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271E3-F2002 - EXAM#2 MATH 271 Federico Tournier Name SS 1...

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Unformatted text preview: EXAM #2 MATH 271 Federico Tournier Name: SS#: 1. Find the point of intersection of the two lines 3322 x=1+s a) y=3-—3t y=4+s z=——2—2t z=—1+s b) Find the equation of the plane determined by the two lines. 2) Find the distance from the point (0,1, 1) to the plane 23: + y + z = 4. 3) Find the parametric equation of the tangent line to the curve r(t) = (sint,t, at) at t = 0 FALL 2002 4) Let r(t) = (t,t3,t) for t 6 [0,3] a) Find the velocity and acceleration vector When t : 1. b) Find the curvature at the point (1,1,1). c) Calculate the normal and tangential components of the acceleration vector at the point (1,1,1). 5) A particle moves on the graph of y = x4 from left to right at a constant speed of 2. a) Find the velocity vector at the point (1, 1). b) Find the acceleration vector at the point (1, 1). 6) A projectile is fired at an initial speed of 80 feet/ sec and aimed at a tangent 100 feet down range (gravity is 32 feet / sec). a) What are the two possible launching angles? b) Using the smaller of the above angles, will the projectile clear a wall which is 10 feet high located 70 feet down range? Explain - ...
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