Question Number 191786 by Mastermind last updated on 30/Apr/23 $$\mathrm{Ques}.\:\mathrm{1}\:\left(\mathrm{Metric}\:\mathrm{Space}\:\mathrm{Question}\right) \\ $$$$\:\:\:\:\:\:\:\:\mathrm{Let}\:\mathrm{X}\:=\:\rho_{\infty} \:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{all}\: \\ $$$$\mathrm{bounded}\:\mathrm{sequences}\:\mathrm{of}\:\mathrm{complex}\: \\ $$$$\mathrm{numbers}.\:\mathrm{That}\:\mathrm{is}\:\mathrm{every}\:\mathrm{element}\:\mathrm{of} \\ $$$$\rho_{\infty} \:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{sequence}\:\overset{−} {\mathrm{x}}=\left\{\overset{−} {\mathrm{x}}\right\}_{\mathrm{k}=\mathrm{1}} ^{\infty} \: \\…
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Question Number 126200 by Dwaipayan Shikari last updated on 18/Dec/20 $$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{5}} }−\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{7}} }+\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{11}} }−\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{13}} }+…. \\ $$ Commented by Olaf last updated on…
Question Number 191688 by Mastermind last updated on 29/Apr/23 $$\mathrm{Divide}\:\mathrm{a}\:\mathrm{113mm}\:\mathrm{line}\:\mathrm{into}\:\mathrm{ratio} \\ $$$$\mathrm{1}:\mathrm{2}:\mathrm{4} \\ $$ Commented by Mastermind last updated on 29/Apr/23 $$\mathrm{Ok}\:\mathrm{my}\:\mathrm{BOSS},\:\mathrm{thank}\:\mathrm{you}! \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{have}\:\mathrm{about}\:\mathrm{four}\:\mathrm{questions}\:\mathrm{on} \\…
Question Number 60587 by behi83417@gmail.com last updated on 22/May/19 $$\boldsymbol{\mathrm{x}}\in\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right] \\ $$$$\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{cosx}}=\boldsymbol{\mathrm{tg}}\mathrm{3}\boldsymbol{\mathrm{x}} \\ $$ Commented by MJS last updated on 22/May/19 $$\mathrm{tried}\:\mathrm{a}\:\mathrm{couple}\:\mathrm{of}\:\mathrm{different}\:\mathrm{substitutions},\:\mathrm{all} \\ $$$$\mathrm{lead}\:\mathrm{to}\:\mathrm{a}\:\mathrm{polynome}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{8}\:\mathrm{without}\:\mathrm{any} \\…
Question Number 126092 by physicstutes last updated on 17/Dec/20 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{at}\:\mathrm{time}\:{t}\:=\:\mathrm{0}\:\mathrm{and}\:\mathrm{moves}\:\mathrm{in}\: \\ $$$$\mathrm{a}\:\mathrm{straightline}\:\mathrm{with}\:\mathrm{variable}\:\mathrm{acceleration}\:{a}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} \:\mathrm{where}\: \\ $$$$\:{a}\:=\:\frac{{t}}{\mathrm{5}}\:,\:\mathrm{0}\:\leqslant\:{t}\:\leqslant\:\mathrm{5}\:,\:{a}\:=\:\frac{{t}}{\mathrm{5}}\:+\:\frac{\mathrm{10}}{{t}^{\mathrm{2}} }\:,\:{t}\:\geqslant\:\mathrm{5},\:{t}\:\mathrm{being}\:\mathrm{measured}\:\mathrm{in}\:\mathrm{seconds}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{velocity}\:\mathrm{is}\:\mathrm{22}\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{m}/\mathrm{s}\:\mathrm{when}\:{t}\:=\:\mathrm{5}\:\mathrm{and} \\ $$$$\mathrm{11}\:\mathrm{m}/\mathrm{s}\:\mathrm{when}\:{t}\:=\:\mathrm{10}. \\ $$$$\mathrm{Show}\:\mathrm{also}\:\mathrm{that}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{travelled}\:\mathrm{by}\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{10}\:\mathrm{seconds}\:\mathrm{is}\:\:\left(\mathrm{43}\frac{\mathrm{1}}{\mathrm{3}}−\mathrm{10}\:\mathrm{ln}\:\mathrm{2}\right)\:\mathrm{m}. \\…
Question Number 191621 by Noorzai last updated on 27/Apr/23 Answered by gatocomcirrose last updated on 27/Apr/23 $$\mathrm{x}^{\mathrm{2}} =\mathrm{x}+\mathrm{1}\Rightarrow\mathrm{x}^{\mathrm{8}} =\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}\right)^{\mathrm{2}} =\left(\mathrm{3x}+\mathrm{2}\right)^{\mathrm{2}} \\ $$$$=\mathrm{9x}^{\mathrm{2}} +\mathrm{12x}+\mathrm{4}=\mathrm{9x}+\mathrm{9}+\mathrm{12x}+\mathrm{4}=\mathrm{21x}+\mathrm{13} \\…
Question Number 60545 by Tawa1 last updated on 21/May/19 Answered by MJS last updated on 22/May/19 $$\mathrm{diameter}\:\mathrm{2}\:\mathrm{volume}\:\mathrm{2}^{\mathrm{3}} =\mathrm{8} \\ $$$$\mathrm{diameter}\:\mathrm{3}\:\mathrm{volume}\:\mathrm{3}^{\mathrm{3}} =\mathrm{27} \\ $$$$\mathrm{diameter}\:\mathrm{4}\:\mathrm{volume}\:\mathrm{4}^{\mathrm{3}} =\mathrm{64} \\…
Question Number 60514 by tanmay last updated on 21/May/19 $${i}\:{found}\:{some}\:{interesting}\:{basic}\:{question} \\ $$$${hence}\:{sharing}… \\ $$$$\left.\mathrm{1}\right){if}\:{A}\in\left[\mathrm{1},\mathrm{4}\right]\:\:{A}^{\mathrm{2}} \:\in\:\:?\:\leftarrow{find}\:{interval}\: \\ $$$$\left.\mathrm{2}\right){if}\:{A}\:\in\:\left[−\mathrm{1},\mathrm{4}\right]\:\:{A}^{\mathrm{2}} \:\in\:? \\ $$$$\left.\mathrm{3}\right)\:{y}=\frac{\mathrm{1}}{{A}\:\:}\:\:{and}\:{A}\in\:\:\:\:\left[\mathrm{1},\mathrm{4}\right]\:\:{y}\in\:? \\ $$$$\left.\mathrm{4}\right){y}=\frac{\mathrm{1}}{\mid{A}\mid}\:\:{A}\in\left[−\mathrm{1},\mathrm{4}\right]\:\:\:{y}\in\:? \\ $$ Commented…
Question Number 60508 by tanmay last updated on 21/May/19 $${prof}\:{Abdo}\:\:{pls}\:{restrict}\:{the}\:\:{numbers}\:{of}\:{input}\:{of}\:{question}… \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com