The expression T(x,y) should have been T(x,y,z); it is clearly a function of three variables.
The temperature in degrees at a point (x,y,z) is given by T(x,y) = 2x2y2 + z2y . A sensor is moving in space with the equations of motion: x = t2 - 2t, y = 2 sin(πt), and z = 2t, where time is measured in seconds.
How fast is the temperature changing in the sensor at time t = 1?
The height of a circular cone is changing at 1 inches per second (in/sec) and the diameter of its base is changing at -7/10 in/sec. What is the rate of change of its volume when the height 100 inches and the diameter is 50 inches?