Let R be the region in the first quadrant bounded above by the curve y = 2 - x2and bounded below by the line y = x. Suppose the shell method is used to determine the volume of the solid generated by revolving R about the y-axis. What is the radius of a cylindrical shell at a point x in [0, 2]?Evaluate the integral.

Josh has a rewards card for a movie theater he receives 15 points for becoming a rewards card holder he earns 3.5 points for each visit to the movie theater he needs at least 55 points to earn a free movie ticket which inequality can josh use to determine x, the minimum number of visits he needs to earn his first free movie ticket.

Solve each quadratic equation by factoring and using the zero product property. 14x - 49 = x^2

If you flip a coin 3 times, what is the probability of flipping heads 3 times? a. p(3 heads) = 3/8 b. p(3 heads) = 1/6 c. p(3 heads) = 1/8 d. p(3 heads) = 1/2