Solutions of the problems and riders proposed in the Senate-house examination for 1854, by the moderators and examiners |
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Side 1
... shew that DE touches the circle . If DE , fig . ( 1 ) , be not a tangent , from D draw DFG to touch the circle . Then , since ( Euc . I. 47 ) BD is equal to DF , and CG to GF ; therefore , BD and CG are together equal to DG . But BD and ...
... shew that DE touches the circle . If DE , fig . ( 1 ) , be not a tangent , from D draw DFG to touch the circle . Then , since ( Euc . I. 47 ) BD is equal to DF , and CG to GF ; therefore , BD and CG are together equal to DG . But BD and ...
Side 2
... b , c be positive integers , geometrical progression , shew that a , geometrical progression . 2 1 and a , b , c be in 1 2 b , c are also in 2 1 2 Since a , b , c are 2 [ Jan. 5 , SENATE - HOUSE PROBLEMS AND RIDERS .
... b , c be positive integers , geometrical progression , shew that a , geometrical progression . 2 1 and a , b , c be in 1 2 b , c are also in 2 1 2 Since a , b , c are 2 [ Jan. 5 , SENATE - HOUSE PROBLEMS AND RIDERS .
Side 5
... shew that the least value of tan A + tan'B + tan2C is 1 . 0 = cot ( A + B + C ) = 1 - tan A tan B - tan B tan C - tan Ctan A tan A + tan B + tan C – tan A tan B tan C ' = 1 . therefore tan A tan B + tan B tan C + tan C tan A But since ...
... shew that the least value of tan A + tan'B + tan2C is 1 . 0 = cot ( A + B + C ) = 1 - tan A tan B - tan B tan C - tan Ctan A tan A + tan B + tan C – tan A tan B tan C ' = 1 . therefore tan A tan B + tan B tan C + tan C tan A But since ...
Side 9
... and let V , V , V , be the velocities of A after impact on these suppositions respectively : shew that 1 2 3 - V1 = { V1 , and that V1 = 7V1 . 2 19 3 Let be the velocity of each ball before impact . 1-4 . ] 9 PROBLEMS .
... and let V , V , V , be the velocities of A after impact on these suppositions respectively : shew that 1 2 3 - V1 = { V1 , and that V1 = 7V1 . 2 19 3 Let be the velocity of each ball before impact . 1-4 . ] 9 PROBLEMS .
Side 10
... shew that , if , when are ground , achromatism is nearly but not quite secured , the de be remedied by slightly separating the lenses . The refractive indices , corresponding to the letters D and orange and blue , for certain kinds of ...
... shew that , if , when are ground , achromatism is nearly but not quite secured , the de be remedied by slightly separating the lenses . The refractive indices , corresponding to the letters D and orange and blue , for certain kinds of ...
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Solutions of the Problems and Riders Proposed in the Senate-House ... Exam Papers Cambridge Univ Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
angular velocity asymptote axes Cambridge catenary centre of force centre of gravity chord circle cloth conic section constant cos² cose cosẞ cota cotß Crown 8vo curvature curve cylinder denoting described diameter direction distance dx dy dy dx ecliptic elastic ellipse equal equation equilibrium Fellow of St fixed point fluid geometrical progression given Hence horizontal hyperbola inclined plane intersection lamina latus rectum length locus longitude M.A. Fellow major axis middle point motion orbit parabola parallel particle passing perpendicular position pressure projection prove radius refraction right angles ring shew sides Similarly sine sino sinẞ straight line string Supposing surface tana tangent tanß triangle Trinity College tube V₁ vertical
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