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The temperature at the point (x, y) on a metal plate is given by T(x, y) = x2 - y + 10. Let P = (1, 1).
a. Find T(P), and draw the level curve through P.
b. Find ∇T, and plot (∇T)(P), with tail located at P.
c. At P, along which direction (i.e. unit vector) does the temperature increase most rapidly? At what rate?
d. Find the rate of change of temperature at P in the direction of the origin.
e. Find the rate of change of temperature at P in the direction of i.
f. A bug at P moves with unit velocity at an angle of 60o with the direction of most rapid decrease of T. At what rate is T changing for the bug?
1) A real estate company sold 300 houses in 2010 and sold 375 houses in 2013. Assume the company's selling pattern follows a linear equation model, with x= the number of years since 2010, and y = the number of houses sold in the year correspon..
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Thirty days later, after regular training supplemented by vitamin E, they are tested again. The new results are listed below. Use the Wilcoxon signed-rank test to find the critical value to test the claim that the vitamin E supplement
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Chuck travels 117 miles in the same time that dana travels 105 miles. If chuck rate of travel is 4mph more than dana's, and they travel the same length of time, at what speed does chuck travel?
What is, at first approximation, the volume of the layer of water between the heights x and x + Δx? What is, in Joules, the work required to pump all the water from the reservoir to a height of 1 m above the reservoir?
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