Suppose That the Temperature T of Any Point (X, Y)is $T ( x , y ) = 100 - x ^ { 2 } - y ^ { 2 }$

question 21

Essay

Suppose that the temperature T of any point (x, y)is given by $T ( x , y ) = 100 - x ^ { 2 } - y ^ { 2 }$ .
Sketch isothermal curves (i.e.contours)for T = 100, T = 75, T = 50 and T = 0.Be sure to label each contour.
What does the graph of T(x, y)look like if it is sliced by the plane x = 4?

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Definitions:

Feedback Element

A component in a control system that provides real-time input based on the output, helping to adjust the system's behavior.

Deadband

A range within which an input signal can vary without initiating a response or change in the output, used to prevent frequent or unnecessary adjustments.

Control Action

A process in which a control system responds to changes in measured variables by adjusting outputs to maintain desired conditions.