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 5539 by Rasheed Soomro last updated on 19/May/16 $$\mathrm{How}\:\mathrm{many}\:\boldsymbol{\mathrm{planes}}\:\mathrm{can}\:\mathrm{pass}\:\mathrm{through} \\ $$$$\boldsymbol{\mathrm{vertices}}\:\mathrm{of}\:\mathrm{a}\:\boldsymbol{\mathrm{cube}}, \\ $$$$\left.{a}\right)\:\mathrm{when}\:\mathrm{each}\:\mathrm{plane}\:\mathrm{contains}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{least}} \\ $$$$\boldsymbol{\mathrm{three}}\:\boldsymbol{\mathrm{vertices}}. \\ $$$$\left.{b}\right)\:\mathrm{when}\:\mathrm{each}\:\mathrm{plane}\:\mathrm{contains}\:\boldsymbol{\mathrm{exactly}} \\ $$$$\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{vertices}}. \\ $$$$\left.{c}\right)\:\mathrm{Could}\:\mathrm{we}\:\mathrm{say}\:\mathrm{that}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{can}\:\mathrm{pass} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{most}}\:\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{vertices}}?…
Question Number 5533 by Rasheed Soomro last updated on 18/May/16 $$\mathrm{Measure}\:\mathrm{of}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{is}\:\mathrm{double} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{inside}\:\mathrm{it}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{empty}\:\mathrm{space}\:\mathrm{in}\:\mathrm{larger}\:\mathrm{cube}? \\ $$ Commented by FilupSmith last updated on 18/May/16 $$\mathrm{Empty}\:\mathrm{space}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{larger}…
Question Number 136597 by Dwaipayan Shikari last updated on 23/Mar/21 Answered by mr W last updated on 23/Mar/21 Commented by otchereabdullai@gmail.com last updated on 25/Mar/21…
Question Number 5529 by Rasheed Soomro last updated on 18/May/16 Commented by Rasheed Soomro last updated on 18/May/16 $$\bigtriangleup\mathrm{ABC}\:\mathrm{is}\:\mathrm{an}\:\mathrm{equilaterl}\:\mathrm{triangle}. \\ $$$$\mathrm{D},\mathrm{E},\mathrm{F}\:\mathrm{are}\:\mathrm{mid}-\mathrm{points}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}. \\ $$$$\mathrm{The}\:\mathrm{centres}\:\mathrm{of}\:\mathrm{arcs}\:\mathrm{are}\:\mathrm{vertices}\:\mathrm{of} \\ $$$$\bigtriangleup\mathrm{ABC}.…
Question Number 5517 by Rasheed Soomro last updated on 17/May/16 Commented by Rasheed Soomro last updated on 17/May/16 $$ \\ $$$$\bullet\mathrm{ABC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{triangle},\:\mathrm{D},\mathrm{E}\:\mathrm{and}\:\mathrm{F}\:\mathrm{are} \\ $$$$\mathrm{midpoints}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{it}. \\ $$$$\bullet\mathrm{Centres}\:\mathrm{of}\:\mathrm{arcs}\:\mathrm{are}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}.…
Question Number 5515 by FilupSmith last updated on 17/May/16 $$\mathrm{If}\:\mathrm{you}\:\mathrm{have}\:\mathrm{a}\:\mathrm{regular}\:{n}−\mathrm{sided}\:\mathrm{polygon}, \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{method}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{area} \\ $$$$\mathrm{from}\:\mathrm{one}\:\mathrm{corner}\:\mathrm{to}\:\mathrm{another}? \\ $$$$ \\ $$$$\mathrm{That}\:\mathrm{is},\:\mathrm{if}\:\mathrm{we}\:\mathrm{start}\:\mathrm{at}\:\mathrm{a}\:\mathrm{corner}\:\left(\mathrm{corner}\:\mathrm{1}\right), \\ $$$$\mathrm{and}\:\mathrm{draw}\:\mathrm{a}\:\mathrm{line}\:\mathrm{to}\:\mathrm{corner}\:{x},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}? \\ $$$$\mathrm{See}\:\mathrm{image}\:\mathrm{in}\:\mathrm{comment}\:\mathrm{for}\:\mathrm{visual}\:\mathrm{representation}. \\ $$ Commented…
Question Number 71034 by ajfour last updated on 11/Oct/19 Commented by ajfour last updated on 11/Oct/19 $${take}\:{R}=\mathrm{12},\:{a}=\mathrm{5},\:{b}=\mathrm{2},\:{c}=\mathrm{3} \\ $$$${Find}\:{minimum}\:{of}\:{x}. \\ $$ Commented by ajfour last…
Question Number 5490 by 123456 last updated on 16/May/16 $$\int\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=? \\ $$$$\underset{−{r}} {\overset{{x}} {\int}}\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=?? \\ $$$$\underset{{x}} {\overset{{y}} {\int}}\sqrt{{r}^{\mathrm{2}} −{x}^{\mathrm{2}} }{dx}=??? \\…
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