Question Number 71089 by 20190927 last updated on 11/Oct/19 $$\left(\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}}\right)^{\mathrm{x}} +\left(\sqrt{\sqrt{\mathrm{2}}+\mathrm{1}}\right)^{\mathrm{x}} =\mathrm{4} \\ $$ Answered by Henri Boucatchou last updated on 11/Oct/19 $$\:\sqrt{\mathrm{2}}\:+\:\mathrm{1}\:=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}\:−\:\mathrm{1}},\:\boldsymbol{{let}}\:\:\boldsymbol{{a}}\:=\:\sqrt{\sqrt{\mathrm{2}}−\mathrm{1}} \\ $$$$\:\left(\sqrt{\sqrt{\mathrm{2}}\:−\mathrm{1}}\right)^{\boldsymbol{{x}}}…
Question Number 71082 by aliesam last updated on 11/Oct/19 $${prove}\:{that}\: \\ $$$$ \\ $$$$\mid\:\sqrt{\mid{x}\mid}\:−\:\sqrt{\mid{y}\mid}\:\mid\:\leqslant\:\sqrt{\mid{x}−{y}\mid}\: \\ $$$$ \\ $$ Answered by Henri Boucatchou last updated on…
Question Number 5546 by FilupSmith last updated on 19/May/16 $$\mathrm{I}\:\mathrm{have}\:\mathrm{two}\:\mathrm{circles}\:\mathrm{side}\:\mathrm{by}\:\mathrm{side}. \\ $$$$\mathrm{Circle}\:\mathrm{1}\:\mathrm{has}\:\mathrm{radius}\:{r}. \\ $$$$\mathrm{Circle}\:\mathrm{2}\:\mathrm{has}\:\mathrm{radius}\:\frac{\mathrm{1}}{\mathrm{3}}{r}. \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{I}\:\mathrm{roll}\:\mathrm{circle}\:\mathrm{2}\:\mathrm{around}\:\mathrm{circle}\:\mathrm{1}\:\mathrm{until} \\ $$$$\mathrm{it}\:\mathrm{reaches}\:\mathrm{the}\:\mathrm{begining}, \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{times}\:\mathrm{will}\:\mathrm{it}\:\mathrm{roll}? \\ $$ Commented…
Question Number 5543 by Rasheed Soomro last updated on 19/May/16 $$\bullet\mathrm{What}\:\boldsymbol{\mathrm{plane}}\:\boldsymbol{\mathrm{geometrical}}\:\boldsymbol{\mathrm{figures}} \\ $$$$\mathrm{could}\:\mathrm{be}\:\mathrm{produced}\:\mathrm{by}\:\mathrm{joining} \\ $$$$\boldsymbol{\mathrm{vertices}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{cube}}? \\ $$$$\left(\mathrm{for}\:\mathrm{example}\::\:\mathrm{square}\right) \\ $$$$\bullet\mathrm{What}\:\mathrm{largest}\:\mathrm{area}\left(\mathrm{2}\:\mathrm{dimensional}\right)\:\mathrm{can}\:\mathrm{be}\:\mathrm{obtained} \\ $$$$\mathrm{by}\:\mathrm{joining}\:\mathrm{vertices}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{when}\:\mathrm{its}\:\mathrm{side}\:\mathrm{is}\:\mathrm{x}? \\ $$ Terms of…
Question Number 5542 by FilupSmith last updated on 19/May/16 $$\mathrm{The}\:\mathrm{surface}\:\mathrm{area}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cylinder}\:\mathrm{is}: \\ $$$${A}=\mathrm{2}\pi{r}^{\mathrm{2}} +\mathrm{2}\pi{rh} \\ $$$$ \\ $$$$\mathrm{As}\:{h}\rightarrow\mathrm{0},\:\mathrm{the}\:\mathrm{shape}\:\mathrm{becomes}\:\mathrm{a}\:\mathrm{2D}\:\mathrm{circle}, \\ $$$$\mathrm{so}\:\mathrm{should}\:\:\:\:\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{A}\:=\:\pi{r}^{\mathrm{2}} \:\:\:??? \\ $$$$\mathrm{Or}\:\mathrm{is}\:\mathrm{it}\:\mathrm{that}\:\mathrm{as}\:{h}\rightarrow\mathrm{0},\:\mathrm{it}\:\mathrm{creates}\:\mathrm{a}\:\mathrm{circle} \\ $$$$\mathrm{of}\:\mathrm{3}\:\mathrm{dimensions}\:\mathrm{with}\:\mathrm{infintesimally}\:\mathrm{small}…
Question Number 136614 by bemath last updated on 24/Mar/21 $${If}\:{a}+\frac{\mathrm{1}}{{a}}\:=\:\mathrm{23}\:{then}\:\sqrt[{\mathrm{4}}]{{a}}\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{a}}}\:=? \\ $$ Answered by mr W last updated on 24/Mar/21 $${a}+\frac{\mathrm{1}}{{a}}=\left(\sqrt{{a}}+\frac{\mathrm{1}}{\:\sqrt{{a}}}\right)^{\mathrm{2}} −\mathrm{2}=\mathrm{23} \\ $$$$\sqrt{{a}}+\frac{\mathrm{1}}{\:\sqrt{{a}}}=\mathrm{5} \\…
Question Number 5539 by Rasheed Soomro last updated on 19/May/16 $$\mathrm{How}\:\mathrm{many}\:\boldsymbol{\mathrm{planes}}\:\mathrm{can}\:\mathrm{pass}\:\mathrm{through} \\ $$$$\boldsymbol{\mathrm{vertices}}\:\mathrm{of}\:\mathrm{a}\:\boldsymbol{\mathrm{cube}}, \\ $$$$\left.{a}\right)\:\mathrm{when}\:\mathrm{each}\:\mathrm{plane}\:\mathrm{contains}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{least}} \\ $$$$\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{vertices}}. \\ $$$$\left.{b}\right)\:\mathrm{when}\:\mathrm{each}\:\mathrm{plane}\:\mathrm{contains}\:\boldsymbol{\mathrm{exactly}} \\ $$$$\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{vertices}}. \\ $$$$\left.{c}\right)\:\mathrm{Could}\:\mathrm{we}\:\mathrm{say}\:\mathrm{that}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{can}\:\mathrm{pass} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{most}}\:\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{vertices}}?…
Question Number 71073 by TawaTawa last updated on 11/Oct/19 Commented by Prithwish sen last updated on 11/Oct/19 $$\mathrm{a}^{\mathrm{2}} =\:\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} +\mathrm{2bc} \\ $$$$\therefore\:\boldsymbol{\mathrm{bc}}\:=\:\frac{\boldsymbol{\mathrm{a}}^{\mathrm{2}} −\boldsymbol{\mathrm{b}}^{\mathrm{2}} −\boldsymbol{\mathrm{c}}^{\mathrm{2}}…
Question Number 136605 by bemath last updated on 23/Mar/21 Answered by peter frank last updated on 25/Mar/21 $$\frac{\mathrm{2}}{\mathrm{1029}} \\ $$ Terms of Service Privacy Policy…
Question Number 136604 by bemath last updated on 23/Mar/21 $$ \\ $$What is the equation of a tangent to a circle whose equation is x^2+y^2−2x−4y=1 at point (1+√5,3)…