Question Number 18448 by ankit kumar sharma last updated on 21/Jul/17 $$\mathrm{If}\:\:{a},\:{b},\:{c},\:{d}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:\:{a}^{{x}} =\:{b}^{{y}} =\:{c}^{{z}} =\:{d}^{{u}} , \\ $$$$\mathrm{then}\:{x},\:{y},\:{z},\:{u}\:\mathrm{are}\:\mathrm{in} \\ $$ Answered by Tinkutara last updated…
Question Number 18282 by aamaguestt last updated on 17/Jul/17 $$\mathrm{Two}\:\mathrm{trains}\:\mathrm{150}\:\mathrm{m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{250}\:\mathrm{m}\:\mathrm{long} \\ $$$$\mathrm{are}\:\mathrm{travelling}\:\mathrm{at}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{30}\:\mathrm{kmph} \\ $$$$\mathrm{and}\:\mathrm{33}\:\mathrm{kmph}\:\mathrm{respectively}\:\mathrm{on}\:\mathrm{parallel} \\ $$$$\mathrm{tracks}\:\mathrm{in}\:\mathrm{opposite}\:\mathrm{directions}.\:\mathrm{What}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{time}\:\mathrm{taken}\:\mathrm{by}\:\mathrm{these}\:\mathrm{trains}\:\mathrm{to}\:\mathrm{cross} \\ $$$$\mathrm{each}\:\mathrm{other}\:\mathrm{completely}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{moment}\:\mathrm{they}\:\mathrm{meet}? \\ $$ Terms…
Question Number 18279 by aamaguestt last updated on 17/Jul/17 $$\mathrm{In}\:\mathrm{an}\:\mathrm{1800}\:\mathrm{m}\:\mathrm{race},\:\mathrm{P}\:\mathrm{beats}\:\mathrm{Q}\:\mathrm{by}\:\mathrm{50}\: \\ $$$$\mathrm{seconds}.\:\mathrm{In}\:\mathrm{the}\:\mathrm{same}\:\mathrm{race},\:\mathrm{Q}\:\mathrm{beats}\:\mathrm{R}\:\mathrm{by} \\ $$$$\mathrm{40}\:\mathrm{seconds}.\:\mathrm{If}\:\mathrm{P}\:\mathrm{beats}\:\mathrm{R}\:\mathrm{by}\:\mathrm{450}\:\mathrm{m},\:\mathrm{by}\: \\ $$$$\mathrm{what}\:\mathrm{distance}\:\mathrm{does}\:\mathrm{P}\:\mathrm{beat}\:\mathrm{Q}\:?\left(\mathrm{in}\:\mathrm{m}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 18207 by potata8 last updated on 16/Jul/17 $$\mathrm{If}\:\frac{\mathrm{3}+\mathrm{5}+\mathrm{7}+…+{n}\:\mathrm{terms}}{\mathrm{5}+\mathrm{8}+\mathrm{11}+…+\mathrm{10}\:\mathrm{terms}}\:=\:\mathrm{7},\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{n}\:\mathrm{is} \\ $$ Answered by Tinkutara last updated on 17/Jul/17 $$\mathrm{3}\:+\:\mathrm{5}\:+\:\mathrm{7}\:+\:…\:+\:\left({n}\:\mathrm{terms}\right)\:=\:\frac{{n}}{\mathrm{2}}\left[\mathrm{6}\:+\:\left({n}\:−\:\mathrm{1}\right)\mathrm{2}\right] \\ $$$$=\:\frac{{n}}{\mathrm{2}}\left(\mathrm{2}{n}\:+\:\mathrm{4}\right)\:=\:{n}\left({n}\:+\:\mathrm{2}\right) \\…
Question Number 18168 by allizzwell last updated on 16/Jul/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{expansion}\:\mathrm{of}\:\mathrm{the}\:\left(\mathrm{1}+{x}\right)^{\mathrm{2}{n}+\mathrm{2}} \:\mathrm{is}\:{p}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{coefficients}\:\mathrm{of}\:\mathrm{middle}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{1}+{x}\right)^{\mathrm{2}{n}+\mathrm{1}} \:\mathrm{are}\:{q}\:\mathrm{and}\:{r},\:\mathrm{then} \\ $$ Answered by ajfour last updated…
Question Number 83226 by 09658867628 last updated on 28/Feb/20 $$\:\underset{\:\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{2}{x}\:\mathrm{cos}\:\alpha+\mathrm{1}}\:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 29/Feb/20 $$\left.{I}\:=\int_{\mathrm{0}}…
Question Number 83225 by 09658867628 last updated on 28/Feb/20 $$\:\underset{\:\mathrm{0}} {\overset{\mathrm{100}} {\int}}\:\mathrm{sin}\:\left({x}−\left[{x}\right]\right)\pi\:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 29/Feb/20 $${A}\:=\sum_{{n}=\mathrm{0}} ^{\mathrm{99}}…
Question Number 83146 by 09658867628 last updated on 28/Feb/20 $$\underset{\:\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\:\frac{\sqrt{\mathrm{cot}\:{x}}}{\:\sqrt{\mathrm{cot}\:{x}}\:+\:\sqrt{\mathrm{tan}\:{x}}}\:{dx}\:= \\ $$ Answered by Kunal12588 last updated on 28/Feb/20 $${I}=\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \frac{\sqrt{{cot}\:{x}}}{\:\sqrt{{cot}\:{x}}+\sqrt{{tan}\:{x}}}{dx} \\…
Question Number 83145 by 09658867628 last updated on 28/Feb/20 $$\:\underset{\:\mathrm{1}} {\overset{\mathrm{4}} {\int}}\:{e}^{\sqrt{{x}}} \:{dx}\:= \\ $$ Commented by mathmax by abdo last updated on 28/Feb/20 $${I}=\int_{\mathrm{1}}…
Question Number 83078 by mhmd last updated on 27/Feb/20 $$\mathrm{If}\:\:\:{I}_{\mathrm{1}} =\underset{{e}} {\overset{{e}^{\mathrm{2}} } {\int}}\:\frac{{dx}}{\mathrm{log}\:{x}}\:\:\mathrm{and}\:\:{I}_{\mathrm{2}} =\:\underset{\:\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\frac{{e}^{{x}} }{{x}}\:{dx},\:\mathrm{then} \\ $$ Commented by mathmax by abdo…