Prove that the sum of the angles in a triangle is equal to 180 degrees. Use trigonometric identities to show that sine of x plus cosine of x is equal to 1.
Define the union and intersection of two sets. Given set A equal to 1, 2, 3 and set B equal to 2, 3, 4, find A union B and A intersection B.
Define the equation of a plane in 3D space. How do you find the distance of a point from a plane?
Define the scalar product of two vectors. If vector A is equal to i plus 2j and vector B is equal to 3i minus j, find the scalar product of A and B.
Explain the concept of feasible region in linear programming. Formulate a linear programming problem to maximize profit given constraints on resources.
A box contains 5 red balls and 7 blue balls. If two balls are drawn at random, find the probability that both balls are red.
Define a first-order differential equation. Solve the differential equation dy over dx equal to 3x squared.
Explain the concept of indefinite integration and how it differs from definite integration. Integrate the function f of x equal to x squared.
Explain the concept of maxima and minima of a function. Find the maximum and minimum values of the function f of x equal to 3x squared minus 12x plus 7.
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