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Author: Tinku Tara

the-particular-integral-of-the-differential-equation-f-D-y-e-ax-where-f-D-D-a-g-D-g-a-0-is-

Question Number 23522 by gopikrishnan005@gmail.com last updated on 01/Nov/17 $${the}\:{particular}\:{integral}\:{of}\:{the}\:{differential}\:{equation}\:{f}\left({D}\right){y}={e}^{{ax}} {where}\:{f}\left({D}\right)=\left({D}−{a}\right){g}\left({D}\right),{g}\left({a}\right)\neq\mathrm{0}\:{is} \\ $$ Commented by 1kanika# last updated on 26/Nov/17 $$\mathrm{xe}\Lambda\mathrm{ax}/\mathrm{g}\left(\mathrm{a}\right) \\ $$ Terms of…

A-wooden-block-of-mass-10-gm-is-dropped-from-the-top-of-a-tower-100-m-high-Simultaneously-a-bullet-of-mass-10-gm-is-fired-from-the-foot-of-the-tower-vertically-upwards-with-a-velocity-of-100-m-sec-

Question Number 23520 by Tinkutara last updated on 01/Nov/17 $$\mathrm{A}\:\mathrm{wooden}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{10}\:\mathrm{gm}\:\mathrm{is} \\ $$$$\mathrm{dropped}\:\mathrm{from}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{100}\:\mathrm{m} \\ $$$$\mathrm{high}.\:\mathrm{Simultaneously},\:\mathrm{a}\:\mathrm{bullet}\:\mathrm{of}\:\mathrm{mass} \\ $$$$\mathrm{10}\:\mathrm{gm}\:\mathrm{is}\:\mathrm{fired}\:\mathrm{from}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tower} \\ $$$$\mathrm{vertically}\:\mathrm{upwards}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of} \\ $$$$\mathrm{100}\:\mathrm{m}/\mathrm{sec}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{bullet}\:\mathrm{is}\:\mathrm{embedded}\:\mathrm{in} \\ $$$$\mathrm{it},\:\mathrm{how}\:\mathrm{high}\:\mathrm{will}\:\mathrm{it}\:\mathrm{rise}\:\mathrm{above}\:\mathrm{the}\:\mathrm{tower} \\ $$$$\mathrm{before}\:\mathrm{it}\:\mathrm{starts}\:\mathrm{falling}?\:\left(\mathrm{Consider}\:{g}\:=\right. \\…

A-ball-of-mass-1-kg-moving-with-velocity-3-m-s-collides-with-spring-of-natural-length-2-m-and-force-constant-144-N-m-What-will-be-length-of-compressed-spring-

Question Number 23518 by Tinkutara last updated on 01/Nov/17 $$\mathrm{A}\:\mathrm{ball}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity} \\ $$$$\mathrm{3}\:\mathrm{m}/\mathrm{s}\:\mathrm{collides}\:\mathrm{with}\:\mathrm{spring}\:\mathrm{of}\:\mathrm{natural} \\ $$$$\mathrm{length}\:\mathrm{2}\:\mathrm{m}\:\mathrm{and}\:\mathrm{force}\:\mathrm{constant}\:\mathrm{144}\:\mathrm{N}/\mathrm{m}. \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{length}\:\mathrm{of}\:\mathrm{compressed} \\ $$$$\mathrm{spring}? \\ $$ Commented by Tinkutara last updated…

0-pi-2-x-tan-x-dx-

Question Number 89052 by M±th+et£s last updated on 15/Apr/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}}{{tan}\left({x}\right)}{dx} \\ $$ Commented by abdomathmax last updated on 15/Apr/20 $${I}\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{{tanx}}{dx}\:\Rightarrow{I}\:=_{{tanx}={t}} \:\:\:\int_{\mathrm{0}}…

Question-154586

Question Number 154586 by Dadoubleny last updated on 19/Sep/21 Answered by ARUNG_Brandon_MBU last updated on 19/Sep/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\left({n}+\mathrm{1}\right)^{\alpha} −{n}^{\alpha} \right) \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left({n}^{\alpha} \left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{\alpha} −{n}^{\alpha}…

cos-x-sin-x-4-5-5sin-x-

Question Number 89047 by jagoll last updated on 15/Apr/20 $$\mathrm{cos}\:{x}+\mathrm{sin}\:{x}=\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\mathrm{5sin}\:{x}\:=\:? \\ $$ Commented by john santu last updated on 15/Apr/20 $$\pm\:\sqrt{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} {x}}\:=\:\frac{\mathrm{4}}{\mathrm{5}}−\mathrm{sin}\:{x} \\…