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Consider the intersection of level surfaces of F = x^3 + y^3 - u^3 - v^3 and G = xu + yv.
(a). Write down the linear equations in matrix form to decide on solving for solving for x and y as functions of u and v near (x0, y0, u0, v0).
(b). Write down the matrix equation for solving for dx/du and dy/du near (x0, y0, u0, v0).
(c). Describe the points (x0, y0, u0, v0) near which you may be unable to solve for x and y as functions of u and v near (x0, y0, u0, v0).
Let K be a normal subgroup of G, and both K and G/K are simple. Show that either K is the only nontrivial proper subgroup of G, OR G is isomorphic to K x (G/K).
Suppose that 8 female and 7 male applicants have been successfully screened for 5 positions. If the 5 positions are filled at random from the 15 finalists, what is the probability of selecting
He is standing at the edge of a rose garden 9.00 meters below her window and 11.0 m from the base of the wall. How fast are the pebbles going when they hit her window?
Which two variables have the strongest strength of relationship?
a survey of 1100 people in a certain city indicates that 850 own microwave ovens, 750 own dvd players and 560 own microwave ovens and dvd players.
A difference between the mean number of volunteer hour
find the equation for the line that passes through the point (-2,-5) that is parallel to the line with the equation y=3/4x+8.
a boat can travel 124 mph in still water. if it travels 203 miles with the current in the same length of time it travels 133 miles against the current, what is the speed of the current?
For each of the following properties, find a binary relation R such that R has that property but R^2 (R squared) does not:
The hypotenuse of a right triangle is 13cm. One arm of the right angle is bigger by 7cm than the other leg. Find the length of the arms of the right angle.
Teesha is in the French club. There are 26 students in the club. The French teacher will pick 3 students at random to guide visiting students from France. What is the probability that Teesha will not be picked as a guide?
The probability of a bit error in a memoryless binary symmetric communication channel is 10^-3. Find the probability of a block of 1000 bits
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