A mass weighing 20 pounds stretches a spring 6 inches. The mass is initially released from rest from a point 4 inches below the equilibrium position.

(a) Find the position x of the mass at the times t = π/12, π/8, π/6, π/4, and 9π/32 s. (Use g = 32 ft/s2 for the acceleration due to gravity.) x(π/12) = ft x(π/8) = ft x(π/6) = ft x(π/4) = ft x(9π/32) = ft
(b) What is the velocity of the mass when t = 3π/16 s? ft/s In which direction is the mass heading at this instant? upward downward
(c) At what times does the mass pass through the equilibrium position? , n = 0, 1, 2,

Enter numbers to write 0.000328 0.000328 in scientific notation. 1 1 0.000328=3.28 × 0 . 000328 = 3 . 28 × =3.28×10 = 3 . 28 × 10

An optical inspection system is used to distinguish among different part types. the probability of a correct classification of any part is 0.92. suppose that three parts are inspected and that the classifications are independent. let the random variable x denote the number of parts that are correctly classified. determine the probability mass function of x. round your answers to four decimal places (e. g. 98.7654). x f(x) 0 1 2 3

Titus works at a hotel. part of his job is to keep the complimentary pitcher of water at least half full and always with ice. when he starts his shift, the water level shows 4 gallons, or 128 cups of water. as the shift progresses, he records the level of the water every 10 minutes. after 2 hours, he uses a regression calculator to compute an equation for the decrease in water. his equation is w –0.414t + 129.549, where t is the number of minutes and w is the level of water. according to the equation, after about how many minutes would the water level be less than or equal to 64 cups?