0 sin ø ,
z = Rcosh x cos 0,
where we fix R to have dimensions of length and take R = 1 AU (AU=astronomical unit). Consider the
plane y = dy = ¢ = 0.
(a) Find the transformation matrix dr"/az" relating the a, z coordinates to the x, 0 coordinates?
(b) Write the line element, ds in x,0 coordinates.
Give numerical answers for (a) and (b) at the point 0 = 2.1, x= 3.4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F942d8395-ce39-44af-9e4d-fbdcfc13f43e%2F2d194887-c8ce-4c5c-860c-89d6c88f6767%2Fnb0zsy8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:"Prolate spheroidal coordinates" are a set of coordinates for flat three dimensional Euclidean space. They
are:
I = Rsinh x sin 0 cos ,
y = Rsinh x sin 0 sin ø ,
z = Rcosh x cos 0,
where we fix R to have dimensions of length and take R = 1 AU (AU=astronomical unit). Consider the
plane y = dy = ¢ = 0.
(a) Find the transformation matrix dr"/az" relating the a, z coordinates to the x, 0 coordinates?
(b) Write the line element, ds in x,0 coordinates.
Give numerical answers for (a) and (b) at the point 0 = 2.1, x= 3.4.
![(c) Compute the distance in AU between the points (x,0) = (1.24,0) and (1.24, 7)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F942d8395-ce39-44af-9e4d-fbdcfc13f43e%2F2d194887-c8ce-4c5c-860c-89d6c88f6767%2F1jjfzpb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) Compute the distance in AU between the points (x,0) = (1.24,0) and (1.24, 7)
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