MATH 114 Midterm: MATH 114 UPenn 114Fall 02Mup short Exam
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Let p be a point on the plane 3x + y 2z = 2 and let q be a point on the plane. Let v be the vector that points from p to q. The football left the ground with an initial horizontal velocity of 45 feet per second toward the goalpost and an initial upward velocity of 67 feet per second. The crossbar of the goalpost is 10 feet high. 3 t for 1 t 3. (a) 8 (e) 54 3 (b) 24 3. Z 2/9 y2 (a) 0 (e) 3 sin x x (b) dx dy. 6 (c) (g) 2 3 1 (d) 1 (h) 2 3: find the volume of the solid bounded above by the plane z = 1 and below by the surface z = ex2+y2. Z zr (x + 2y) da. (a change of coordinates will help. )
