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1. Suppose U and V are conformally equivalent. Prove that if U is simply connected, then so is V. Note that this conclusion remains valid if we merely assume that there exists a continuous bijection between U and V.
2. Does there exist a holomorphic surjection from the unit disc to C?
[Hint: Move the upper half-plane "down" and then square it to get C.]
In a four-factor analysis used in a multifactor evaluation process, it is desired to have the F1 importance weight four times as much as the F2 importance weight.
In a hexagon, all but one of the angles have a measure of 110 degrees. What is the measure of the remaining angle?
A rectangular park measures 300 ft by 400 ft. A sidewalk runs diagonally from one corner to the opposite corner. Find the length of the sidewalk.
Find the relevant equilibrium and use the stability criterion to determine when it is stable. Draw a cob webbing diagram.
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 552 feet of fencing is used. Find the maximum area of the playground.
a 34% solution is mixed with a 66% solution to produce 216 liters of a 42% solution. How many liters of each solution were mixed?
Details: A grandmother is looking for a plan to finance her new grandchild's college education. She has $25,000 to invest. Search the internet and locate a long-range investment plan, CD, Savings Bond, etc, for the grandmother. The plan is to earn..
Suppose that X is exponentially distributed and for a certain value of d the LER is 0.3. If r = 0.10 and d is unchanged, what is the new LER?
Find the future value of an ordinary annuity that has $270 monthly payments for 9 years if the account receives 3 3/4% interest.
The length of a rope required to wrap around a circular wheel exactly is 8.8cm. What is the diameter of the wheel to the nearest tenth?
a walkway forms the diagonal of a square playground. The walkway is 24 m long. to the nearest tenth of a meter how long is a side of the playground.
Let F be a finite field. Prove that F[x] contains infinitely many primes. (note that over an infinite field the polynomials of degree 1 are an infinite set of primes in the ring of polynomials).
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