A treatise on differential equations by George Boole

By George Boole

This Elibron Classics ebook is a facsimile reprint of a 1877 variation by way of Macmillan and Co., London.

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Aidan is considering a pond kit that is rated for 140 inches of goldfish. How many full-size fantail and common goldfish can be supported in this pond? Be sure to include the following in your response: • an equation that represents the question; • a table showing several combinations of numbers of full-size fantail and common goldfish that meet the pond rating limit; • a graph of all possible solutions. c. As the number of common goldfish in a pond increases, how will the number of fantail goldfish that can be supported in the pond change?

D. Make a conjecture about the symmetries of the graphs of functions of the form y = xn, where n is an odd integer. 12 From television sets and radios to X-rays, microwave, and wireless telephone signals, we are surrounded by the energy of electro-magnetic fields (EMF). As sources of EMF have become more common in our everyday lives, scientists have become concerned about possible health hazards caused by exposure to EMF. Data in the following table show patterns of EMF measurements (in a unit called milligauss) at various distances from the front and back of a television set and from a VCR.

A. Write a rule that shows how fund-raiser profit P depends on the number of customers c and the number of winners w. b. How does profit change as the number of customers increases? As the number of wins increases? c. If the basketball shooting game has 25 customers and 8 winners, it will earn a profit of $10. i. Find 4 other pairs of number of customers and number of winners that will result in profit for the game that is greater than 0. ii. Write an algebraic condition that describes all pairs (c, w) that will guarantee a positive profit for the game.

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