You wish to fill a child's inflatable wading pool by using a garden hose. the hose you are using has an inside diameter of 3.0 cm and water travels though it at a speed of 1.5 m/s. if the pool is circular with an inside diameter of 3.1 m and you wish to fill it to a depth of 43 cm, determine the time (in minutes) required to fill the pool to this depth.

Asolid cylinder and a cylindrical shell have the same mass, same radius, and turn on frictionless, horizontal axles. the cylindrical shell has light-weight spokes connecting the shell to the axle. a rope is wrapped around each cylinder and tied to blocks of equal masses that are held the same height above the ground. both blocks are released simultaneously. the ropes do not slip. which block hits the ground first? or is it a tie?

The second largest public utility in the nation is the sole provider of electricity in 32 counties of southern florida. to meet the monthly demand for electricity in these counties, which is given by the inverse demand function p = 1,200 – 4q, the utility company has set up two electric generating facilities: q1 kilowatts are produced at facility 1, and q2 kilowatts are produced at facility 2 (so q = q1 + q2). the costs of producing electricity at each facility are given by c1(q1) = 8,000 + 6q12 and c2(q2) = 6,000 + 3q22, respectively. determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profit

Is the number of complete movements of a wave per second.