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1. A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at the shallow end, and 9 ft deep at is deepest point. A cross-section is shown in the figure. If the pool is being filled at a rate of 0.5 ft3/min, how fast is the water level rising when the depth at the deepest point is 5 ft?
2. The top of a ladder slides down a vertical wall at a rate of 0.125 m/s. At the moment when the bottom of the ladder is 5 m from the wall, it slides away from the wall at a rate of 0.3 m/s. How long is the ladder?
3. A plane flying with a constant speed of 330 km/h passes over a ground radar station at an altitude of 3 km and climbs at an angle of 30 degree. At what rate is the distance from the plane to the radar station increasing a minute later?
the engine of a sports car rotates at 5000 revolutions per minute. calculate the angular speed of the engine in radians persecond, given 2TT radians = 1 revolution
Suppose that during the past year the following is Jim's distribution of home sales. If one assumes that this a typical distribution for Jim's monthly sales, which salary plan should Jim select?
AppleBerry (AB) is a high-tech manufacturer of digital products. Recently, it has been very successful at manufacturing a portable MP3 player, the Curvy. The Curvy comes in two forms: one with 32 GB of storage and one with 64 GB of storage. In doing ..
suppose that a connected planar simple graph with edges and vertices contain no simple circuit of length 4 or less.
A company is planning to re-equip one of its major production plants and one of two types of machine, the Zeta and the Precision II, is to be purchased. The prices of the two machines are very similar so the choice of machine is to be based on two..
Maximize Z = 5 X1 + 6 X1 X2 + 2 X2Subject to: 3 X1 + 2 X2 ≥ 6X1 + X2 ≤ 8X1, X2 ≥ 0
Find the distance between the points with polar coordinates (6, π/3) and (8, 2π/3).
Assuming k ≤ n, we want to distribute k balls among n bins such that each bin may at most one ball?
The sum of the cubes of three consecutive positive integers is always a multiple of 9. Factorize x2n +1 - 1 as a product of real linear and quadratic polynomials.
When b=2 show that the differential equation in the above figure has a solution of period k. Show that det A(t)= 1 for all t then use this to show that the floquet multipliers are roots of x2-bx+1=0 when b is the trace of A(k).
Find the number of units x that produce a maximum revinue R. Find the number of unites x that produce the minimum average cost per unit C.
The spot rate of the British pound to the dollar is 1.68 ($/£). The 180 day forward rate is $1.71, what is the annualized forward premium?
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