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Let X be a set and f : X → R be a real-valued function. Show that the relation givenby x ∼ y if and only if f(x) = f(y) is an equivalence relation on X.Remark: Equivalence classes for this relation are called level sets of f.
Directions: 1-2 pages, typed, double-spaced. For this assignment, you need to apply the doctrine of double effect to two cases and explain why the principle would entail different conclusions about the two cases. I recommend that you explain the D..
Find the probability that a bag of fertilizer will weigh between 45 and 55 pounds?
Consider a beam of length L and a fulcrum a length x away from one end. There are weights, W1 and W2, placed on opposite ends of the beam. Find x so that the system is in equilibrium.
The mass of a cube of iron is 385 g. Iron has a density of 7.87 g/cm3. What is the mass of a cube of lead that has the same dimensions?
Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit. If it diverges to infinity
Find the rate of change.
Find the median for the following group of data items 12,9,8,7,13,10,6,8 round to the nearest tenth
Suppose that 320 feet of fencing material with which to enclose a rectangular field that borders on a straight stream. If the farmer does not enclose the side bordering on the stream, what are the dimensions of the field of maximum area?
The diameters of Douglas firs grown at a Christmas Tree Farm are normally distributed with a mean of 4 inches and a standard deviation of 1.5 inches. What proportion of the trees are expected to have diameters greater than 5 inches?
A particle starts at the point (-4, 0), moves along the x-axis to (4, 0), and then along the semicircle y = √16 - x2 to the starting point. Use Green's Theorem to find the work done on this particle by the force field F(x, y) = ‹9x, x3 + 3xy2›.
Find the most economical path for the transmission line from the power station to the factory.
Show that B is a symmetric matrix and B2 = B.
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