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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?
Knowing that the magnitude of P is 35 N, determine by trigonometry (a) the required angle a if the resultant R of the two forces applied to the support is to be horizontal, (b) the corresponding magnitude of R.
Some hypothetical alloy is composed of 12.5 wt% of metal A and 87.5 wt% of metal B. If the densities of metals A and B are 4.27 and 6.35 g/cm3, respectively, whereas their respective atomic weights are
Water flows down a wide and shallow rectangular channel of concrete (n=0.015) laid on a slope of 0.004. find the depth and the rate of flow in SI units for critical conditons in the channel.
Colette Lake has a surface area of 103 ha and a mean depth of 8 m. The pH of the water is 7.6. The lake receives surface water from a lake upstream, rainfall, and diffuse groundwater input. Atmospheric inorganic N deposition is insignificant.
What are the major policy aspects of the Clean Water Act? What is the history and statutory basis for federal regulation of wetlands? What are the national permits? What are the origin and significance of the no net loss policy?
When a net amount of work is done on a closed system undergoing an INTERNALLY REVERSIBLE process, a net heat transfer of energy from the system also occurs.
What are the bearings of the sides CD,DE,EA, and AB if the side CB has a bearing S 20° 44' 36" W, point A is westerly of B and interior angles in each apex are as follows: A = 95° 14' 23"; E=81° 16' 54"
The velocity of a body is given by v(t) = 2t+t3. The body starts from rest at time t = 0 at position s(0) = (2,-10). What are the position and acceleration of the body as functions of time At what time, t, does the body cross the X-axis
assessment task critical review the decision making of a failed major constructionproperty project within the uk in the
A consolidated-drained triaxial shear test on a normally consolidated clay yielded a drained friction angle of 28 degrees. If the confining pressure during the test was 15 psi, what was the major principal stress at failure.
A. List of all possible resistance combinations that can be formed with these springs. indicate drawings and calculation of each unique configuration. B. How many unique combinations can be formed
A flow of 28 m3s-1 occurs in an earth-lined canal having a base width of 3 m, side slopes of 1(vertical) to 2 (horizontal) and the Manning's n value of 0.022. Calculate the critical depth and critical slope.
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