1. Find two sets of parametric equations for the given rectangular equation. y = 9x + 5 O x = t, y = 9t + 5; x = t, y=. + 5 9 O x = t, y = 9t + 5; X = y=t+5 O x = t, y = 9t + 5; x = 9t, y = t + 5 O x = 9t, y = t + 5; X = 9 ,y=t+52. Solve the problem. The position of a projectile fired with an initial velocity Vo feet per second and at an angle 0 to the horizontal at the end of t seconds is given by the parametric equations * = (0 cos 8)t, y = (vo sin 0)t- 1of-. Suppose the initial velocity is 9 feet per second. Obtain the rectangular equation of the trajectory and identify the curve. y= 16 x2 81 cos2 0 - + (tan 0)x; parabola O y = _ 16 x2 81 cos2 0 + (cot 0)x; hyperbola O y = _ 16 x 2 + (cot 0)x; parabola 81 cos2 0 O y = - 16 x2 81 cos2 0 + (tan 0)x; ellipse3. Tell whether the given rational expression is proper or improper. x3 - 11x + 28 x2-9x +20 (O Improper O Proper 4. Find the parametric equations that define the curve shown. (-2, DI 10 6 8 10 X -10 x = t - 2, y = - t + 1; 0 sts2 O x = t - 2, y = - t + 1; Ost=3 x = -t - 2, y = -t + 1; Osts2 x = -t - 2, y= t + 1; Osts35. Set up the linear programming problem. A steel company produces two types of machine dies, part A and part B. The company makes a $3.90 profit on each part A that it produces and a $6:99 profit on each part B that it produces. Let = te number of part A produced in a week and =the number of part B produced in a week. Write the objective function that describes the total weekly profit. O z=3x+6y O z=9(x+y) (O z=3(x-6)+6(y-3) O Z=6x+3y \f\f8. Graph the solution set of the system of inequalities or indicate that the system has no solution. [-2x + y > 10 1- 2x + y-18 y 10 \f15. Graph the solution set of the system of inequalities or indicate that the system has no solution. {9}(*}'29 Sx+y=z0 \f17. Solve the problem. Ron throws a ball straight up with an initial speed of 70 feet per second from a height of 6 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball? O x=0,y=-162+701+6 4.288 sec, 2.188 sec, 5.969 feet O x=0,y=-162+70t+6 4,459 sec, 2,188 sec, 82.563 feet O x=0,y=162+70t+6 8.575 sec, 2.188 sec, 504.351 feet O x=0,y=-162+70t+6 8.918 sec, 2.188 sec, 76.563 feet 18. Set up the linear programming problem. Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 5 hours to make a hat and 2 hours to make an afghan, and she has no more than 37 hours available. She has material for no more than 11 items, and she wants to make at least two afghans. Let x = the number of hats she makes and y = the number of afghans she makes. Write a system of inequalities that describes these constraints. O sx+2y=37 x+ys11 y=z2 O 2x+5ys37 Xx+y=11 X=2 O sx+2ys37 x+ys=11 Xz2 O sx+2y=37 x+ys11 y=2 19. Set up the linear programming problem. The liquid portion of a diet is to provide at least 300 calories, 36 units of vitamin A, and 90 units of vitamin C daily. A cup of dietary drink X provides 60 calories, 12 units of vitamin A, and 10 units of vitamin C. A cup of dietary drink Y provides 60 calories, 6 units of vitamin A, and 30 units of vitamin C. Set up a system of linear inequalities that describes the minimum daily requirements for calories and vitamins, Let X =number of cups of dietary drink X, and y = number of cups of dietary drink Y. Write all the constraints as a system of linear inequalities. C> 60x + 60y = 300 12x+ 67236 10x + 30y = 90 xz20 y=0 60x + 60y = 300 12x+ 6y >36 10x + 30y 290 60x + 60y =300 12x +6y =36 10x + 30y =90 60x + 60y > 300 12x+ 6y> 36 10x + 30y > 90 x>0 y>0 20. Tell whether the given rational expression is proper or improper. x2-11x+28 (x2-9x +18)(x +3) O Improper (O Proper 21. Solve the problem. Car A (travelling north at 70 mph) and car B (traveling west at 60 mph) are heading toward the same intersection. Car A is 3 miles from the intersection when car B is 5 miles from the intersection. . Find a formula for the distance between the cars as a function of time, using the parametric equations that describe the motion of cars A and B. Using a graphing utility, find the minimum distance between the cars. When are the cars closest? 5 mi car B 60mph 3 mi car A 70mph O d= V(70t - 3)2 + (5 - 60t); 1.84 mi; 0.06 min O d= V(70t - 3)2 + (5 - 60t)2; 326.38 mi; 3.60 min O d= V(70t - 3)2 + (5-60t)2; 1.84 mi; 3.60 min O d= V(70t + 3)2 + (5 -60t)2; 1.84 mi; 3.60 h22. Solve the linear programming problem. An airline with two types of airplanes, P, and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane P, costs $10,000 to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost? 9 P 1 planes and 13 P2 planes 7 P1 planes and 11 P2 planes 5 P, planes and 17 P2 planes 11 P, planes and 7 P2 planes\f24. Tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. x 2 + 6 O improper; x - 4 ( x+~/6)(x -16) O improper; 4 X +16 x-16 O proper O improper; x+16 x - 1625. Solve the linear programming problem. Maximize and minimize z = 5x - 18y subject to: x20, y=20, 4x+5y=30, 4x+3y=20, xs5 ys8 (O maximum: 25; minimum: -108 O maximum: 25; minimum; 0 O maximum:; -83.75; minimum: -108 (O maximum: -108; minimum: 0 26. An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. Objective Function z = 7x - 5y Constraints x = 0 Osys=5 x-y=0 X+2y=12 O maximum: -11; at (2, 5) O maximum: 0; at (0, 0) O maximum: 8; at (4, 4) (O maximum: -25; at (0, 5) \f\f29. Graph the solution set of the system of inequalities or indicate that the system has no solution. dx+3y=12 xzy \f