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Consider the vector field F = (x^2 - y^2)i + (y^2 - Z^2)j + (z^2 - x^2)k.
a) Calculate the line integral of F from P_0 at (1,0,0) to P_1 at (-1,0,0) along the direct line path joining these points.
b) Calculate the line integral of F from P_0 at (1,0,0) to P_1 at (-1,0,0) along the horizontal semicircular path joining these points, traversed anti-clockwise (through the point (0,1,0)), which forms part of the circle centred at the origin. You may need to use sin^3t = sint(1-cos^2t).
What are two or more other curves or graphs that you use or observe in the business environment? Why are they important and how are they used?
What is the total defect rate? I came up with 6%. A randomly selected product was defective. What is the probability that it came from Plant A?
A silver dollar is flipped twice, calculate the probability of each of the following occurring: A, a head on the first flip
Let n be a natural number, and let f: R-->R be the function f(x) :=x^n. Show that f is differentiable on R and f '(x)=nx^n-1 for all x belonging to R
Use Gaussian elimination with partial pivoting to find matrices L and U such that U is upper triangular, L is lower triangular with | l_ij| = j and LU = A', where A' can be obtained from A by interchanging rows.
Which pair has equally likely outcomes? List the letters of the two choices below which have equal probabilities of success, separated by a comma.
In each of the attached cases show that the set U is linearly independent subset of the vector space V. Give, with justification, a basis of V which contains the set U.
Probability: Working with the standard distribution curve. A company installs 5000 light bulbs, each with an average life of 500 hours and a standard deviation of 100 hours, and a distribution approximated by a normal curve
If the train were announced to be running thirteen minutes late, how many times would you predict the man next to you would check the time?
The same experiment as in part (a) above is done with the 7 letters from CHICAGO. Find the probability that the result spells CHICAGO. Find probability that the result spells NEW YORK
An employee of the National Parks Service told you about a location in Washington, DC. It is a large grassy area south of the White House known as the Ellipse. The National Tree Lighting Ceremony is held annually on the Ellipse.
Let G sub1 and G sub 2 be groups, with subgroups H sub 1 and H sub 2, respectivetly. Show that {(x sub 1, x sub 2) | H sub 1 is an element of H sub 1, x sub 2 is an element of H sub 2} is a subgroup
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