The temperature at a point (x, y, z) is given by t(x, y, z) = 100e−x2 − 5y2 − 7z2 where t is measured in °c and x, y, z in meters. (a) find the rate of change of temperature at the point p(2, −1, 3) in the direction towards the point (5, −4, 5). °c/m (b) in which direction does the temperature increase fastest at p? (c) find the maximum rate of increase at p.

Aball tossed vertically upward from the ground next to a building passes the bottom of a window 1.8 s after being tossed and passes the top of the window 0.20 s later. the window is 2.0 m high from top to bottom. what was the ball's initial velocity? the unit vector j^ is directed upward. how far is the bottom of the window from the launch position? how high does the ball rise above the launch position?

What is the magnitude of the resultant vector round your answer to the nearest tenth

The human body stores chemical energy from digested food. some of the chemical energy is converted into mechanical energy when the body moves. which statement best supported by this information