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Given that the acceleration vector is a(t) = (-9cos(-3t)) i + (-9sin(-3t)) j + (-2t) k , the initial velocity is v(0) = i + k , and the initial position vector is r(0) = i+j+k , compute:
A. The velocity vector
B. The position vector
Suppose you have two functions f and g and you use them to form a composite function. Under what conditions will they be the same? Include a numerical example in your answer.
Use the integrating capabilities of a graphing utility to approximate the surface area of that portion of the surface z=e^x that lies over the region in the xy-plane bounded by the graphs of y=0, y=x and x=1.
The expected future of Achworth, which presently has 2000 residents, can be approximated by the formula y=2000(e).02t , where t is the number of years in the future.
Determine if the following conforms to the intermediate value theorem. Clearly give the conditions and, if appropriate, find an appropriate value for c.
Suppose we want to determine the (binomial) probability (p) of getting 5 heads in 15 flips of a 2-sided coin. Using the Binomial table in the appendix of the text, what values of n, x, and p would we use to look up this probability, and what would..
Let p(x) = Ax^2 + Bx + C. Prove that for any interval [a,b], the value c guaranteed by the Mean Value Theorem is the midpoint of the interval.
Poisson Kernel and Harmonic Function, Let P_r(t)=R((1+z)/(1-z)), z=re^it be the Poisson kernel for the unit disc |z|
b. Calculate the number of days with a demand for 3 days. Calculate the probability of two bottles per day
Distributive Laws (I) Prove that A intersection (B union C) = (A intersection B) union (A intersection C)
Estimate all the stationary points
Alice's Restaurant has a total of 205 seats. The number of seats in the non-smoking section is 73 more than twice the number of seats in the smoking section. How many seats are in each section? Please show work.
What is the approximate probability that the blood test will be positive and so at least one person has the disease? Suppose that the blood test yields a positive result.
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