Question Number 90069 by ajfour last updated on 21/Apr/20 Commented by ajfour last updated on 21/Apr/20 $${dont}\:{know}\:{why}\:{i}\:{get}\:{two}\:{answers}; \\ $$$$\frac{{r}}{{R}}\:\approx\:\mathrm{0}.\mathrm{49172},\:\mathrm{0}.\mathrm{39253} \\ $$ Commented by ajfour last…
Question Number 24526 by ajfour last updated on 20/Nov/17 Commented by ajfour last updated on 20/Nov/17 $${A}\:{thin}\:{rod}\:{rotates}\:{in}\:{horizontal} \\ $$$${plane}\:{with}\:{a}\:{constant}\:{angular}\: \\ $$$${velocity}\:\boldsymbol{\omega}.{From}\:{its}\:{farther}\:{end} \\ $$$${a}\:{needle}\:{emerges}\:{at}\:{a}\:{constant} \\ $$$${relative}\:{velocity}\:\boldsymbol{{u}}\:{along}\:{the}\:{rod}.…
Question Number 90060 by jagoll last updated on 21/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{sin}\:\mathrm{x}\right)}{\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{2}+\mathrm{x}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{2}+\mathrm{3x}}}\:=\:? \\ $$ Commented by john santu last updated on 21/Apr/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{6}}{x}^{\mathrm{3}} +{o}\left({x}^{\mathrm{3}}…
Question Number 24524 by mondodotto@gmail.com last updated on 20/Nov/17 Answered by mrW1 last updated on 20/Nov/17 $${x}\geqslant\mathrm{0} \\ $$$$\mathrm{2}\left({x}+\mathrm{1}\right)\mathrm{log}\:\mathrm{9}={x}^{\frac{\mathrm{1}}{\mathrm{2}}} \\ $$$$\left(\mathrm{2log}\:\mathrm{9}\right)^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{2}} ={x} \\ $$$$\left(\mathrm{2log}\:\mathrm{9}\right)^{\mathrm{2}}…
Question Number 90058 by mr W last updated on 21/Apr/20 Commented by mr W last updated on 21/Apr/20 $${find}\:\frac{{b}}{{a}}=?\:{if}\:\Delta{PQR}\:{is}\:{equilateral} \\ $$ Answered by ajfour last…
Question Number 155594 by mathdanisur last updated on 02/Oct/21 Answered by ghimisi last updated on 02/Oct/21 $$\Leftrightarrow\Sigma\left(\sqrt{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} +\left(\mathrm{2}−\sqrt{\mathrm{2}}\right){xy}\right)\geqslant\mathrm{0} \\ $$$$\sqrt{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }−{x}^{\mathrm{2}}…
Question Number 24520 by Tinkutara last updated on 19/Nov/17 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{moves}\:\mathrm{in}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{along} \\ $$$${x}-\mathrm{axis}.\:\mathrm{At}\:{t}\:=\:\mathrm{0}\:\mathrm{it}\:\mathrm{passes}\:\mathrm{origin}\:\mathrm{with} \\ $$$$\mathrm{some}\:\mathrm{velocity}\:\mathrm{towards}\:\mathrm{positive}\:{x}-\mathrm{axis} \\ $$$$\mathrm{and}\:\mathrm{with}\:\mathrm{an}\:\mathrm{acceleration}\:{a}\:\mathrm{which}\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{as},\:{a}\:=\:−\:{Kx},\:\mathrm{where}\:{x}\:\mathrm{is}\:\mathrm{in}\:\mathrm{metre} \\ $$$$\mathrm{and}\:{K}\:\mathrm{is}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{constant}.\:\mathrm{The}\:\mathrm{time} \\ $$$$\mathrm{at}\:\mathrm{which}\:\mathrm{its}\:\mathrm{velocity}\:\mathrm{becomes}\:\mathrm{half}\:\mathrm{of}\:\mathrm{its} \\ $$$$\mathrm{value}\:\mathrm{at}\:{t}\:=\:\mathrm{0}\:\mathrm{for}\:\mathrm{the}\:\mathrm{first}\:\mathrm{time},\:\mathrm{is} \\…
Question Number 90055 by awlia last updated on 21/Apr/20 Commented by jagoll last updated on 21/Apr/20 $$\mathrm{vol}\:=\:\pi\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\left(\mathrm{4x}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} \:\mathrm{dx}\: \\ $$$$=\:\pi\:\left\{\:−\frac{\mathrm{x}^{\mathrm{2}} \left(\mathrm{4}−\mathrm{x}\right)^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{x}\left(\mathrm{4}−\mathrm{x}\right)^{\mathrm{4}}…
Question Number 155585 by mathdanisur last updated on 02/Oct/21 $$\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{and}\:\mathrm{prove}\:\mathrm{by}\:\mathrm{the} \\ $$$$\varepsilon−\delta\:\mathrm{definition}\:\mathrm{that}\:\mathrm{as}\:\mathrm{n}\rightarrow\infty\:\mathrm{for}\:\mathrm{z}\geqslant\mathrm{1} \\ $$$$\left(\mathrm{2}\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{z}}\:−\:\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \:\rightarrow\:\mathrm{z}^{\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 90048 by jagoll last updated on 21/Apr/20 $$\mathrm{5}^{\sqrt{\mathrm{x}}} \:−\mathrm{5}^{\mathrm{x}−\mathrm{7}} \:=\:\mathrm{100} \\ $$ Answered by jagoll last updated on 21/Apr/20 Terms of Service Privacy…