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You have 600 yards of fencing to build a rectanglular fence. You use a long straight wall to form one side to save fencing. What is the maximum possible area that can be enclosed?
The group of even permutations of n symbols is denoted by A_n and is called the alternating group of degree n. Show that A_8 contains an element of order 15.
For a fish swimming at a speed v relative to the water, the energy expenditure per unit time is proportional to v^3. It is believed that migrating fish try to minimize the total energy required to swim a fixed distance.
You are told that a line is tangent to the circle centred at (3,2) with radius 2. If the tangent line and circle intersect at the point (4, 2+ sqrt(3)) find the equation of the tangent.
If G = and H is a subgroup of G, show that H is the normal subgroup of G if and only if x^-1Hx contained in H for all x belonging to X. ALSO show that is normal in G if and only if gXg^-1 contained in for all g belonging to G.
Find all the xed points, and study their stability and Draw the phase portrait of the system, as well as the graphs of the solutions in all relevant cases.
Find the product as a sum containing only sines or cosines
Using minimax regret criterion, what decision should be made by the decision maker?
A printer has a contract to print 100,000 invitations for a political candidate. He can run the invitations by using any number of metal printing plates from 1 to 20 on his press.
If we draw one card from a 52 card deck, what is the probability that it is red? That it is a diamond? That it is an ace? That it is the ace of diamonds? Find Gambling Probability
Probability of Lamp Failure, A lamp has two bulbs, each of a type with an average lifetime of 6 hours. The probability density function for the lifetime of a bulb
Give an example of a nonlinear system of two equations in two unknowns having: Based on your work, how would you devise a method for finding such a system having exactly n solutions?
Evaluate the area of the rectangle - Write a polynomial that represents the area.
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