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A campus has 5000 students. After the Christmas break one student returns carrying a flu virus. Assume that the rate at which the virus spreads is proportional to the number of infected students P(t), but also to the number 5000?P(t) of students not yet infected. Here time is measured in days.
(a) Our assumptions mean that the function P(t) satisfies the initial value problem, dP dt = kP(5000? P), P(0) = 1 where the parameter k is initially unknown. Find the solution of this IVP by solving the DE as a separable equation.
(b) After seven days 50 students are infected. Use this to determine the parameter k .
(c) How long does it take before 10 percent of the students are infected?
Heat transfer through the walls and roof is estimated to be 5 40 kJ/hr per degree temperature difference between the inside and outside. a. If the outside temperature in the winter is - 5 C, what power required to drive the heat pum p (kJ/hr
A pump has the following pump curve is pumping at a rate of 5000gpm. Calculate (a) the total head the pump is pumping against. (b) brake horsepower required to drive the pump.
For a cantilever beam 20 ft long under a uniformly distributed load of 500 pounds/foot, calculate the deflection v and the slope dv/dx as a function of x by integrating differential equations.
Fixed GPS broadcast stations enable users to make differential measurements to other points whose positions are needed. In the US, there are two such networks two such networks of broadcast stations, name one (blank)
An excursion train, travelling at 80ft/s, encounters a rain shower. The point A lies directly 8ft. beneath the lip of an overhang in the observation car. The raindrops can be assumed to be falling at a constant speed of 40ft/s.
Find the center of gravity of the given composite body when the specific weight of brass is .306 lb/in^3 and the specific weight of aluminum is .101 lb/in^3
A new machine will cost $25,000. The machine is expected to last 4 years and has no salvage value. If the interest rate is 12%, determine the return and the risk associated with the purchase. The estimated annual savings and its probability
A slender 9 lb rod can rotate in a vertical plane about a pivot at b. a spring of constant k=30 lb/ft and of unstretched length is 6in is attached to the rod as shown.
1. introductionthe groundwater level has risen and now is present in the cut. answer the following questions. show
Design a hollow steel shaft with an inside diameter 1/3 that of the outside diameter. The shaft transmits 200 kW at a speed of 20 Hz. The allowable shearing stress is 55 MPa, and the allowable angle of twist is 1 degree per meter of length.
Collar A is dropped 30 inches onto collar B, which is resting on a spring of constant k= 4 lb/in. Assuming perfectly plastic impact (coefficient of restitution e=0), determine the maximum deflection of collar B.
A proposed square footing carrying a total load of 500 kips is to be constructed on a uniform thick deposit of dense cohesionless soil. The soil's unit weight is 135 pcf, and its angle of internal friction is 38 degrees.
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