If the first term of an arithmetic progression is 5 and the common difference is 3, find the tenth term of the progression.
Prove that the sine squared of an angle plus cosine squared of the angle equals 1 for any angle.
Solve the system of equations: x plus y equals 5 2x minus y equals 3
Given set A equals the set of all even numbers and set B equals the set of all prime numbers, find the union and intersection of sets A and B.
If vector A is equal to 2i plus 3j and vector B is equal to i minus j, find the dot product of vectors A and B.
A die is rolled. Calculate the probability of getting an even number and the probability of getting a number greater than 4.
Evaluate the definite integral of the function f of x equal to x cubed from 1 to 3.
Differentiate the function f of x equal to x squared plus 3x plus 2 with respect to x and find the equation of the tangent at the point where x equals 1.