(1) The Set A ={11k+8|k∈Z},B={4m|m∈Z}and C = {11(4n + 1) − 3|n ∈ Z} are given. P

(1) The Set A ={11k+8|k∈Z},B={4m|m∈Z}and C = {11(4n + 1) − 3|n ∈ Z} are given.
Prove that A ∩ B = C.
(2) Given f(x) = x3+2×2+x, find the domain, range, behaviour x2 −x−2
of f(x) and hence sketch the graph of the function.
(3) Determine the values of the real parameter m for which the set A = {X ∈ R|(m−1)x2 −(3m+4)x+12m+3 = 0} has:
(a) one element (b) two elements
(c) has no element.

solve for α in the oblique triangle ABC; AB = 30; AC = 15, and angle B = 20° typ

solve for α in the oblique triangle ABC; AB = 30; AC = 15, and angle B = 20°
type out the two equations substituting the numbers from the diagram.
First, type out the Law of Sines set of relationships.
Next, type out the most appropriate version to use the Law of Cosines for this solution.
Write both equations and make a prediction of which method will be easier to use in finding a solution and why you think that is the case.