Question Number 101247 by 175 last updated on 01/Jul/20 Answered by 1549442205 last updated on 06/Jul/20 $$\boldsymbol{\mathrm{Note}}\::\mathrm{the}\:\mathrm{integral}\:\mathrm{part}\:\mathrm{of}\:\mathrm{a}\:\mathrm{real}\:\mathrm{number} \\ $$$$\mathrm{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{grearest}\:\mathrm{integer}\:\mathrm{which}\:\mathrm{don}'\mathrm{t}\:\mathrm{exceed}\:\mathrm{x} \\ $$$$\mathrm{and}\:\mathrm{is}\:\mathrm{denoted}\:\mathrm{by}\:\mathrm{symbol}\:\left[\mathrm{x}\right] \\ $$$$\mathrm{Put}\:\mathrm{A}_{\mathrm{n}} =\:\left(\mathrm{2}+\sqrt{\mathrm{2}}\right)^{\mathrm{n}} +\left(\mathrm{2}−\sqrt{\mathrm{2}}\right)^{\mathrm{n}}…
Question Number 101243 by Dwaipayan Shikari last updated on 01/Jul/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\: \\ $$$$\:\:\mathrm{xa}^{\frac{\mathrm{1}}{\mathrm{x}}} +\frac{\mathrm{1}}{\mathrm{x}}\mathrm{a}^{\mathrm{x}} =\mathrm{2a}\:\:\:\mathrm{a}\in\left\{−\mathrm{1},\mathrm{0},\mathrm{1}\right\}\:\:\:{and}\:{also}\:{find}\:{when}\:{a}\:\:{is}\:{not}\:{given} \\ $$ Commented by mr W last updated on 01/Jul/20…
Question Number 101231 by 175 last updated on 01/Jul/20 Commented by Dwaipayan Shikari last updated on 01/Jul/20 $$\frac{\mathrm{1}}{{n}}.\frac{\pi}{\mathrm{6}}\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{2}^{\frac{\mathrm{1}}{{n}}} −\mathrm{1}}{\frac{\mathrm{1}}{{n}}}\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\left(\mathrm{2}^{\frac{{r}}{{n}}} {cos}\left(\mathrm{2}^{\frac{{r}}{{n}}} \frac{\pi}{\mathrm{6}}\right)\right) \\…
Question Number 35656 by Rasheed.Sindhi last updated on 21/May/18 $$\mathrm{Following}\:\mathrm{alphabet}\:\mathrm{lacks}\:\mathrm{one}\:\mathrm{letter}. \\ $$$$\:\:\:\:\:\mathrm{abcdefghijklmnopqrstuvxyz} \\ $$$$\mathrm{I}\:\mathrm{request}\:\mathrm{that}\:\mathrm{letter}, \\ $$$$\mathrm{please}\:\mathrm{come}\:\mathrm{and}\:\mathrm{make}\:\mathrm{the}\:\mathrm{alphabet} \\ $$$$\mathrm{complete}. \\ $$$$ \\ $$ Commented by Rasheed.Sindhi…
Question Number 101159 by hardylanes last updated on 30/Jun/20 $${given}\:{the}\:{complex}\:{number}\:{z}\:{such}\:{that} \\ $$$${z}−\mathrm{4}{i}={a}+\mathrm{3}{zi}.\: \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\:{if}\:\:{z}\:{is}\:{purwly}\:{imaginary} \\ $$$$ \\ $$ Answered by Rio Michael last updated on…
Question Number 35602 by Rio Mike last updated on 20/May/18 $$\mathrm{Q}_{\mathrm{1}} .{p}\left(\mathrm{x}\right)\:=\:\mathrm{3x}^{\mathrm{3}} +\:\mathrm{4x}^{\mathrm{2}} +\mathrm{5x}\:−\:\mathrm{k}\:\mathrm{and}\: \\ $$$$\left(\mathrm{x}−\mathrm{1}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{p}\left(\mathrm{x}\right)\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remaining}\: \\ $$$$\mathrm{two}\:\mathrm{factors}. \\ $$$${Q}_{\mathrm{2}} .\:{Evaluate}\:\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{3}^{\mathrm{2}−{r}}…
Question Number 35594 by Rio Mike last updated on 20/May/18 $${Given}\:{that}\:\mathrm{18},\mathrm{24},{and}\:{k}\:+\:\mathrm{14}\:{are}\: \\ $$$${three}\:{consecutive}\:{terms}\:{of}\:{an}\: \\ $$$${arithmetic}\:{progression}\:{Find} \\ $$$$\left.{a}\right)\:{the}\:{common}\:{difference} \\ $$$$\left.{b}\right)\:{the}\:{value}\:{of}\:{k} \\ $$$$\left.{c}\right){the}\:{first}\:{term}\:{if}\:{the}\:\mathrm{4}^{{th}} \:{term}\:{is} \\ $$$$\mathrm{12}. \\…
Question Number 35595 by Rio Mike last updated on 20/May/18 $${Find}\:{the}\:{surface}\:{Area}\:{of}\:{a}\:{solid} \\ $$$${cone}\:{of}\:{raduis}\:\mathrm{3}{cm}\:{and}\:{slant}\: \\ $$$${height}\:\mathrm{4}{cm}.\:\left({take}\:\pi=\mathrm{3}.\mathrm{1}\right) \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 20/May/18 $$\Pi{rl}+\Pi{r}^{\mathrm{2}}…
Question Number 35512 by Rio Mike last updated on 19/May/18 $$\:{Given}\:{that}\:\left({x}+\mathrm{1},\mathrm{3},{x}\right)\:{are}\:{lengths} \\ $$$${of}\:{the}\:{sides}\:{of}\:{a}\:{right}\:{angled} \\ $$$${triangle}\left({pythagoras}\:{tripple}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{x}. \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 35513 by Rio Mike last updated on 19/May/18 $${g}\left({x}\right)=\:\mathrm{6}{x}^{\mathrm{2}} −\:\mathrm{5}{ax}\:+\:{b}^{\mathrm{2}} \\ $$$${given}\:{that}\:{g}\left({x}\right)\:{has}\:{only}\:{two}\:{roots} \\ $$$${and}\:{are}\:\left({x}−\mathrm{1}\right)\:{and}\:\left({x}−\mathrm{2}\right) \\ $$$${find}\:{the}\:{value}\:{of}\:{a}\:{and}\:{b}.{Using} \\ $$$$\left({x}−\mathrm{1}\right)\:{as}\:{a}\:{root}\:{detemine}\:{the}\: \\ $$$${extend}\:{to}\:{which}\:\left({x}−\mathrm{2}\right)\:{is}\:{a}\:{root} \\ $$$$\left({occurance}\:{as}\:{a}\:{root}\right). \\…