Let x and y denote the coordinates of a point uniformly chosen in the circle of radius 1 centered at the origin. that is, their joint density is f(x, y) = 1 π for x 2 + y 2 ≤ 1. find the joint density function of the polar coordinates r = (x2 + y 2 ) 1/2 and θ = atan( y x ).

Cameron indoor stadium at duke university is one of the most revered sites in all of college basketball, as well as in all of sports period. duke’s men’s and women’s basketball programs have attained quite a few wins in the building over the last seventy years. cameron indoor stadium is capable of seating 9,460 people. for each game, the amount of money that the duke blue devils’ athletic program brings in as revenue is a function of the number of people in attendance. if each ticket costs $45.50, find the domain and range of this function.

Arestaurant chef made 1 1/2 jars of pasta sauce. each serving of pasta requires 1/2 of a jar of sauce. how many servings of pasta will the chef be able to prepare using the sauce?

Ab and bc are tangent to circle d. find x is ab = 3x + 8 and bc = 26. find x