Question Number 24428 by dhandhaliyachandra@gmail.Com last updated on 17/Nov/17 $$\mathrm{In}\:\mathrm{a}\:\mathrm{race}\:\mathrm{on}\:\mathrm{a}\:\mathrm{track}\:\:\mathrm{of}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{length}, \\ $$$$\mathrm{A}\:\:\mathrm{beats}\:\mathrm{B}\:\mathrm{by}\:\mathrm{20}\:\mathrm{m}.\:\mathrm{When}\:\mathrm{A}\:\mathrm{was}\:\mathrm{10}\:\mathrm{m} \\ $$$$\mathrm{ahead}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mid}−\mathrm{point}\:\mathrm{of}\:\mathrm{the}\:\mathrm{track}\:\mathrm{B} \\ $$$$\mathrm{was}\:\mathrm{2}\:\mathrm{m}\:\mathrm{behind}\:\mathrm{it}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{track}\:\left(\mathrm{in}\:\mathrm{m}\right). \\ $$ Answered by ajfour last updated…
Question Number 24426 by dhandhaliyachandra@gmail.Com last updated on 17/Nov/17 $$\mathrm{A}\:\mathrm{number}\:\mathrm{is}\:\mathrm{multiplied}\:\mathrm{by}\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{times} \\ $$$$\mathrm{itself}\:\mathrm{and}\:\mathrm{then}\:\mathrm{61}\:\mathrm{is}\:\mathrm{subtracted}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{product}\:\mathrm{obtained}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{final}\:\mathrm{result} \\ $$$$\mathrm{is}\:\mathrm{9200},\:\mathrm{then}\:\mathrm{the}\:\mathrm{number}\:\mathrm{is} \\ $$ Answered by ajfour last updated on 17/Nov/17…
Question Number 24417 by dhandhaliyachandra@gmail.Com last updated on 17/Nov/17 $$\mathrm{The}\:\mathrm{time}\:\mathrm{taken}\:\mathrm{by}\:\mathrm{a}\:\mathrm{train}\:{l}\:\mathrm{metres}\:\mathrm{long} \\ $$$$\mathrm{running}\:\mathrm{at}\:{x}\:\mathrm{km}/\mathrm{h}\:\mathrm{to}\:\mathrm{pass}\:\mathrm{a}\:\mathrm{man}\:\mathrm{who} \\ $$$$\mathrm{is}\:\mathrm{running}\:\mathrm{at}\:{y}\:\mathrm{km}/\mathrm{h}\:\mathrm{in}\:\mathrm{the}\:\mathrm{direction} \\ $$$$\mathrm{opposite}\:\mathrm{to}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{train}\:=\:\mathrm{The}\:\mathrm{time} \\ $$$$\mathrm{taken}\:\mathrm{to}\:\mathrm{cover}\:{l}\:\mathrm{metres}\:\mathrm{at}\:\_\_\_\_\_\:\mathrm{km}/\mathrm{h}. \\ $$ Answered by ajfour last updated…
Question Number 88882 by Zainal Arifin last updated on 13/Apr/20 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:\:{x}^{\mathrm{3}} \:\mathrm{in}\:\left(\sqrt{{x}^{\mathrm{5}} }\:+\frac{\mathrm{3}}{\:\sqrt{{x}^{\mathrm{3}} }}\right)^{\mathrm{6}} \:\:\mathrm{is} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 88872 by Zainal Arifin last updated on 13/Apr/20 $$\mathrm{The}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}\:\:\:{kx}+{y}+{z}=\mathrm{1}, \\ $$$${x}+{ky}+{z}={k}\:\:\:\mathrm{and}\:\:\:{x}+{y}+{kz}={k}^{\mathrm{2}} \:\mathrm{have} \\ $$$$\mathrm{no}\:\mathrm{solution}\:\mathrm{if}\:\:\:{k}\:\:\mathrm{equals} \\ $$ Commented by john santu last updated on…
Question Number 88681 by NicolasXd last updated on 12/Apr/20 $$\mathrm{If}\:\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{periodic}\:\mathrm{function},\:\mathrm{with} \\ $$$$\mathrm{period}\:{T},\:\mathrm{then} \\ $$ Commented by jagoll last updated on 12/Apr/20 $${then}\:\underset{\mathrm{0}} {\overset{{nT}} {\int}}\:{f}\left({x}+{mT}\right)\:{dx}\:=\:{n}\:\underset{\mathrm{0}} {\overset{{T}}…
Question Number 22871 by keshavnimgade85@gmail.com last updated on 23/Oct/17 $$\mathrm{If}\:\:{f}\left({n}\right)=\frac{\mathrm{1}}{{n}}\left[\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)…\left({n}+{n}\right)\right]^{\mathrm{1}/{n}} , \\ $$$$\mathrm{then}\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}{f}\left({n}\right)\:= \\ $$ Answered by ajfour last updated on 23/Oct/17 $${f}\left({n}\right)=\left[\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\left(\mathrm{1}+\frac{\mathrm{2}}{{n}}\right)…\left(\mathrm{1}+\frac{{n}}{{n}}\right)\right]^{\mathrm{1}/{n}} \\…
Question Number 22745 by Sahib singh last updated on 22/Oct/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{equation}\:\:\mathrm{log}_{\mathrm{101}} \mathrm{log}_{\mathrm{7}} \left(\sqrt{{x}+\mathrm{7}}+\sqrt{{x}}\right)=\mathrm{0}\:\mathrm{is} \\ $$ Answered by mrW1 last updated on 22/Oct/17 $$\mathrm{log}_{\mathrm{101}}…
Question Number 88210 by bagjamath last updated on 09/Apr/20 $$\mathrm{If}\:{f}\left({x}\right)=\begin{cases}{\mathrm{1}−{x},\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}}\\{\mathrm{0},\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:\:\:\:}\\{\left(\mathrm{2}−{x}\right)^{\mathrm{2}} ,\:\:\:\mathrm{2}\leqslant{x}\leqslant\mathrm{3}}\end{cases}\:\mathrm{and}\: \\ $$$$\phi\left({x}\right)=\underset{\:\mathrm{0}} {\overset{\mathrm{x}} {\int}}\:{f}\left({t}\right)\:{dt}.\:\mathrm{Then}\:\mathrm{for}\:\mathrm{any}\:{x}\:\in\:\left[\mathrm{2},\:\mathrm{3}\right],\: \\ $$$$\phi\left({x}\right)\:= \\ $$ Answered by MJS last updated on…
Question Number 88198 by topman2020 last updated on 08/Apr/20 $$\mathrm{Factorize}\:\:−{r}^{\mathrm{2}} +{p}^{\mathrm{2}} +{q}^{\mathrm{2}} −\mathrm{2}{pq}\:. \\ $$ Answered by TANMAY PANACEA. last updated on 08/Apr/20 $$\left({p}−{q}\right)^{\mathrm{2}} −{r}^{\mathrm{2}}…