please answer all the following questions correctly

1)

A dkg object's position, p, is changing with [aspect to time, i. The object expeliences a force, F, that is proportional to the object's acuelelation times its mass. What ditferential equation represents this dynamic? OF=' OF=' ' OF=4V ' OF=M A slope field for which of the following differential equations is shown? 4 3 - - -- X 0 --- /- -2 ---/- --- - --/- -3------- ---- -4---J-------J- - - - ---- O =X-y dx O dy LEY-X dx O % = X+y dx O dy = X dxWhich step is necessary in verifying that InB + 3 = -3t is a solution to dB -3B? dt O elnB + e3 = O 1 dB =-3 B dt O edB = -3dt [ (InB +3) dB = [-3t dtThe differential equation y ' = 3y will produce which of the following? O A slope field with parallel tangents along the diagonal O A slope field that does not have rows or columns of parallel tangents O A slope field with columns of parallel tangents O A slope field with rows of parallel tangentsWhich of the following could be a slope field for the differential equation ~% = sin(x)? dx O - 64 - X- -.. O x --X--X---\\Of 0 -1 -2 -.. ...)...f .../.... J. ... -Z - -./-../ .../-.../.... X O - -- - - --- -X- -.. --- -5-The average value of a function g on the interval [-4, -2] is -10, and the average value of g over the interval [-2, 0] is 2. What is the average value of g over the interval [-4, 0]? O-8 O -4 O-2 0 4A particle is moving along the x-axis on the interval 0 s t 10, and its position is given by x(1) = = x - x3 +6x -10. At what time(s), t, is the particle at rest? 2 Of = 0 Ot = 2 and 3 Of = 1 and 5 Of= 6What is the average value of f(x) = cosxsinx on the closed interval [0,? O O HIN O OFor time measured in seconds, where t 2 0, the velocity of a particle moving along the y-axis is given by v(t) = Vt+4, and the particle is at y = 2 when t= 0. Which of the following gives the position of the particle after 4 seconds? O y(4) = lov(t) dt O y(4) = Solv(t)dt O y ( 4 ) = 2 + 16 v(t)dt O y(4) = 2+ 1/ v(t )itFor time t 2 0, the velocity of a particle moving along the x-axis is given by v(t) = sint, where t is measured in seconds and v(t) is in meters per second. The initial position of the particle at time t = 0 is x = 8. What is the total distance the particle traveled from time t = 0 to t = 2TT? 0 2 04 O 12