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Question Number 21973 by Joel577 last updated on 08/Oct/17 $$\Delta{ABC}\:\mathrm{with}\:\mathrm{sides}\:{a},\:{b},\:{c}\:\in\:\mathbb{Z}\:\mathrm{and}\:\angle{A}\:=\:\mathrm{3}\angle{B} \\ $$$$\mathrm{If}\:\mathrm{its}\:\mathrm{circumference}\:\mathrm{is}\:\mathrm{minimum},\:\mathrm{then} \\ $$$$\mathrm{find}\:{a},\:{b},\:{c} \\ $$ Commented by Rasheed.Sindhi last updated on 08/Oct/17 $$\mathrm{Let}\:\angle\mathrm{B}=\theta\Rightarrow\angle\mathrm{A}=\mathrm{3}\theta\:,\:\angle\mathrm{C}=\pi−\mathrm{4}\theta \\…
Question Number 21903 by Joel577 last updated on 06/Oct/17 $$\Delta{ABC}\:\mathrm{with}\:\mathrm{sides}\:{a},\:{b},\:{c}\:\in\:\mathbb{Z}\:\mathrm{and}\:\angle{A}\:=\:\mathrm{3}\angle{B} \\ $$$$\mathrm{If}\:\mathrm{its}\:\mathrm{circumference}\:\mathrm{is}\:\mathrm{minimum},\:\mathrm{then}\:\mathrm{find}\:{a},\:{b},\:{c} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152949 by Riyoziyot last updated on 03/Sep/21 Answered by mr W last updated on 03/Sep/21 $${say}\:{AB}={AC}=\mathrm{1} \\ $$$${AD}={CD}=\frac{\mathrm{1}}{\mathrm{2}\:\mathrm{cos}\:\mathrm{42}} \\ $$$${BC}=\mathrm{2}\:\mathrm{cos}\:\mathrm{66} \\ $$$$\angle{BCD}=\mathrm{66}−\mathrm{42}=\mathrm{24}° \\…
Question Number 87413 by ajfour last updated on 04/Apr/20 Commented by ajfour last updated on 04/Apr/20 $${Express}\:{r}_{{min}} \:{in}\:{terms}\:{of}\:{a},\:{b}\:. \\ $$ Answered by mr W last…
Question Number 21840 by Joel577 last updated on 05/Oct/17 $$\mathrm{A}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{placed}\:\mathrm{inside}\:\mathrm{a}\:\mathrm{sphere}. \\ $$$$\mathrm{If}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{is}\:\mathrm{maximum}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{radius}\:\mathrm{from}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{and}\:\mathrm{sphere} \\ $$ Answered by mrW1 last updated on 05/Oct/17 $$\mathrm{R}=\mathrm{radius}\:\mathrm{of}\:\mathrm{sphere} \\…
Question Number 87369 by ajfour last updated on 04/Apr/20 Commented by ajfour last updated on 04/Apr/20 $${I}\:{think},\:\frac{{R}}{{r}}=\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\:\:\:\:{only},\:{Sir}. \\ $$ Commented by ajfour last updated on…
Question Number 21825 by Joel577 last updated on 05/Oct/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{simplest}\:\mathrm{form}\:\mathrm{of} \\ $$$$\underset{{k}\:=\:\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{2}^{{k}} \left[\mathrm{sin}^{\mathrm{2}} \:\left(\frac{\mathrm{2}{k}\pi}{\mathrm{3}}\right)\:+\:\frac{\mathrm{1}}{\mathrm{4}}\right] \\ $$ Commented by sma3l2996 last updated on 05/Oct/17…
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Question Number 21782 by drbl.gnbd last updated on 03/Oct/17 $${a}_{\mathrm{1}} =\mathrm{1},\:{a}_{{n}+\mathrm{1}} =\frac{{a}_{{n}} }{\:\sqrt{{a}_{{n}} +{n}+\mathrm{1}}} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} =? \\ $$ Terms of Service Privacy…