The temperature T (in °C) at any point in the region -10 ≤ x ≤ 10, −10 ≤ y ≤ 10 is given by the function T(x, y) = 100 – x² - y². (a) On a sheet of paper, sketch isothermal curves (curves of constant temperature) for T = 100° C, T = 75° C, T = 50° c, T = 25° C, and T = 0° C. (b) Suppose a heat-seeking bug is put down at each of the following points on the xy-plane. Thinking of the positive y direction as north and the positive x direction as east, pick the direction in which it should move to increase its temperature fastest. (i) (0, 5) the bug should go ? (ii) (-7.5, 0) the bug should go ? (iii) (-5, -5) the bug should go ? (Think about how your answers to these questions are related to the level curves through that point!)
The temperature T (in °C) at any point in the region -10 ≤ x ≤ 10, −10 ≤ y ≤ 10 is given by the function T(x, y) = 100 – x² - y². (a) On a sheet of paper, sketch isothermal curves (curves of constant temperature) for T = 100° C, T = 75° C, T = 50° c, T = 25° C, and T = 0° C. (b) Suppose a heat-seeking bug is put down at each of the following points on the xy-plane. Thinking of the positive y direction as north and the positive x direction as east, pick the direction in which it should move to increase its temperature fastest. (i) (0, 5) the bug should go ? (ii) (-7.5, 0) the bug should go ? (iii) (-5, -5) the bug should go ? (Think about how your answers to these questions are related to the level curves through that point!)
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:The temperature T (in °C) at any point in the region -10 ≤ x ≤ 10, −10 ≤ y ≤ 10 is given by
the function
T(x, y) = 100 – x² - y².
(a) On a sheet of paper, sketch isothermal curves (curves of constant temperature) for T = 100° C,
T = 75° C, T = 50° c, T = 25° C, and T = 0° C.
(b) Suppose a heat-seeking bug is put down at each of the following points on the xy-plane. Thinking of
the positive y direction as north and the positive x direction as east, pick the direction in which it should
move to increase its temperature fastest.
(i) (0, 5) the bug should go ?
(ii) (-7.5, 0) the bug should go ?
(iii) (-5, -5) the bug should go ?
(Think about how your answers to these questions are related to the level curves through that point!)
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