An office worker uses an immersion heater to warm 250 g of water in a light, covered, insulated cup from 20°c to 100°c in 4.00 minutes. the heater is a nichrome resistance wire connected to a 120-v power supply. assume the wire is at 100°c throughout the 4.00-min time interval. specify a diameter and a length the wire can have. can it be made from less than 0.5 cm3 of nichrome?

The temperature at a point (x, y) is t(x, y), measured in degrees celsius. a bug crawls so that its position after t seconds is given by x = 6 + t , y = 8 + 1 3 t, where x and y are measured in centimeters. the temperature function satisfies tx(3, 9) = 5 and ty(3, 9) = 4. how fast is the temperature rising on the bug's path after 3 seconds? (round your answer to two decimal places.)

Abasketball star covers 2.65 m horizontally in a jump to dunk the ball. his motion through space can be modeled precisely as that of a particle at his center of mass. his center of mass is at elevation 1.02 m when he leaves the floor. it reaches a maximum height of 1.90 m above the floor and is at elevation 0.910 m when he touches down again. (a) determine his time of flight (his "hang time"). (b) determine his horizontal velocity at the instant of takeoff. (c) determine his vertical velocity at the instant of takeoff. (d) determine his takeoff angle. (e) for comparison, determine the hang time of a whitetail deer making a jump with center-of-mass elevations yi = 1.20 m, ymax = 2.45 m, and yf = 0.750 m.

Match each type of lever with the correct diagram. 1. first-class 2. third-class 3. second-class