17. A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t) =-4.912 +2291 +234. a. From what height was the rocket launched? b. How high above sea level does the rocket reach its peak? c. Assuming the rocket will splash down in the ocean, at what time does splashdown occur? W18. The height of a ball thrown in the air is given by h(x) =-x2 + 6x +3, where x is 12 the horizontal distance in feet from the point at which the ball is thrown. a. How high is the ball when it was thrown? b. What is the maximum height of the ball? c. How far from the thrower does the ball strike the ground? 19. A farmer wishes to enclose two pens with fencing, as shown. If the farmer has 500 feet of fencing to work with, what dimensions will maximize the area enclosed?20. A hot air balloon takes off from the edge of a mountain lake. Impose a height above lake (ft) balloon coordinate system as pictured and assume that the path of the balloon follows the 200 balloon path graph of S (x) = --2x2 +4x. The land 2500 100 rises at a constant incline from the lake at the rate of 2 vertical feet for each 20 horizontal feet. lake 500 1000 (n) a. What is the maximum height of the balloon above water level? b. What is the maximum height of the balloon above ground level? c. Where does the balloon land on the ground?3 (*+5)(x - 1) II. (X)=- ( * - 4 ) 12. J X) =- 13. (3, 5), down, D = R, R = (-co, 5], x = 3 14. (-1, -2), up, D = R, R = [-2, 00), x = -1 15. 7tiv39 16. 2 + 2V6 4 17 a. 234m b. 2909.561 ft c. 47.735 seconds 18 a. 3 ft b. 111 ft c. 72.497 ft 19. 125 ft by 83- ft 3 20. a.200ft, b. 150ft, c. 875ft from the lake