A thin plate made of iron is located in the xy-plane. The temperature 7 in degrees Celsius at a point P(x, y) is inversely proportional to the square of its distance from the origin. (a) Express T as a function of x and y. (Use k for your constant of proportionality.) T(x, y) = °C (b) Using the temperature function, determine the proportionality constant if the temperature at point P(1, 2) is 60°C. k= Use this constant to determine the temperature in degrees Celsius at point Q(3, 4). °℃ (c) Find the level curves for T = 50°C. Describe what the level curve represents. O hyperbola O parabola O non-circle ellipse O circle O none of the above Find the level curves for T = 100°C. Describe what the level curve represents. O hyperbola O parabola O non-circle ellipse O circle O none of the above
A thin plate made of iron is located in the xy-plane. The temperature 7 in degrees Celsius at a point P(x, y) is inversely proportional to the square of its distance from the origin. (a) Express T as a function of x and y. (Use k for your constant of proportionality.) T(x, y) = °C (b) Using the temperature function, determine the proportionality constant if the temperature at point P(1, 2) is 60°C. k= Use this constant to determine the temperature in degrees Celsius at point Q(3, 4). °℃ (c) Find the level curves for T = 50°C. Describe what the level curve represents. O hyperbola O parabola O non-circle ellipse O circle O none of the above Find the level curves for T = 100°C. Describe what the level curve represents. O hyperbola O parabola O non-circle ellipse O circle O none of the above
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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Transcribed Image Text:A thin plate made of iron is located in the xy-plane. The temperature T in degrees Celsius at a point P(x, y) is inversely proportional to the square of its distance from the origin.
(a) Express T as a function of x and y. (Use k for your constant of proportionality.)
T(x, y) =
°C
(b) Using the temperature function, determine the proportionality constant if the temperature at point P(1, 2) is 60°C.
k=
Use this constant to determine the temperature in degrees Celsius at point Q(3, 4).
°C
(c) Find the level curves for T = 50°C.
Describe what the level curve represents.
O hyperbola
O parabola
O non-circle ellipse
O circle
O none of the above
Find the level curves for T = 100°C.
Describe what the level curve represents.
O hyperbola
O parabola
O non-circle ellipse
O circle
O none of the above
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