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Let R be the region in the first quadrant bounded by the graph of y = -x2 + 4x and the x-axis. A solid is generated when R is revolved around the horizontal line y = -1. What is the definite integral that gives the volume of this solid? On Jo (-x2 + 4x - 1)2 dx O TE Jo (-x2 + 4x + 1)2 dx OF Jo [(-x2 + 4x - 1)2 - 1] dx Ox. JO[(-x2 +4x + 1)2 - 1]dxdy 3 What are all the solutions to the differential equation ? dx x +2 Oy = 3In(x| + C Oy = In|x + 2| + C Oy = 3In|x + 2 + CI Oy = 3In|x + 2| + CFind the area of the region(s) bounded by y = - x - 3x* - x- and y = 3x. O 21.266 O-21.266 O 19.8 O-19.8X- 3 What is the general solution to the differential equation dy dx 3y O 3x+C y=e 2 Oy= ( x2 - 3x13 +C Oy= 3x + C 2 O 2 V = -3x + C 2For time t 2 0, the velocity of a particle moving along the x-axis is given by v(t) = sin(e ."). The initial position of the particle at time t = 0 is x = 1.25. What is the displacement of the particle from time t = 0 to time t = 10? O 8.027 O 6.777 O 2.830 O 1.580Let R be the region in the first quadrant bounded by the graph of y = -x- + 9 and the x-axis. R is the base of a solid whose cross sections perpendicular to the x-axis are semicircles. What is the volume of the solid? O 81 5 81x 40 4 O 9nt 32\fAt the time a casserole is cut, its temperature is 300 degrees Fahrenheit. The casserole's temperature then decreases at a rate of C(t) = 49e-0.0s degrees Fahrenheit per minute, where t is the time in minutes since the casserole was cut. Which of the following integrals would give the temperature of the casserole at t = 4 minutes? 300 - If C(f) dt 300 - [ C(t) dt 300 + [ C(t)dt 300 + Jf C(f) dtThe concentration of a medication Min mg/L present in the bloodstream decreases over time such that the concentration of medication is proportional to the amount of medication t hours after the first dose. The concentration of medication 30 minutes after the first dose is 40 mg/L and was decreasing at a rate of 50 mg/L per hour. Which differential equation represents this relationship? aM = -0.042M it dM =-0.66M it -1.25M it = -1.875M itDuring flu season, the number of people that contract the flu virus at any time increases at a rate proportional to the number of people that contract the flu virus at that time. There were 700 people that contracted the virus when flu season began, and 1,051 contracted it seven days later. How many people contracted the virus 14 days after it first began? Round to the nearest person. O 1, 151 O 1,578 O 1,751 O 2,369Let R be the region in the first quadrant enclosed by the graphs of y = x-, x = 1, and the x-axis. What is the volume of the solid generated when R is rotated about the y-axis? O O 2TT O 4TTA slope field for which of the following differential equations is shown? -- - -- - 3 ----/- ---7 4 - -] - - - - - X -3 -2 0 2 3 4 5 -2 -3 O dy -=x+1 dx O dy -=X-1 dx O dy -=y+1 dx O dy =y-1 dxWhat is a particular solution to the differential equation dy with the initial condition y(0) = 3? dx Oy= 0+ 1*t Is t's dt Oy= 3+lots at Oy= 1 3t dt Oy= 3+10+3 dtThe region R in the first quadrant is bounded by the graph of y = tan(x), the x-axis, and the vertical line x = 1. What is the volume of the solid formed by revolving R around the vertical line x = 1? O 0.3751 O 0.7012 O 1.1783 O 2.203Select the possible solution(s) to the differential equation (1-2v)- dv =1. I.v- v + 1=1 II. t - 2tv = t Ill. V - V- = v+ C OI O III Ol and II Oil and Ill