The Competitor, Volumes 1-21882 |
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Page 13
... root of ( 1 + x ) , by the ordinary process for the extraction of roots in algebra . 5. Solve for x , for y , and for z , from the three simple equations : - 5y + 62-7x = 57 , 5z + 6x - 7y = 43 , 5x + 6y - 7x = 32 . 6. Show by any ...
... root of ( 1 + x ) , by the ordinary process for the extraction of roots in algebra . 5. Solve for x , for y , and for z , from the three simple equations : - 5y + 62-7x = 57 , 5z + 6x - 7y = 43 , 5x + 6y - 7x = 32 . 6. Show by any ...
Page 14
... root , then always ( a , b , ing accounts , viz . : - + ba , -2hh , ) = 4 ( a , b , —h3 ) ( a , b , —h23 ) . 8. Clear of radicals , each separately by itself , the equations , x + y * + z1 = 0 and xz + y * + z3 = 0 ; and arrange ...
... root , then always ( a , b , ing accounts , viz . : - + ba , -2hh , ) = 4 ( a , b , —h3 ) ( a , b , —h23 ) . 8. Clear of radicals , each separately by itself , the equations , x + y * + z1 = 0 and xz + y * + z3 = 0 ; and arrange ...
Page 16
... root of 967-068262369 . 3. Find the value of 6.45 tons + 8-60714285 of 168 lbs . - 18.09375 cwt . 4. Find by duodecimals the volume of a cubical tank whose edge is 3 yds . 2ft . 6 ins . Express the result in cubic feet and cubic inches ...
... root of 967-068262369 . 3. Find the value of 6.45 tons + 8-60714285 of 168 lbs . - 18.09375 cwt . 4. Find by duodecimals the volume of a cubical tank whose edge is 3 yds . 2ft . 6 ins . Express the result in cubic feet and cubic inches ...
Page 18
... roots . .. 16b2c- ( a - b2 - 4c22 = [ 4bc + ( a2 — b2 - 4c2 ) ] [ 4bc- ( a2- b2 — 4c2 ) ] = ( a2 - b2 + 4bc - 4c2 ) ( 4bc - a2 + b2 + 4c2 ) = { a- ( b - 2c ) } { ( b + 2c ) 3 — a2 } = ( a + b - 2c ) ( a + 2c - b ) ( a + b + 2c ) ( b + 2c ...
... roots . .. 16b2c- ( a - b2 - 4c22 = [ 4bc + ( a2 — b2 - 4c2 ) ] [ 4bc- ( a2- b2 — 4c2 ) ] = ( a2 - b2 + 4bc - 4c2 ) ( 4bc - a2 + b2 + 4c2 ) = { a- ( b - 2c ) } { ( b + 2c ) 3 — a2 } = ( a + b - 2c ) ( a + 2c - b ) ( a + b + 2c ) ( b + 2c ...
Page 22
... root of 1+ is identical with expanding ( 1 + x ) in a series . Thus ( 1 + x ) = 1 + nx + n ( n - 1 ) x + 1.2 + n ( n − 1 ) ( n − 2 ) 1.2.8 - · 203 + . n ( n − 1 ) ( n − 2 ) ( n − 8 ) ( n −4 ) 1. 2. 3. 4. 5 - - n ( n − 1 ) ( n − 2 ) ...
... root of 1+ is identical with expanding ( 1 + x ) in a series . Thus ( 1 + x ) = 1 + nx + n ( n - 1 ) x + 1.2 + n ( n − 1 ) ( n − 2 ) 1.2.8 - · 203 + . n ( n − 1 ) ( n − 2 ) ( n − 8 ) ( n −4 ) 1. 2. 3. 4. 5 - - n ( n − 1 ) ( n − 2 ) ...
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Popular passages
Page 60 - Then ensued a scene of woe, the like of which no eye had seen, no heart conceived, and which no tongue can adequately tell. All the horrors of war before known or heard of, were mercy to that new havoc. A storm of universal fire blasted every field, consumed every house, destroyed every temple.
Page 60 - ... blasted every field, consumed every house, destroyed every temple. The miserable inhabitants flying from their flaming villages in part were slaughtered ; others, without regard to sex, to age, to the respect of rank or sacredness of function, fathers torn from children, husbands from wives, enveloped in a whirlwind of cavalry, and amidst the goading spears of drivers and the trampling of pursuing horses, were swept into captivity in an unknown and hostile land. Those who were able to evade this...
Page 60 - Having terminated his disputes with every enemy, and every rival, who buried their mutual animosities in their common detestation against the creditors of the nabob...
Page 230 - All murder'd: for within the hollow crown That rounds the mortal temples of a king Keeps Death his court, and there the antic sits, Scoffing his state and grinning at his pomp...
Page 225 - If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle.
Page 402 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Page 456 - Howe'er it be, it seems to me, Tis only noble to be good. Kind hearts are more than coronets, And simple faith than Norman blood.
Page 124 - ... may be indicted, tried, convicted, and punished in all respects as if he were a principal felon.
Page 128 - ... acts both of charity and generosity. It was a frugality founded not upon avarice, but upon the love of independency. The extreme gentleness of his nature never weakened either the firmness of his mind or the steadiness of his resolutions.
Page 239 - A married woman shall, in accordance with the provisions of this Act, be capable of acquiring, holding, and disposing by will or otherwise, of any real or personal property as her separate property, in the same manner as if she were a feme sole, without the intervention of any trustee.