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Version 2.31i, Aug 15, 2004
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 Homework Assignment Submitted Successfully.

 Submission number:  42721
 Submission certificate:  HI877395
 Submission time:  13 Dec 2004 10:17:41 PST (GMT-8:00)

 Title:  General Science/Math    
 Positive points per question:  3.0    
 Negative points per question:  1.0    
 Number of questions:  4    
 Your score:  0.0    

  A collection of questions from High-School/Early College analytic subjects. This assignment shows an ongoing homework, where students see the choice explanations every time they make an incorrect answer, but they do not get to see the full explanations.

 1.Which of the following elements binds most strongly with Oxygen? 
   a)  Helium
   b)  Hydrogen
   c)  Silicon
   d)  Aluminum

 Answer submitted:  b)
  You have answered the question correctly.
  Hydrogen, with a +1 valence (one electron in the outermost shell) will bind strongly with Oxygen. Oxygen has a -2 valence, or two missing electrons in the outermost shell, so there is a strong tendency for one Oxygen atom to bind with two Hydrogen atoms (forming water).

 2.A projectile is fired with an initial velocity in the x (horizontal) direction of 1000 ft./sec. and an initial velocity in the y (vertical) direction of 500 ft./sec. Write the equation that gives y as a function of x. Demonstrate the correctness of your solution by selecting, from the list below, the (x,y) point that is on the trajectory of the projectile. 
   a)  x = 3000; y = 1212.
   b)  x = 3000; y = 1500.
   c)  x = 4000; y = 2000.
   d)  x = 4000; y = 1744.

 Answer submitted:  c)
  Your answer is incorrect.
  A possible error: don't forget to take into account the vertical acceleration due to gravity.

 3.Suppose we try to estimate the area under the curve f(x) = x2, from x=0 to x=1, using the trapezoidal rule. The error in the estimate decreases as we use more trapezoids. Suppose we use k trapezoids; i.e., we use the values of f(x) at x=0, x=1/k, x=2/k,...,x=(k-1)/k, x=1. Compute the error in the estimate for k=2, k=3, and k=4. Then, identify the correct statement below. 
   a)  For k=3, the error is 1/18.
   b)  For k=4, the error is 1/96.
   c)  For k=3, the error is 0.
   d)  For k=2, the error is 5/12.

 Answer submitted:  a)
  Your answer is incorrect.
  Possible error: you may be forgetting that the values at the ends of the interval receive less weight than the interior values, according to the trapezoidal rule.

 4.A farmer has 100 yards of fence, with which to create a rectangular cow pasture along a straight river. The side facing the river does not have to be fenced, but the other three sides do. Find, in feet, the sides and area of the pasture that has the largest possible area. Then identify the correct statement from the list below. 
   a)  The area is 11,250 sq. ft.
   b)  One side is 100 ft. long
   c)  One side is 200 ft. long
   d)  One side is 25 ft. long

 Answer submitted:  b)
  Your answer is incorrect.
  This answer would be correct if the best way to divide the fence among the three sides were to divide it equally. However, intuitively, there is an advantage to making the side parallel to the river longer, since if you add a foot to the dimension of the pasture along the river, you only have to remove half a foot from the other dimension of the pasture. Hint: Try deriving a formula for the area in terms of one of the sides, and then take the derivative with respect to that side to find the maximum.