MATH 115 Pre-calculus March 2022 SHORT ANSWER, with work required to be shown, as indicated. 18. Find the equation for a line which passes through the points (-8, 9) and (-6, 3). Write the equation in slope-intercept form. Show work. 19. Find the exact solutions and simplify as much as possible: 5x = 6x + 3. Show work. 20. Let f (x) = 3x- + 9 and g(x) = x - 2. (a) Find the composite function (f o g)(x) and simplify. Show work. (b) Find (fog)(-3). Show work. 21. A projectile is launched from a platform 6 feet high with an initial velocity of 80 feet per second, The height h of the projectile at / seconds after launch is given by h = -161 + 80t + 6 feet. (a) How many seconds after launch does the projectile attain maximum height? Show work. (b) What is the maximum height? Show work. . x+5 22. Solve: 28 x2 -49 Show work. x+7 23. Suppose that cos 0 = 12/13 and that O 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 1 - (cos x - sin x) = sin 2x MATH 115 Pre-calculus March 2022 25. From a point 62 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 47.30. Find the height of the tree to the nearest foot. Show work. (sketch is not to scale) 47.30 62 feet 26. For the triangle ABC, we are given that A = 420, B = 580, and c = 16.0. 580 C = 16 Find the length of side b, rounded to the nearest tenth. Show work. 27. Let u = (9, -3) and v = (4, 12). b) Calculate the dot product u . v. Show work. (c) Determine the angle between u and v. Round the result to the nearest degree. Show work. 28. An ellipse has the equation (x+7) (1-6)2 - = 1 49 (a) Is the major axis horizontal or vertical? (b) Find the exact values of the foci of the ellipse. Show work.SHORT ANSWER with Wo Problem Number Math 1 15 Final Examination Spring, 2022 19 20 Math 1 15 Final Examination Spring, 2022 Work for both parts 21 Work 22 Math 1 15 Final Examination Spring, 2022 Work for both parts 23 Math 1 15 Final Examination Spring, 2022 25 Math 1 15 Final Examination Spring, 2022 (by Work for both parts : work for part (by 28