Choose the one alternative that hex complete the statement or answers the questi

Question

Choose the one alternative that hex complete the statement or answers the question. A factory discharges pollutants into a large river at a rate that is estimated by a water quality control agency to be P(t) = t squareroot 1 + t^2 for 0 lessthanorequalto t lessthanorequalto 5, where P(t) is the total number of tons of pollutants discharged into the river after t years of operation. What quantity of pollutants will be discharged into the river from the end of the third year to the end of the fifth year? (Round to two decimal places.) 50.67 tons 32.67 tons 75.71 tons 33.65 tons Find the area between the graph of f(x) = x^2 - 4x and the x-axis over the interval -3 lessthanorequalto x lessthanorequalto 2. (Round answer to two decimal places) 5.33 21.67 32.33 27 The life expectancy (in years) of a certain type of computer chip is a continuous random variable with probability density function: f(x) = 4/(x + 4)^2 x greaterthanorequalto 0 0 otherwise Find the probability that a randomly selected chip will last from three to seven years. (Round answer to two decimal places) 0.36 0.33 0.21 0.57 The rate of flow of a continuous income stream (in thousands of dollars per day) is given by f(t) = 1/t + 1. Find the total income produced during the first ten days of operation. $2843.18 $58,874.14 $239.79 $2397.90

Explanation / Answer

9)

quatity of pollutents discharged from end of year 3 to year 5 is P=[3 to 5]t(1+t2) dt

P=[3 to 5]t(1+t2) dt

let us substitute 1+t2 =u =>2t dt =du =>tdt =du/2

t =3 =>u =1+32=10, t =5 =>u=1+52=26

P=[10 to 26]u  du/2

P=[10 to 26] (1/2)u  du

P=[10 to 26] (1/2)(2/3)u3/2

P=[10 to 26] (1/3)u3/2

P=(1/3)263/2 -(1/3)103/2

P=33.65tons

33.65tons of pollutents discharged from end of year 3 to year 5

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