A body was found in a room when the room's temperature was 66°F. Let f(t) denote the temperature of the body, t hours from the time of death. According to Newton's law of cooling, f satisfies a differential equation of the form y' = k(T-y). Answer parts (a) - (d) below. (a) Find T. T= 66 ° F (b) After several measurements of the body's temperature, it was determined that when the temperature of the body was 79 degrees, it was decreasing at a rate of 5 degrees per hour. Find k. k= .385 (Round to three decimal places as needed.) (c) Suppose that at the time of death, the body's temperature was about normal, say 98°F. Determine f(t). f(t) = 32 e - 385t, (Use integers or decimals for any numbers in the expression.) + 66 (d) When the body was discovered, its temperature was 86°F. Determine how long ago the person died. The person died hours before discovery. (Do not round until the final answer. Then round to three decimal places needed.)

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In a nursery, the reason for spreading a virus epidemic is equal to half of those who have not gotten sick yet. if 200 children are enrolled in the nursery, give a differential equation for the number of children infected N with respect to time t in days. Solve the differential equation to answer the following: If a sick  child started the epidemic, will they all be infected three days later?

Find ?′. a. ??^x = ? cos ? b. ln(3?) = 2? + 3?^2   thank you, will upvote