(2 points extra credit) J.B is on his nightly run, and his speed is a constant 3 m/s. The ground is shaped like the grap

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2 Points Extra Credit J B Is On His Nightly Run And His Speed Is A Constant 3 M S The Ground Is Shaped Like The Grap 1 (93.29 KiB) Viewed 10 times

(2 points extra credit) J.B is on his nightly run, and his speed is a constant 3 m/s. The ground is shaped like the graph of z = 0.1x³ – 0.3x + 0.2y² + 1, where x, y, and z are measured in meters. J.B. doesn't like hills, so he is running along the contour z = 2, in a direction such that his velocity in the x-direction is positive. As J.B. is running, the moon comes out from behind a cloud, and moonlight shines on the ground with intensity function I(x, y) = x² + 3x + y² millilux. When J.B. is at (x, y) = (2,2), find the rate (with respect to time) at which the inten- sity of the moonlight shining on him is changing. Hints: Start by calling his path r(t) = (x(t), y(t)), and let to be the time when he is at (2, 2). Use the chain rule! Also recall that the speed of an object with velocity (tt) dy) dx 2 2 is √ (d)² + (dz) ². dt dt