Answer the question plz

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yvnatfuh

Mathematics

Fisher College

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Just show me the process of solving the question step by step. 12 questions total. Each of them needs the procedure.

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You Must Show Appropriate Work to Receive Full Credit Due at the beginning of class on Tuesday Dec 10th 1. (10 pts) Find the absolute maximum and absolute minimum value of the function 5 f(x) = 2x -- on the interval (1,5] х 2. (16 pts) The owner of the Rancho Grande has 3600 yd of fencing to enclose a rectangular piece of grazing land situated along the straight portion of a river. No fencing is required along the river. The ranch owner wants the dimensions (in yd) corresponding to the largest area he can enclose. A) Make a diagram including sides labeled with variables. B) State the function of a single variable that requires optimization. C) State the domain of the function as an interval, (0, A). D) Use the second derivative test to prove why you are finding a maximum. E) Give the dimensions. 3. (4 pts) Find the solution to the equation 62x-3 = 1 36 4. (6 pts) A function has the form f(t) = Aekt. Find the specific formula if we have that f(0) = 40 and f(3) = 210. 5. (6 pts) Use the laws of logarithms to expand and simplify x? (x4 – 3x) In e 5x 6. (9 pts) The concentration of a drug in an organ at any time x (in seconds) is given by C(x) = 0.21 - 0.19e-.035x measured in milligrams per cubic centimeter (mg/cm3). Round to three decimals. A) Find the concentration and the rate of change in concentration at time x = 3. B) Find the concentration and the rate of change in concentration at time x = 9. 7. (5 pts) Find the derivative of the function g(x) = (2x + e6x)5 8. (7 pts) Find the second derivative of f(x) = ln(5x - 2) 9. (8 pts) The average life for an American woman from 1907 through 2007 is given by w(t) = 49.9 + 17.11n(+/20) on [1,60] where t = 1 means the beginning of 1907. Discuss the increasing/decreasing aspects of this function on the interval. 10. (8 pts) For y = (in x)x2 - 2-4 use logarithmic differentiation to find y'. 11. (6 pts) Find the effective rate for each nominal rate: a) 4% per year compounded quarterly b) 3.8% annual compounded continuously. 12. (7 pts) Skeletal remains had lost 79% of the C-14 they originally contained. Using the half-life of 5730 years, determine the approximate age rounding to the nearest whole year.
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