Assignment:
Q1) Solve the following inequality. Write the answer in interval notation. X/X+3 ≤ -2/5(X-3)
Q2) Solve the inequality. 3 < |5X+3| < 5
Q3) a)Find an equation of the line, say y=mx+b, which passes through the point (-3,8) and is perpendicular to the line 3x+3y=33. y=?
b)What is the shortest distance from the point (-3,8) to the line 3x+3y=33? Shortest distance=?
Q4) Answer the following, assuming that all angels are in radian.
a) Suppose that X=6π /19 is a solution of the equation sin X= A, where A is some constant. Then A must be equal to ________, and the other solution of the equation in the interval [0,2π ] must be X=_______.
b)Suppose that X=π /13 is a solution of the equation cos X= B, where B is some constant. Then B must be equal to _______, and the other solution of the equation in the interval [0,2π ] must be X=_______.
c)Suppose that X=4π /7 is a solution of the equation tan X= C, where C is some constant. Then C must be equal to _______, and the other solution of the equation in the interval [0,2π ] must be X=__________.
Provide complete and step by step solution for the question and show calculations and use formulas.