ABCD is a square force of magnitude 14N, 4N, 2N, and 2\(\sqrt{2}\)N act along the sides AB, BC, CD, and DA, respectively. Find in Newton, the magnitude of the resultant of the force.
1. The sum of the 2nd and 5th terms of an arithmetic progression (A.P) is 42. If the difference between the 6th and 3rd terms is 12, find:
a. the common difference
b. the first term
c. the 20th term.
2. If 2\(^{2x -2y}\) = 32 and log\(_y\) x = 2, find the values of x and y
Leave your answer in this format "+ x,- y"
3. If (x + 2) and (x -1) are factors of f(x) = 6x\(^4\) + mx\(^3\) - 13x\(^2\) + n x + 14, find the:
a. value of m and n. Leave your answer in this format 'm,n.'
b. remainder when f(x) is divided by (x + 1)
4. Find the equation of a tangent to the curve y = \(\frac{x - 1}{2x + 1}\), x \(\pm\) \(\frac{-1}{2}\) at the point(1, 0)
Leave your answer in this format: ay - bx + c = 0
