3.7 Homework - Rates of Change (Homework)

1. [-/1 Points] DETAILS SCALCET9 3.7.010.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If a ball is thrown vertically upward with an initial velocity of 160 ft/s, then its height after t seconds is s = 160t - 16t . (Consider up to be the positive direction.) (a) What is the maximum height (in ft) reached by the ball? |ft (b) What is the velocity (in ft/s) of the ball when it is 384 ft above the ground on its way up? ft /s What is the velocity (in ft/s) of the ball when it is 384 ft above the ground on its way down? ft/s Need Help? Read It Watch It Master It 2. [-/1 Points] DETAILS SCALCET9 3.7.012. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A particle moves with position function s = t4 - 4+3 - 20t2 + 15t, t 2 0 (a) At what time does the particle have a velocity of 15 m/s? (Enter your answers as a comma-separated list.) t = (b) At what time is the acceleration 0? (Round your answer to two decimal places.) t = What is the significance of this? O At this time, the acceleration changes from negative to positive and the velocity attains its maximum value. O At this time, the acceleration changes from positive to negative and the velocity attains a value of zero. At this time, the acceleration changes from negative to positive and the velocity attains its minimum value. O At this time, the acceleration changes from positive to negative and the velocity attains its maximum value. At this time, the acceleration changes from positive to negative and the velocity attains its minimum value.3. [-/1 Points] DETAILS SCALCET9 3.7.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 4 to each of the following. (i) 4 to 5 (ii) 4 to 4.5 (iii) 4 to 4.1 (b) Find the instantaneous rate of change when r = 4. A'(4 ) = Need Help? Read It Watch It4. [-/1 Points] DETAILS SCALCET9 3.7.017. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A spherical balloon is being inflated. Find the rate (in ft2/ft) of increase of the surface area (S = 4x2) with respect to the radius r when r is each of the following. (a) 4 ft Ft 2 / ft (b) 7 ft ft2/ft (c) 8 ft ft 2 / ft Need Help? Read It Watch It 5. [-/1 Points] DETAILS SCALCET9 3.7.039. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The gas law for an ideal gas at absolute temperature 7 (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 9.0 atm and is increasing at a rate of 0.14 atm/min and V = 13 L and is decreasing at a rate of 0.16 L/min. Find the rate of change of T with respect to time (in K/min) at that instant if n = 10 mol. (Round your answer to four decimal places.) dT it K/min Need Help? Read It Watch It