18. Find the equation for a line which passes through the points (1, 7) and (3,1). . Write the equation in slope-intercept form. Show work. 19. Find the exact solutions and simplify as much as possible: 9x- + 4 = 24x. Show work. 20. Let f(x) = 5x- + 9 and g(x) = x - 3. (a) Find the composite function (fog)(x) and simplify. Show work. (b) Find (fog)(-1). Show work. 21. A projectile is launched from a platform 12 feet high with an initial velocity of 112 feet per second, The height h of the projectile at f seconds after launch is given by h = -16f- + 112 + 12 feet. (a) How many seconds after launch does the projectile attain maximum height? Show work. (b) What is the maximum height? Show work. x+7 12 22. Solve = 0. Show work. x+6 x2 - 36 23. Suppose that cos e = 4/5 and that e is a Quadrant IV angle. (a) Find the exact value of sin e. Show work. (b) Find the exact value of sin 20. Show work. 24. Prove the identity (sin x - cos x) = 1 - sin(2x)25. From a point 47 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 54.30. Find the height of the tree to the nearest tenth of a foot. Show work. (sketch is not to scale) 54.30 47 feet 26. For the triangle ABC, we are given that A = 440, B = 620, and c = 30.0. 440 620 C = 30 Find the length of side b, rounded to the nearest tenth. Show work. 27. Let u = (-5, 10) and v = (12, 6). (a) Calculate the dot product u . v. Show work. (b) Determine the angle between u and v. Round the result to the nearest degree. Show work. (x - 4)2 (y - 1)2 28. An ellipse has the equation + = 1 9 16 (a) Is the major axis horizontal or vertical? (b) Find the exact values of the foci of the ellipse. Show work