Determine the isotherms (curves of constant temperature T) of the temperature fields in the plane given by the following scalar functions. Sketch some isotherms. 1. T = xy - 3. T = ²x² 5. T y/(x² + y²) 2. T 4x - 3y 4. T = x/(x² + 1.²) 6. T = x² - y² + 8y

Determine the isotherms (curves of constant temperature T) of the temperature fields in the plane given by the following scalar functions. Sketch some isotherms. 1. T = xy - 3. T = ²x² 5. T y/(x² + y²) 2. T 4x - 3y 4. T = x/(x² + 1.²) 6. T = x² - y² + 8y

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 21E

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Question

quadratic surfaces and spherical, cylindrical coordinate systems solve the questions.

11-6 SCALAR FIELDS
Determine the isotherms (curves of constant temperature
T) of the temperature fields in the plane given by the
following scalar functions. Sketch some isotherms.
2. T = 4x - 3y
4. T = x/(x² +1.²)
6. T = x² - y² + 8y
1. T = xy
3.
5. T = y/(x² + 1.²)
T=²12
-

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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