MATH 114 Final: MATH 114 UPenn 114S11Final s Exam
Document Summary
Math 114 spring 2011 final exam: the set of points equidistant from the points (2, 1, 1) and (4, 3, 5) is a plane. First-baseman ryan howard hits a home run over the right- eld fence that starts out 3 feet above home plate with horizontal velocity 66 ft/sec toward the wall and initial upward velocity 84 ft/sec. What point on p is closest to the origin? (a) ( 1, 1, 3) (e) ( 1. 5 ) (b) ( 1, 1, 0) (f) ( 3. 5 ) (c) (2, 0, 3) (d) ( 1. 0 z 4 x2 (e) e 2: find the volume of the solid bounded above by the paraboloid z = 5 x2 y2 and below by the paraboloid z = 4x2 + 4y2. (a) (e) 2: use the transformation u = 3x + y, v = x + 2y to evaluate.
