Atruck has a minimum speed of 14 mph in high gear. when traveling x mph, the truck burns diesel fuel at the rate of 0.0065413(1024x+x)gal/mile assuming that the truck can not be driven over 56 mph and that diesel fuel costs $1.69 a gallon, find the following. (a) the steady speed that will minimize the cost of the fuel for a 580 mile trip. x= 31366.4 (b) the steady speed that will minimize the total cost of a 580 mile trip if the driver is paid $18 an hour. x= (c) the steady speed that will minimize the total cost of a 360 mile trip if the driver is paid $28 an hour.

Which term best describes the phrase “something that happens”?

Suppose that two tanks, 1 and 2, each with a large opening at the top, contain different liquids. a small hole is made in the side of each tank at the same depth 1.57 m below the liquid surface, but the hole in tank 2 has 2.49 times the cross-sectional area of the hole in tank 1. (a) what is the ratio ρ1/ρ2 of the densities of the liquids if the mass flow rate is the same for the two holes? (b) what is the ratio rv1/rv2 of the volume flow rates from the two tanks? (c) at one instant, the liquid in tank 1 is 14.9 cm above the hole. if the tanks are to have equal volume flow rates, what height above the hole must the liquid in tank 2 be just then?

Aregion of space in which a measurable gravitational force is indicated by the force exerted on a test mass is called