Calculus and vectors

2. Find the equation of the following lines in the required form: a. through the points P(, -3,2) and 209,20) [vector equation] b . with direction vector d - (5,3, -4) and z-intercept 7 [symmetric equations] C. perpendicular to (x, y, z) = (1, -2,0) + r(1, -1,D) through P(1, 3,5) [parametric equations] d. through 7(2,-5) and perpendicular to the line 3x -6y = 5 [scalar equation] 1. A boat travels on a heading of 3350 at a constant speed of 28 km/h relative to the water. If the current is 18 km/h with a heading of 60, what is the velocity of the ship and its bearing? 3. Skew lines are lines that are not parallel, yet do not intersect, as shown in the diagram below. Show that the lines (x, y, z) = (2, 1, 0) + s(1, 1, -1) and x = 3 +21 ; y = 31 ; z=-1-1 are skew. 4. Find the derivative of the following functions: a. y = Vx b y = x-4/7 C. y = sin x2 d. y = (x') (3") e. f. g. y = (x' - 1)' (x2 + 1)2 5 . RockHard Productions holds weekly events in an arena with a seating capacity of 15 000 spectators. With ticket prices at $12, the average attendance is 11 000 fans. A market survey indicates that for every dollar that ticket prices are lowered, the average attendance will increase by 100 fans. How should the production company set ticket prices to maximize their revenue? 6. Sketch the function y = using the following steps. i. Domain ii. Intercepts iii. Symmetry iv . Asymptotes V. Intervals of increase or decrease vi. Maximum and minimum points vii. Intervals of concavity vili. Points of inflection ix. Sketch the curve