mock_final-1.doc

mock_final-1.doc - off as rapidly as possible. Question 5....

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Concordia University Course Number: ENGR 233 Date: Wednesday, April 2, 2008 Time: 10:15-11:30 hrs. Total Marks: 100 Pages: 2 MOCK FINAL EXAMINATION Special Instructions: Use of calculators and outside materials is NOT permitted. _____________________________________________________________________________________ Question 1. Find the volume of the parallelepiped for which the given vectors are three edges. a = 3 i + j + k , b = i + 4 j + k , c = i + j + 5 k . Question 2. Find the parametric equations for the line of intersection of 2 x – 3 y + 4 z = 1 and x y z = 5. Question 3. A quarterback throws a football with the same initial speed at an angle of 60˚ from the horizontal and then at an angle of 30˚ from the horizontal. Show that the range of the football is the same in each case. Question 4. Consider the rectangular plate shown in the figure. The temperature at a point ( x , y ) on the plate is given by T ( x , y ) = 5 + 2 x 2 + y 2 . Determine the direction an insect should take, starting at (4, 2), in order to cool
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Unformatted text preview: off as rapidly as possible. Question 5. Use the divergence theorem to find the outward flux of the given vector field F . F = x 3 i + y 3 j + z 3 k ; D the region bounded by the sphere x 2 + y 2 + z 2 = a 2 . Question 6. Find the surface area of that portion of the plane 2 x + 3 y + 4 z =12 that is bounded by the coordinate planes in the first octant. Question 7. Use Green’s theorem to evaluate the following line integral: ; where C is the boundary of the region determined by the graphs of y = x 2 , y = 4. Question 8. Evaluate the given iterated integral by changing to polar coordinates. Question 9. Find the work done by the force F ( x , y ) = 8 xy 3 i +12 x 2 y 2 j acting along the circle r ( t ) = 2cos t i + 2sin t j from (2, 0) to (0, 2 [ Hint : F is conservative]. Question 10. Evaluate ; where C is given by x = y 2 from (1, 1) to (1, 1)....
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This note was uploaded on 05/08/2009 for the course AAE 580 taught by Professor Nnjkl during the Spring '09 term at Ohio State.

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mock_final-1.doc - off as rapidly as possible. Question 5....

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