The temperature in degrees celsius on the surface of a metal plate is given by t(x, y), where x and y are measured in centimeters. find the direction from point p where the temperature increases most rapidly. t(x, y) = 45 − x2 − 2y2, p(1, −3)

Suppose there is a simple index of three stocks, stock abc, stock xyz, and stock qrs. stock abc opens on day 1 with 4000 shares at $3.15 per share. stock xyz opens on day 1 with 5000 shares at $4.30 per share. stock qrs opens on day 1 with 6000 shares at $4.60 per share. the price of stock abc on day 8 begins at $3.50. the price of stock xyz on day 8 begins at $3.90. stock qrs opens on day 8 with a price of $4.50 per share. assume that each stock has the same number of shares that it opened with on day 1. what is the rate of change of this simple index over 1 week?

What is the length of the segment joining the points at (4,5) and (6,-2) round to the nearest tenth if necessary

Find the number of liters in 12.8 gal of gasoline. round to the nearest hundredths