Geometry and Passport to Advanced Math

  1. Find the surface area of a sphere with the volume of 27π.
  2. A factory in Hackensack manufactures T-shirts. The factory has monthly operating costs of $14,000 per month regardless of how many shirts are produced. Additionally, the factory must spend $7.45 for each shirt produced.
    1. In July, the total factory costs were $19,000. Approximately how many shirts were produced?
    2. Find an expression for C(n) where cost is a function of the number of shirts produced (n).
    3. The factory charges $22.90 per shirt. Find a function for revenue in terms of n (number of shirts produced).
    4. Find the number of shirts at which the company makes zero profit.
  3. 9xy+14x=15y-40+100x. Find an expression for y in terms of x.
  4. Line s is perpendicular to line t and passes through (12,32). Find an equation to describe line s.