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(a) A farmer has a field bordering a straight river. He wants to design a rectangular plot for an organic crop with the river acting as a natural border. If 400 feet of fencing will be used on the three other sides, what should the dimensions of the plot be if its area is to be maximized?
(b) What are the dimensions if the river side is also to be fenced?
Determine whether the series is convergent or divergent: 9/(n(n+2)) from n=1 to infinity.
the sampp 500 index tracks the overall movement of the stock market by considering the stock prices of 500 large
a function is defined as a correspondence between two sets of numbers. what does the notation fx
kelly fisher has a total of $30,000 invested in two municiapl bonds that have yields of 8% and 10% interest per year. If the interest Kelly recieves from the bonds in a year is $2640, how much does she have invested in each bond?
Let P be a polyhedron with at least one extreme point. Is it possible to express an arbitrary element of P as a convex combination of its extreme points plus a nonnegative multiple of a single extreme ray?
A moving body is opposed by a force per unit mass of value cx and resistance per unit mass value of bv^2 where x and v are the displacement and velocity of the particle at that instant. Determine the velocity of the particle in terms of x, if it s..
A tree on a hillside casts a shadow 206 ft down the hill. If the angle of inclination of the hillside is to the horizontal and the angle of elevation of the sun is , find the height of the tree. Please round your answers to the nearest whole.
Construct a finite-state machine with output that produces an output of 1 if the bit string read so far as input contains four or more 1s. Then construct a deterministic finite-state automaton that recognizes this set.
A rectangular field measure 212 yards by 265 yards. What is the distance from one corner of the field to the opposite corner of the field?
A chain of convenience stores tested a display for a new snack product by placing the display in four different locations in various stores;
Find the volume of the solid generated by revolving the following region about the y-axis. The region in the first quadrant bounded above by the parobola y=x^2, below by the x-axis, and on the right by the line x=3.
Given the same conditions in the initial question, how long will it take Per Capita GDP to double if the population grows at 2%?
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