Algebraic factors, how to find ... and ... use them

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Pàgina 58 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Pàgina 63 - ... £a. What had they at first ? (34.) A cistern can be filled in 6 hours by one pipe, and in 8 hours by another. It was filled in 5 hours by the two running partly together and partly separately. The time they ran together was two-thirds of the time they ran separately. How long did each ran f (35.
Pàgina 62 - Divide 36 into two such parts, that the square of the greater shall exceed the square of the less by 360.
Pàgina 65 - Two men start at the same time to meet each other from towns which are 25 miles apart. One takes 18 minutes longer than the other to walk a mile, and they meet in 5 hours. How fast does each walk ? Let x = the number of minutes it takes the first man to walk a mile.
Pàgina 57 - A cistern has a supply cock, and also a three-way cock which can be used either for supply or discharge at pleasure. When both are used to fill it, it fills in half an hour. When the three-way cock is used to draw off, the other fills it in an hour and a half, notwithstanding the discharge going...
Pàgina 3 - As a rule, this branch of the subject is hurried over with but a slight notice, both in books and in the schoolroom. Nothing could be more injudicious, since a true conception of factorial analysis enables the student to traverse, with the greatest ease, branches of Algebra which in other cases prove veritable Sloughs of Despond.
Pàgina 62 - A railway train travels 288 miles at a certain average speed, and, if the speed were 4 miles an hour greater, would perform the journey in an hour less. What is the...
Pàgina 63 - A number of persons undertake to erect a public building, contributing equally to the cost, which is £5002.
Pàgina 60 - A carpet, in shape a rectangle, has an area of 315 square feet ; if a piece is taken off so as to reduce its width by 3...
Pàgina 65 - Prove that any trinomial is a complete square, if the square of the middle term is equal to four times the product of the first and last terms.

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