Algebraical Problems, Producing Simple and Quadratic Equations, with Their Solutions: Designed as an Introduction to the Higher Branches of AnalyticsDeighton & Sons, 1824 - 383 σελίδες |
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Σελίδα
... Quadratic is one which involves the square of the unknown quantity , and also the simple power and known ... both multiplied and divided by another , its value will not be altered . ( 17. ) Any quantity may be transposed from one side ...
... Quadratic is one which involves the square of the unknown quantity , and also the simple power and known ... both multiplied and divided by another , its value will not be altered . ( 17. ) Any quantity may be transposed from one side ...
Σελίδα
... both sides by that common divisor ; ax Thus , if ax2 - a2x = abx - a3b , each side is divisible by a2 , whence x = b . -- COR . 4. Hence also any term of an equation may be made a square , by multiplying all the terms of the equation by ...
... both sides by that common divisor ; ax Thus , if ax2 - a2x = abx - a3b , each side is divisible by a2 , whence x = b . -- COR . 4. Hence also any term of an equation may be made a square , by multiplying all the terms of the equation by ...
Σελίδα
... side of the equation which contains the unknown quantity be a perfect square , cube , or other power , by extracting the square root , cube root , & c . of both sides , the equation will be reduced to one of lower dimen- sions : Thus ...
... side of the equation which contains the unknown quantity be a perfect square , cube , or other power , by extracting the square root , cube root , & c . of both sides , the equation will be reduced to one of lower dimen- sions : Thus ...
Σελίδα
... squaring each side , x2 + √√x2 + 21 = x2 + 2x + 1 ; .. ( 17 . Cor . 3. ) √x2 + 21 = 2x + 1 , and ( 19 ) by squaring each side , x2 + 21 = 4x2 + 4x + 1 , which is free from surds . 3 And , if √a3x + √a3 x3 = c , ( 19 ) by cubing each ...
... squaring each side , x2 + √√x2 + 21 = x2 + 2x + 1 ; .. ( 17 . Cor . 3. ) √x2 + 21 = 2x + 1 , and ( 19 ) by squaring each side , x2 + 21 = 4x2 + 4x + 1 , which is free from surds . 3 And , if √a3x + √a3 x3 = c , ( 19 ) by cubing each ...
Σελίδα 2
... Quadratic is one which involves the square of the unknown quantity , and also the simple power and known ... both multiplied and divided by another , its value will not be altered . ( 17. ) Any quantity may be transposed from one side ...
... Quadratic is one which involves the square of the unknown quantity , and also the simple power and known ... both multiplied and divided by another , its value will not be altered . ( 17. ) Any quantity may be transposed from one side ...
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Algebraical Problems, Producing Simple and Quadratic Equations, With Their ... Miles Bland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A's money a²x² addition answer the conditions arithmetical progression brandy casks completing the square contained cost cube difference digits distance Divide the number equal quantities equation involving equation of fractions extracting the root extracting the square find the values gain gallons of brandy geometrical progression Given 3x Given x+y guineas least common multiple length less Let 2x Let the number multiplying every term number of acres number of days number of gallons number of miles number of pounds number of shillings number of yards paid pence pieces problem proportion quantity of brandy quotient received Required the number second equation sheep sherry sold square root squaring both sides Substituting this value subtraction third three numbers transposition travelled turkeys unknown quantity values of x wheat whence whole number wine xy²
Δημοφιλή αποσπάσματα
Σελίδα 18 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.
Σελίδα 354 - Each man received one third as many shillings as there were persons relieved ; and each woman received twice as many shillings as there were women more than men. The men received all together 18s.
Σελίδα 360 - From two places at a distance of 320 miles, two persons, A and B, set out at the same time to meet each other. A travelled 8 miles a day more than B, and the number of days in which they met was equal to half the number of miles B went in a day. How many miles did each travel, and how far per day ? 20.
Σελίδα 354 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the...
Σελίδα 358 - Is. ; for each of which I paid as many shillings per yard as there were yards in its side. Now had each of them cost as many shillings per yard as there were yards in a side of the other, I should have paid 17s.
Σελίδα 374 - A traveller set out from a certain place, and went 1 mile the first day, 3 the second, 5 the next, and so on, going every day 2 miles more than he had gone the preceding day. After he had been gone three days, a second sets out, and travels 12 miles the first day, 13 the second, and so on. In how many days will the second overtake the first?
Σελίδα 373 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Σελίδα 141 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.
Σελίδα 223 - A person bought some sheep for £. 72 ; and found that if he had bought 6 more for the same money, he would have paid £. 1 less for each. How many did he buy...