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 6ECP: The resistance of a copper wire carrying an electrical current is directly proportional to its...
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F396d222c-d143-43b2-a82f-45edb3cd4d1d%2F4b1e9b79-db73-435f-a248-e0d446ae60ea%2Fokhglf_processed.png&w=3840&q=75)
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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