A car is traveling at a rate of 42 feet per second when the brakes are applied. The position function for the car is given by s(t) = -5.25t? + 42t, where s is measured in feet and t is measured in seconds. Use this function to complete the table. 2 3 1 4 5 78.75 s(t) 36.75 63 v(t) 31.50 21 10.50 a(t) -10.50 -10.50 -10.50 -10.50 -10.50 -10.50 Find the average velocity during each time interval. ft/sec for [0, 1] 36.75 ft/sec for [1, 2] 26.25 ft/sec for [2, 3] 15.75 ft/sec for [3, 4] 5.25

The amount of growth of plants in an ungrazed pasture is a function of the amount of plant biomass already present and the amount of rainfall.t For a pasture in the arid zone of Australia, the following formula gives an approximation of the growth. Y = -55.12 - 0.01535N - 0.00056N? + 3.946R Here Ris the amount of rainfall, in millimeters, over a 3-month period, Nis the plant biomass, in kilograms per hectare, at the beginning of that period, and Y is the growth, in kilograms per hectare, of the biomass over that period. (For comparison, 100 millimeters is about 3.9 inches, and 100 kilograms per hectare is about 89 pounds per acre.) Now we consider the amount of growth Y as a function of the amount of plant biomass N already present. (a) First we assume that the rainfall is 80 millimeters, so R = 80. (1) Find a formula for the growth Y as a function of the amount N of plant biomass already present. kg/ha (ii) Make a graph of Y versus N. Include biomass levels N from 0 to 800 kilograms…

The height of the falling sheet of paper, in feet from the ground, is given by s(t)=-1.5t+9 after t seconds. ​ When will the sheet of paper reach the ground? ​ a. after 3 seconds b. after 15 seconds c. after 9 seconds d. after 7.5 seconds e. after 6 seconds

A runner runs in a straight line and their distance traveled at time t is given by the formula d(t)=3t-0.05t2, where distance is in feet and t is in minutes.  Find the runners' average speed during the 2-minute interval beginning at time t=1. ANSWER:  ________ feet per minute  If rounding is necessary, round to two digits after the decimal.