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13.3-13.4 - (1 at time t = 0 6 At what point on the curve x...

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MATH 231 Group Work Quiz Related 1. Compute T ( t ), N ( t ), B ( t ) and κ ( t ) for the following curves: (a) r ( t ) = t 3 j - 4 t k (b) r ( t ) = 1 2 sin t i + 1 2 cos t j + 1 2 t k 2. A gun is fired with angle of elevation 30 . What is the muzzle speed if the maximum height of a shell is 500 m? 3. At what point does the curve have maximum curvature? (a) y = x 4 (b) y = ln x 4. The position function of a particle is given by r ( t ) = 5 t 2 , t, t 2 - 16 . When is the speed minimal? 5. Find the equations of the normal and osculating planes for the functions in
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Unformatted text preview: (1) at time t = 0. 6. At what point on the curve x = t 3 , y = 3 t , x = t 4 is the normal plane parallel to the plane 6 x +6 y-8 z = 1? 7. A man throws a football to his son who is 30 ft away. The ball leaves his hand at an angle of 30 ◦ and a speed of 5 ft/s. How high will his son need to reach to catch the ball? 1...
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