Write the equation of a circle with center at (3, -2) and radius 5. Find the coordinates of any two points on this circle.
Prove by mathematical induction that the sum of the first n odd natural numbers is equal to n squared.
Define an equivalence relation. Give an example of an equivalence relation on the set of integers.
A factory manufactures two products, P and Q. Each unit of P requires 3 hours in the manufacturing department and 2 hours in the packaging department. Each unit of Q requires 4 hours in manufacturing and 3 hours in packaging. The total available hours in the manufacturing and packaging departments are 120 and 90 hours, respectively. Formulate this problem as a linear programming problem to maximize profit.
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