A pot of piping hot stew has been removed from the stove and left to cool. The relationship between the elapsed time, m, in minutes, since the stew was removed from the stove, and the temperature of the stew, T(m), measured in °C, is modeled by the following function. T(m) = 20+ 50 - 10–0.04m How many minutes will it take for the stew to cool to a temperature of 30°C ? Round your answer, if necessary, to the nearest hundredth. minutes Show Calculator

An object is thrown down from a height of 208 feet with a velocity of 72 feet per second. The objects distance from the ground, ss , at time tt seconds after being thrown down is given by the function  s(t)=−16t2−72t+208 How many seconds after being thrown down will the object hit the ground?

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = – 4.9t + 325t + 346. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round to the nearest tenth.) The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? (Round to the nearest tenth.) The rocket peaks at meters above sea-level.

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…