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(a) Prove that a closed k-form w on S^k is exact if and only if int_(S^k) w = 0. [Hint: dim H^k(S^k) = 1.](b) Conclude that the linear map int_(S^k): H^k(S^k) -> R is an isomorphism.Reference: Ex. 4.8.5 of Guillemin.
Compute the inverse of matrix A below, and use this to express A as a product of elementary matrices
construct a hypothetical 95 confidence interval for a hypothetical case of your choosing. use your own unique choice of
How many small screen televisions must be produced in a month in order to minimize the company's average cost? Show all steps and justify your answer.
the probability of passing english 0.72 and the probability of passing statistics 0.81and the probability of passing both 0.68. what is the probability of pasinng at least one subject or none.
One hundred stones are placed on the ground 3 feet apart, the first being 3 feet from a basket. If the basket and all of the stones are in a straight line, how far does a person travel who starts from the basket and brings the stones to it one by ..
Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 39 feet?
Give five interesting facts about group theory (or tensor calculus). Each one need only be 1 to just a few sentences - please list separately and under each fact provide any links to websites or pictures etc.
Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue.
given that a position vector of the points abc are 6i2j6k 2i3jk and14i16k respectively .find vector ab and ac and
Determine the volume of the solid of revolution formed when R is revolved about the x-axis. Use the washer method (and no other method) to dertermine the volume of the solid of revolution formed when R is revolved about the line x=7.
Task: Apply curve-fitting techniques and interpret the results. As such, your work will include doing scatterplots, determining the equation and graph of the curve on the scatterplot, finding the r^2 value,
Pronet has annual sales of $724 million from its 600 retail stores. Pronet can reduce its mail float by 2 days through the use of wire transfers. The annual cost of the wire transfers is expected to be $105,610.
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