Suppose that a change in biomass B(t} at timet during :18 n: the interval [0.6] follows the equation E0) = 2 cos [E ] for 0 5 t 5 6. and that B(0)=BD. Use this information to answer parts a through d below. (:3 dB (a) Use the graphing tool to graph the function a as a function of t. Click to enlarge \\ graph I (For any answer boxes shown with the grapher, type an exact answer. Type the word pi to insert the symbol 1! as needed.) dBi'dt Let g(t) = 2 cos (xt). Compute the average value of g(t) over the interval The average value is (Type an exact answer, using x as needed.)Suppose that the concentration (measured in gm' 3} of nitrogen in the soil along a transect of land yields data points that follow a straight line with equation y = 608.3 - 30.45: for 0 s x s 10. where x is the distance to the beginning of the transect. What is the average concentration of nitrogen in the soit along this transect? .1...) What expression invotuing a definite integral needs to be evaiuated to calculate the average concentration of soil nitrogen? H=|| Find the area of the region bounded by the curve y = 2:2 - 1 and the line y = 49. The area is E. Find the area of the region bounded by the graphs of the given equations. y = 6x - x", y= - 6x The area is (Type an integer or a simplified fraction.)Find the area of the following region. Sketch the bounding curves and the region in question. The region in the first quadrant bounded by y = 4 and y = 4 sin x on the interval |0.2 Choose the correct graph below. O A. O B. O C. O D. 5- 5- 5T 5- a X X NINFind the volume of the solid generated by revolving the region bounded by the lines and curves y = , y = 0, x = 0, and x = 4 about the x-axis. (The solid generated is called a paraboloid.) The volume is (Type an exact answer in terms of a.)Find the volume of the solid generated by revolving the region bounded by the lines and curves y = r". y = 0. x = - 2. and it = 2 about the x-axis. The volume ofthe resulting solid is | | units cubed. (Type an exact answer. using it and v as needed.) . Find the area of the region enclosed by the curves 3 = 12 2x and y = x2 + 6x. The area of the region enclosed by the curves is I _. (Type an integer or a simplied fraction.) Find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis. Sketch the bounded region together with a typical disk element. Fm. y=x.0:x56 The volume ofthe rotated solid is [ml (Type an exact answer in terms of It.) Find the length of the curve 93:2 = 4x3 from x = 0 to x = 15 when y 2 0. The length of the curve is :| (Type an integer or fraction. Simplify your answer.)