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Problem 17. (5 points) Section VII. Crawling Ant Problem code (print legibly at top of answer page): 7CA-148525 An ant is crawling along the floor along a predetermined path. At time, $t$, the $(x, y)$ position of the ant is given by: $(x(t), y(t)) = ((t - 1)^2, 1 - t^2)$ The temperature of the floor varies throughout the room. At location $(x, y)$, the temperature, $T$ is: $T(x, y) = x^2 + 2y^2$ (Note: throughout the question, distances are measured in meters, time is measured in seconds, and temperatures are measured in degrees Celsius). (a) What is the ant's position at time 0? (b) At time 0, how quickly is the temperature of the floor underneath the ant changing? (Remember to include units in your answer.) (c) Suppose now that the ant does not need to follow the predetermined path. From the position that you found in part (a), in which direction should the ant travel if it wishes to decrease the temperature around it most efficiently? State your answer as a vector.

          Problem 17.
(5 points) Section VII. Crawling Ant
Problem code (print legibly at top of answer page): 7CA-148525
An ant is crawling along the floor along a predetermined path. At time, $t$, the $(x, y)$ position of the ant is given by:
$(x(t), y(t)) = ((t - 1)^2, 1 - t^2)$
The temperature of the floor varies throughout the room. At location $(x, y)$, the temperature, $T$ is:
$T(x, y) = x^2 + 2y^2$
(Note: throughout the question, distances are measured in meters, time is measured in seconds, and temperatures are measured in degrees Celsius).
(a) What is the ant's position at time 0?
(b) At time 0, how quickly is the temperature of the floor underneath the ant changing? (Remember to include units in your answer.)
(c) Suppose now that the ant does not need to follow the predetermined path. From the position that you found in part (a), in which direction should the ant travel if it
wishes to decrease the temperature around it most efficiently? State your answer as a vector.

Problem 17.
(5 points) Section VII. Crawling Ant
Problem code (print legibly at top of answer page): 7CA-148525
An ant is crawling along the floor along a predetermined path. At time, t, the (x, y) position of the ant is given by:
(x(t), y(t)) = ((t - 1)^2, 1 - t^2)
The temperature of the floor varies throughout the room. At location (x, y), the temperature, T is:
T(x, y) = x^2 + 2y^2
(Note: throughout the question, distances are measured in meters, time is measured in seconds, and temperatures are measured in degrees Celsius).
(a) What is the ant's position at time 0?
(b) At time 0, how quickly is the temperature of the floor underneath the ant changing? (Remember to include units in your answer.)
(c) Suppose now that the ant does not need to follow the predetermined path. From the position that you found in part (a), in which direction should the ant travel if it
wishes to decrease the temperature around it most efficiently? State your answer as a vector.

Added by Jennifer L.

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