Mathematical Problems and Examples, Arranged According to Subjects, from the Senate-House Examination Papers, 1821 to 1836 InclusiveW.P. Grant, 1836 - 335 sider |
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Resultat 1-5 av 100
Side 7
... Prove that log ( n + 1 ) - log n + 2 log ( 2n + 2 ) ( 2n + 1 ) 2 + log ( 2n + 1 ) 2 — I ' - 27. A and B can do a piece of work in m days ; B and C in n days : in what time can A and C do the same , it being sup- posed that A can do p ...
... Prove that log ( n + 1 ) - log n + 2 log ( 2n + 2 ) ( 2n + 1 ) 2 + log ( 2n + 1 ) 2 — I ' - 27. A and B can do a piece of work in m days ; B and C in n days : in what time can A and C do the same , it being sup- posed that A can do p ...
Side 8
... Prove that ( Aa + Bb + Cc + . ) ( Aa2 + Bb2 + Cc2 + + - - AC ( a -- c ) 2 — BC ( b — c ) 2 – · · • · · • · . ) 2 ( A + B + C . ) = - AB ( a - b ) 2 40. A and B are at play together , and the latter having lost p stakes , is determined ...
... Prove that ( Aa + Bb + Cc + . ) ( Aa2 + Bb2 + Cc2 + + - - AC ( a -- c ) 2 — BC ( b — c ) 2 – · · • · · • · . ) 2 ( A + B + C . ) = - AB ( a - b ) 2 40. A and B are at play together , and the latter having lost p stakes , is determined ...
Side 9
... Prove that log x = n ( x ” — 1 ) nearly , when ʼn is very great . 53. If Nnth term of the expansion of a * , determine n when the series reckoned from that term begins to converge ; and shew that the sum of all the terms which follow N ...
... Prove that log x = n ( x ” — 1 ) nearly , when ʼn is very great . 53. If Nnth term of the expansion of a * , determine n when the series reckoned from that term begins to converge ; and shew that the sum of all the terms which follow N ...
Side 11
... Prove that 1 , 3 , 5 , 7 , .... is the only arithmetical pro- gression beginning from unity , in which the sum of the first half of any even number of terms has to the sum of the second half the same constant ratio ; and find that ratio ...
... Prove that 1 , 3 , 5 , 7 , .... is the only arithmetical pro- gression beginning from unity , in which the sum of the first half of any even number of terms has to the sum of the second half the same constant ratio ; and find that ratio ...
Side 12
... prove that the equated time of payment is expressed by P + P PP2 2 1 P1 + P2 ( P1 + P2 ) 2 ( t1 — të ) 2 r , very nearly , 2 where r is the interest of £ 1 . for 1 year . 82. Find the least whole numbers which satisfy the equation 83. Prove ...
... prove that the equated time of payment is expressed by P + P PP2 2 1 P1 + P2 ( P1 + P2 ) 2 ( t1 — të ) 2 r , very nearly , 2 where r is the interest of £ 1 . for 1 year . 82. Find the least whole numbers which satisfy the equation 83. Prove ...
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Mathematical Problems and Examples: Arranged According to Subjects, from the ... University of Cambridge Uten tilgangsbegrensning - 1837 |
Mathematical Problems and Examples: Arranged According to Subjects, from the ... Uten tilgangsbegrensning - 1837 |
Mathematical Problems and Examples: Arranged According to Subjects, From the ... University of Cambridge Ingen forhåndsvisning tilgjengelig - 2023 |
Vanlige uttrykk og setninger
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Populære avsnitt
Side 3 - ... cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 280 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Side 126 - If two straight lines meeting one another, be parallel to two straight lines which also meet one another, but are not in the same plane with the first two : the plane which passes through the first two is parallel to the plane passing through the others.
Side 2 - IN right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle...
Side 2 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles.
Side 255 - If a body be projected from a given point in a given direction with a given velocity...
Side 4 - If a solid angle be contained by three plane angles, any two of them are greater than the third.
Side 157 - To find the magnitude, direction, and point of application of the resultant of any number of parallel forces acting on a rigid body in one plane.
Side 7 - A and B can do a piece of work in m days, B and C in n days, and C and A in p days. In what time can each alone jjerform the work ? 39.
Side 314 - ... varies inversely as the square of the distance of the particle from the centre.