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an oil refinery is located at point R on the north bank of a straight river that is 2 km wide. a pipeline is to be constructed from the refinery to storage tanks located at point T on the south bank of the river 6 km east of the refinery. the cost of laying pipe is $400,000/km to run pipe over land to a point P on the north bank of the river and then $800,000/km to run pipe under the river to the tanks. where should the point P be located.
What is the difference between domain and range? Provide an example and identify the domain and range.
I get the critical points are(0,0) and(-2^1/5, 4^1/5). Then I get det(0,0)=2 and det(-2^1/5, 4^1/5)=-10, so index of the system is -8 and the index of periodic orbit is 1, so there's no periodic orbit.
a moving company wishes to design an open-top-box with square base whose volume is exactly 32 cubic feet. find the dimensions of the box requiring the least amount of materials.
A motorboat travels 469km in 7 hours going upstream. It travels 493km going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?
Solve the following linear, first-order differential equations and ensure that the initial conditions are satisfied. Show whether or not the steady-state solutions are stable.
the everton college store paid $1824 for an order of 52 calculators. The store paid $ 8 for each scientific calculator. The others, all graphing calculators, cost the store $ 52 each. How many of each type of calculator was ordered?
Distributive Laws (I) Prove that A intersection (B union C) = (A intersection B) union (A intersection C)
Apply DeMoivre's Theorem to solve the following: any angles that are multiples of pi/6, pi/4, pi/3, pi/2 or pi must be converted back into regular complex form!
Of the students at a certain college, 50% regularly attend the football games, 40% are first-year students, and 40% are upper-class students who do not regularly attend football games. Suppose that a student is selected at random.
In a survey of 250 dancers, 167 knew the ballroom dances, 140 knew the Latin dances, and 106 knew the swing dances. Of these, 65 knew the ballroom and swing dances
Let m'(A) = inf sum of |M_i| where i is from 1 to infinity, such that A is a subset of M_i. M_i's are disjoint.
Suppose A is an m×n matrix and B is the n×m matrix obtained by rotating A ninety degrees clockwise on paper ( not exactly a standard mathematical transformation!). Do A and B have the same singular values? Prove that the answer is yes or give a co..
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