Approximate the integral of f(x)=2−x2 from 0 to 1 using Riemann sums. Lisa calculates the upper sum using the maximum function value, while Theo calculates the lower sum using the minimum function value. Compare the results for 5 and 500 rectangles.
Find the number of nonunion members in a company with 135 employees, where the ratio of union to nonunion members is 2:3. Solution: Let the number of union members be 2x and the number of nonunion members be 3x, where x is a constant. The total number of employees is 2x+3x=135, so x=15. Therefore, the number of nonunion members is 3x=3×15=45.
Find the total surface area of a cone with radius 4cm and slant height 6cm using the formula πrl, where r is the radius and l is the slant height. Give the answer in terms of π.