The harmonic mean of two numbers is 4. Their arithmetic mean A and geometric mean G satisfy the relation 2A +G2 = 27. Find the numbers.
Find the image of the point (- 8, 12) with respect to the line 4x + 7y + 13 = 0.
Let image of a point be B (h, k). Mid point of AB is B which lies on a line
4x + 7y + 13 = 0
Slope of given line is -4/7, then slope of line AB is 7/4
On solving Eqs. (i) and (ii), we get
k = - 2,h = - 16.
Hence, required image is (- 16, - 2).
If cos(A) + cos(B) + cos(C) = 0, prove that
cos(3A) + cos(3B) + cos(3C) = 12 cos(A) cos(B)cos(C)
Let IR be the set of real numbers and f : IR ➔ IR be such that for all x, y ∈ IR, . Prove that f is a constant function.