Question 1 A magic eight ball is sitting on top of a placemat. When it sits in the center, itis perfectly inscribed. The square placemat has sides of 4 inches in length. What is the volume of the magic eight ball? O 4 16 O 5w O 100w 2 O 5 Question 2 A magic eight ball is sitting on top of a placemat. When it sits in the center, itis perfectly inscribed. The square placemat has sides of inches in length. What is the volume of the magic eight ball? 26 O O 9 O 36x O% Question 3 A placemat is used to hold a canister. The canister fits exactly across the 15 inch length of the placemat, when laid on its side. The canister has a diameter of inches. What is the volume of the canister? O 1207 O 240w O 60m O 407 Question 4 A placemat is used to hold a canister. The canister fits exactly across the 1( inch length of the placemat, when laid on its side. The canister has a diameter of 4 inches. What is the volume of the canister? O 80m O 40m O 107 O 207 Question 5 A placematis used to hold two dinner plates. The dinner plates are circles with a radius of 3 inches. Placed right next ta each other (with no gap), they span the width of the placemat. The length of the placemat has 1 inch of extra space on each end. What s the total area of the placemat? O 21 O 84 O 62 O 42 Question 6 A placemat is used to hold a conic party hat. The hat is perfectly inscribed in the square placemat, which is 8 inches on each side. The hat has a height of g inches. What is the volume of the party hat? O 48/pi O 36/pi O 24/pi O 12/pi Question 7 The base of asolid, 8, is the region bounded by the curve y = 2%, the -axis, the -axis, and a line y = 1. Cross sections perpendicular to the &-axis are squares. What is the exact volume of the solid, ? o O O O | Question 8 The base of asolid, , is a triangle bounded by the g-axis, -axis, and the line 2z + y = 4. Cross sections perpendicular to the g-axis are semi-circles. What is the exact volume of the solid, 7 Question 9 A region is enclosed by the -axis, the y-axis, the line a = 2, and the curve y = cos . When this region is rotated around the -axis, what expression represents the volume of the solid? Question 10 A region is enclosed by the -axis, the line x = 1, the line x = 2, and the curve y = 2. When this region is rotated around the -axis, what is the volume of the solid generated? O - O MT Question 11 A region is enclosed by the y-axis, the line y = 4 and the curve y = va3. When this region is rotated around the a-axis, what is the volume of the solid generated? O 128 16 O 64 32 Question 12 A region is enclosed by the y-axis, the line y = 1 and the curve y = =2 on the interval [0, 2]. When this region is rotated around the y-axis, what is the expression for the volume of the solid generated? O 27Question 13 Which of the following satisfies the differential equation y' - xy = 0? O ez O ezz/2 O -24 Question 14 Which of the following satisfies the differential equation y" +y' = 0? O y = tan(2) O y= e Oy = ex Oy=22 Question 15 Which of the following satisfies the differential equation y" + y = 0? O y = sin(x) O y = In(x) Oy = 24 O y = sin? (x) Question 16 Which of the following satisfies the differential equation xy' - 2y = 0? O y = sin(x) Oy=22 O y = = O y = ezQuestion 17 Which of the following satisfies the differential equation y' + 3y = 0? O y = = O y = cos(z) Oy =e-3x O y = sin(z) Question 18 Which of the following satisfies the differential equation y' - y = 0? Oy= ex Oy=23 O y = = Oy = = Question 19 What is the slope of the equation dy/ (da) = 2x2? O Cannot be determined without a slope field. 0 4 O -2 O 4x Question 20 The slope field for a differential equation is shown below. Which statement is true for solutions of the differential equation? . For x 0 all solutions are decreasing.O II and Ill only O Ill only O I, II, and Ill O I only O II only Question 21 The slope field for the differential equation dy/(dx) = (x?y + y?)/(4x + 2y) will have vertical segments when... O y = 2x, only O None of the options are correct Oy= -2x2, only Oy= -x2, only Question 22 Which statement is true about the solutions y(x), of a differential equation whose slope field is shown below? I. If y (0) > 0 then II. If -2