How many permutations are there of 47 objects when taken 6 objects at a time, if a particular one of these objects must always be included? O a. 6(47 - 1)!/(47-6)! O b. 6(47)!/(47-6)! O c. (47 - 1)!/(47-6-2)! O d. 6(47-1)!/(47-6-1)! O e. 47 (47 - 1)!/(47-6-2)!Consider two functions y1 = f(x) and y2 - g(x), 2 that y1 / 32 except where they intersect. If these two functions intersect at 130 places, how many different integrals do you need to find the total area enclosed by the two curves? Answer:Evaluate the following integral e a dx given that dx V TT and a = 8.3. Round your answers to five decimal places