Version 2.31i, Aug 15, 2004
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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.
Which of the following elements binds most strongly with Oxygen?
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.
Suppose we try to estimate the area under the curve f(x) = x
, 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.
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