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MATH 16A WORKSHEET 12-
(1) The mass of a sample of radioactive material is described by the function f(t), which satisfies the differential equation
F'(t) = (ln 6)f(t)
and satisfies f(1) = 24. Find the formula for f(t). What is f(0)? At what time is f(t) = 144?
(2) Let f and g be two differentiable functions. Find an anti-derivative (in terms of f and g) for each of the following expressions.
(a) f'(x)g(x) + f(x)g'(x)
(b) f'(g(x)) · g'(x)
(c) ef(x)f'(x)
(d) f'(t)/f(t)
(e) 2g(x)g'(x)
(f) x4
(g) (1/x) + x + e3x
(3) Find all functions f(t) such that f'(t) = (-1/x2) + x2 and f(1) = 0.
Find the slope
How do you write a system of linear equations in two variables? ??Explain this in words and by using mathematical notation in an equation.
Jill's father bought Jill a car with the understanding that she would pay the car off in four years by making equal monthly installments. The car cost her father $5000 plus 9% sales tax. How much are the monthly payments Jill must make to her fath..
Prove the following statement using contraposition: If n, is a positive integer such that n(mod 3) = 2, then n is not a perfect square and find a solution (if it exists) to the linear diophantine equation 234x + 65y = 325.
Prove that there exist real numbers which are not algebraic.
Solve the system of equations by using the substitution method
A one story building is 140 ft by 200 ft. If a square patio with sides 24ft occupies the center of the building, how much area remains for offices?
To finance the $15,000 cost of their kitchen remodeling, the Chews will make equal payments at the end of each month for 36 months. They will pay interest at the rate of 7.2% compounded monthly. Find the amount of each payment.
Find the average of x2 + y2 over the triangle with vertices (0, 0), (1, 0), and (1, 1). Find the coordinates of the centroid of the region bounded by the curves y = 2x2 and y=12 - x2.
Let s(t) = 64t - 2t2 represent the height in feet of a paper clip that is shot straight up in the air with a rubber band where t is in seconds. At what time is the paper clip at its maximum height
jim writes down the numbers from 1 to 100. ben puts a red spot on all the even numbers and heen puts a blue spot on all
A used motorcycle can be purchased for $500 cash or on credit with a $200 down payment plus payments of $70 per month for 5 months. How much would be saved by paying cash?
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