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a-particle-is-projected-from-a-point-at-a-height-3h-metres-above-a-horizontal-play-ground-the-direction-of-the-projectile-makes-an-angle-with-the-horizontal-through-the-point-of-projection-show-t

Question Number 91946 by Rio Michael last updated on 03/May/20 $$\mathrm{a}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{projected}\:\mathrm{from}\:\mathrm{a}\:\mathrm{point}\:\mathrm{at}\:\mathrm{a}\:\mathrm{height}\:\mathrm{3}{h}\:\mathrm{metres}\:\mathrm{above}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{play}\:\mathrm{ground}.\:\mathrm{the}\:\mathrm{direction}\:\mathrm{of}\:\mathrm{the}\:\mathrm{projectile}\:\mathrm{makes}\:\mathrm{an}\:\mathrm{angle}\:\alpha\:\mathrm{with}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{projection}.\:\:\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{th}\:\mathrm{greatest} \\ $$$$\mathrm{height}\:\mathrm{reached}\:\mathrm{above}\:\mathrm{the}\:\mathrm{point}\:\mathrm{lc}\:\mathrm{projection}\:\mathrm{is}\:{h}\:\mathrm{metres},\:\mathrm{then}\:\mathrm{the}\:\mathrm{horizontal} \\ $$$$\mathrm{distance}\:\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{before}\:\mathrm{striking}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{6}{h}\:\mathrm{cot}\alpha\:\mathrm{metres}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{vertical}\:\mathrm{and}\:\mathrm{horizontal}\:\mathrm{component}\:\mathrm{of}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{particle}\:\mathrm{just} \\ $$$$\mathrm{before}\:\mathrm{it}\:\mathrm{hits}\:\mathrm{the}\:\mathrm{ground}. \\ $$…

lim-x-0-cos-1-x-

Question Number 91930 by Ozoda last updated on 03/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}cos}\:\frac{\mathrm{1}}{{x}}= \\ $$ Commented by mr W last updated on 03/May/20 $${when}\:{x}\rightarrow\mathrm{0},\:\frac{\mathrm{1}}{{x}}\rightarrow\infty,\:\mathrm{cos}\:\frac{\mathrm{1}}{{x}}\:{doesn}'{t} \\ $$$${approach}\:{a}\:{certain}\:{value},\:{therefore} \\…

0-1-ln-x-dx-

Question Number 91931 by  M±th+et+s last updated on 03/May/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\Gamma\left({x}\right)\right)\:{dx} \\ $$ Commented by mathmax by abdo last updated on 04/May/20 $${we}\:{have}\:\Gamma\left({x}\right).\Gamma\left(\mathrm{1}−{x}\right)\:=\frac{\pi}{{sin}\left(\pi{x}\right)}\:\Rightarrow \\…

Question-26354

Question Number 26354 by Tinkutara last updated on 24/Dec/17 Answered by ajfour last updated on 24/Dec/17 $${K}=\frac{\mathrm{1}}{\mathrm{2}}{mv}^{\mathrm{2}} \\ $$$$\frac{{dK}}{{dx}}\:=\frac{{mvdv}}{{dx}}={ma} \\ $$$${a}=\frac{\mathrm{1}}{{m}}\left(\frac{{dK}}{{dx}}\right)\:\:\:\:{hence}\:\left(\mathrm{4}\right)\:{is}\:{correct}. \\ $$ Commented by…

x-x-9-x-3-x-7-10-

Question Number 26352 by sanjib bibhar last updated on 24/Dec/17 $${x}\left({x}+\mathrm{9}\right)=\left({x}+\mathrm{3}\right)\left({x}+\mathrm{7}\right)−\mathrm{10} \\ $$ Answered by jota@ last updated on 24/Dec/17 $$\mathrm{0}={x}+\mathrm{21}−\mathrm{10} \\ $$$${x}=−\mathrm{11}. \\ $$…

A-small-particle-moving-with-a-uniform-acceleration-a-covers-distances-X-and-Y-in-the-first-two-equal-and-consecutive-intervals-of-time-t-Show-that-a-Y-X-t-2-

Question Number 26329 by tawa tawa last updated on 24/Dec/17 $$\mathrm{A}\:\mathrm{small}\:\mathrm{particle}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{acceleration}\:\mathrm{a}\:\mathrm{covers}\:\mathrm{distances}\: \\ $$$$\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{and}\:\mathrm{consecutive}\:\mathrm{intervals}\:\mathrm{of}\:\mathrm{time}\:\mathrm{t}.\:\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{a}\:=\:\frac{\mathrm{Y}\:−\:\mathrm{X}}{\mathrm{t}^{\mathrm{2}} } \\ $$ Answered by ajfour last updated on 24/Dec/17…