The rotational speed of a driven gear is inversely proportional to the number of teeth on the gear. You are replacing a 200 tooth gear which runs at 500 RPM with a gear that runs at 2,000 RPM. How many teeth does the new gear have?

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

The focal length of a relaxed human eye is approximately 1.7 cm. when we focus our eyes on a close up object, we can change the refractive power of the eye by about 16 diopters. (a) does the refractive power of our eyes increase or decrease by 16 diopters when we focus closely? explain. (b) calculate the focal length of the eye when we focus closely.

6–48 bananas are to be cooled from 24 to 138c at a rate of 215 kg/h by a refrigeration system. the power input to the refrigerator is 1.4 kw. determine the rate of cooling, in kj/ min, and the cop of the refrigerator. the specific heat of banana above freezing is 3.35 kj/kg·8c.