1. Suppose a dead body was found in a closed room of a house where the temperature was kept at a constant Tm = 70°F. Also assume that the dead body cools according to Newton's law of cooling given by the following ODE: dT dt = k (T − Tm), where T (t) is the body temperature at time t, Tm is the ambient room temperature, and k is a constant of proportionality. (a) At the time of discovery, the core temperature of the body was 80°F and one hour later the core temperature was measured to be 75°F. Let t = 0 be the time of death, and assume the body had a core temperature of 98.6°F at the time of death. How much time has passed since the person died? (Hint: rst solve the general ODE. Then use the given data to solve for the constant k in the ODE and the constant C in your general solution solution.) (b) Suppose the person had a fever of 102°F at the time of death. Now how much time do you determine has passed since death?

High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. because the number of slots remains relatively stable, some colleges reject more early applicants. suppose that for a recent admissions class, an ivy league college received 2851 applications for early admission. of this group, it admitted 1033 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. in the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. counting the students admitted early and the students admitted during the regular admission process, the total class size was 2375. let e, r, and d represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool.suppose a student applies for early admission. what is the probability that the student will be admitted for early admission or be deferred and later admitted during the regular admission process?