The displacement of a particle on a vibrating string is given by the equation s(t) = 2 + 1 5 sin(2πt) where s is measured in centimeters and t in seconds. Find the velocity of the particle after t seconds. v(t) = cm/s

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Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?

Find the maximum value of p= 4x + 5y subject to the following constraints :