Question Number 21582 by Isse last updated on 28/Sep/17 $$\int_{\pi/\mathrm{2}} ^{\pi/\mathrm{4}} \left(\mathrm{3}{x}+\mathrm{7}\right) \\ $$ Answered by Joel577 last updated on 29/Sep/17 $${I}\:=\:\underset{\frac{\pi}{\mathrm{2}}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\:\mathrm{3}{x}\:+\:\mathrm{7}\:{dx} \\…
Question Number 87116 by lémùst last updated on 02/Apr/20 $$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+{x}^{\mathrm{2}} {y}=\mathrm{0} \\ $$ Answered by redmiiuser last updated on 03/Apr/20 $$\frac{{y}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{4}} .{y}}{\mathrm{12}}=\mathrm{0}…
Question Number 21581 by mondodotto@gmail.com last updated on 28/Sep/17 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21580 by ketto last updated on 28/Sep/17 Answered by Joel577 last updated on 29/Sep/17 $$\mathrm{Because}\:{A}\:\mathrm{and}\:{B}\:\mathrm{mutually}\:\mathrm{exclusive},\:\mathrm{then} \\ $$$${P}\:\left({A}\:\cap\:{B}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{and} \\ $$$${P}\:\left({A}\:\cup\:{B}\right)\:=\:\mathrm{1} \\ $$$$…
Question Number 21578 by ANTARES_VY last updated on 28/Sep/17 $$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{whole}}\:\:\boldsymbol{\mathrm{part}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{A}}? \\ $$$$\boldsymbol{\mathrm{A}}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{4}}}+……+\frac{\mathrm{1}}{\:\sqrt{\mathrm{9999}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{10000}}}. \\ $$ Commented by Tinkutara last updated on 28/Sep/17 $$\mathrm{Almost}\:\mathrm{similar}\:\mathrm{to}\:\mathrm{KVS}\:\mathrm{JMO}\:\mathrm{2016}. \\ $$$$\mathrm{Solutions}\:\mathrm{are}\:\mathrm{available}\:\mathrm{on}\:\mathrm{net}. \\…
Question Number 21574 by Tinkutara last updated on 27/Sep/17 $$\mathrm{The}\:\mathrm{cyclic}\:\mathrm{octagon}\:{ABCDEFGH}\:\mathrm{has} \\ $$$$\mathrm{sides}\:{a},\:{a},\:{a},\:{a},\:{b},\:{b},\:{b},\:{b}\:\mathrm{respectively}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{that} \\ $$$$\mathrm{circumscribes}\:{ABCDEFGH}\:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:{a}\:\mathrm{and}\:{b}. \\ $$ Answered by mrW1 last updated…
Question Number 152647 by mr W last updated on 30/Aug/21 Commented by mr W last updated on 30/Aug/21 $${find}\:\frac{{FG}}{{GB}}=? \\ $$ Answered by mr W…
Question Number 21573 by Tinkutara last updated on 27/Sep/17 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{1}\:<\:\frac{\mathrm{1}}{\mathrm{1001}}\:+\:\frac{\mathrm{1}}{\mathrm{1002}}\:+\:\frac{\mathrm{1}}{\mathrm{1003}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{3001}}\:<\:\mathrm{1}\frac{\mathrm{1}}{\mathrm{3}}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21572 by Tinkutara last updated on 27/Sep/17 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{largest}\:\mathrm{3}-\mathrm{digit}\:\mathrm{prime} \\ $$$$\mathrm{factor}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integer}\:^{\mathrm{2000}} {C}_{\mathrm{1000}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 21571 by Tinkutara last updated on 27/Sep/17 $${ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{cyclic}\:\mathrm{quadrilateral};\:{x},\:{y},\:{z} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{distances}\:\mathrm{of}\:{A}\:\mathrm{from}\:\mathrm{the}\:\mathrm{lines} \\ $$$${BD},\:{BC},\:{CD}\:\mathrm{respectively}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\frac{{BD}}{{x}}\:=\:\frac{{BC}}{{y}}\:+\:\frac{{CD}}{{z}}. \\ $$ Answered by revenge last updated on 29/Sep/17…