The surface of an island is defined by the following function over the region on which the function is nonnegative. Find the volume V of the island shown to the right. z= 23 - Wx + Z = 23 - x + +y Set up the double integral, in polar coordinates, that is used to find the volume. drdo (Type exact answers.)Find the volume V of the solid below the hyperboloid 51 z = I" '1.||1+}{2 +y2 and above the following region. R={{r.}:15rs2.s521t} / \"- [Type an exact answer. using 1: as needed 3 Let u(t) = 21'i+ (t- - 1)j-8k. Compute the derivative of the following function. (+ 19 + 91) u(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function O B. The derivative is the vector-valued function K.Find the average value of over the annulus {(r,0): 6Ers 7}. The average value is (Type an exact answer.)Consider the following position function. Find (a) the velocity and the speed of the object and (b) the acceleration of the object. r(t) = (6t,4t" ) for t 2 0 (a) v(t) =Find the following derivatives. 2 zg and z, where z = 9xy - 5x y, x =2s +t, andy = 2s -t III dz (Type an expression using x and y as the variables.)When converted to an iterated integral, the following double integral is easier to evaluate in one order than the other. Find the best order and evaluate the integral. [5x sec"(xy)dA; R= {(x.y): 0=x5 5, 0sys1} R Select the correct answer below and fill in the answer box to complete your choice. A. It is easier to integrate with respect to x first. The value of the double integral is (Type an exact answer.) B. It is easier to integrate with respect to y first. The value of the double integral is (Type an exact answer.)Use a double integral to find the area of the region bounded by all leaves of the rose r = sin 70. Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area the leaf that is closest to the positive x-axis. Ajeat = r dr do (Type exact answers, using x as needed.)