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Consider the following linear mapping from C[-pi,pi] into itself:
L(f)=integral from -pi to pi of G(x),h(y),f(y)dy for any function f(x) in C[-pi,pi]. Here G(x), H(x) are given continuous functions. Find a function f such that L*f=lambda*f for some lambda and find the value of lambda. This is a generalization of the notion for particular case G(x)=cosx,H(x)=x^2. Hint Look for f(x)=aG(s). Explain why this assumption is reasonable.
Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?
What would you do if supply exceeded demand? What if demand exceeded supply?
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 500 liters in the pond to start.
What is the probability that a sale will be made to a contact who already owns a policy?
Determine the Fourier series for this function and find the period, frequency and angular frequency of the waveform
Conditions for Linear transformation. This chapter starts as follows rotations about the origin and all reflections in lines through the origin can be expressed as functions with rules of the form
What is the probability that the six numbers chosen by the player match all 6 numbers in the state's sample? What is the probability that 5 of the 6 numbers chosen by the player match all 6 numbers in the state's sample?
Law of sines.
Find an equation in the form y=ms +b (where possible) for each line. Solve each system of equation. Let z be the parameter.
Consider 4 couples (4 husbands and their wives) stand in random order in a line. What is the probability that no husband is lined up directly
Service station cars arive randomly at a rate of 1 car every 30 min. the average time to change oil on a car is 20 min. both the time between arrivals and service time can be modeled using the negative exponential Poisson distribution.
Objective questions based on regression.
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