Question Number 18945 by Tinkutara last updated on 01/Aug/17 $$\mathrm{A}\:\mathrm{point}\:'\mathrm{A}'\:\mathrm{is}\:\mathrm{randomly}\:\mathrm{chosen}\:\mathrm{in}\:\mathrm{a} \\ $$$$\mathrm{square}\:\mathrm{of}\:\mathrm{side}\:\mathrm{length}\:\mathrm{1}\:\mathrm{unit}.\:\mathrm{Find}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{from}\:\mathrm{A}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{centre}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{does}\:\mathrm{not}\:\mathrm{exceed}\:\mathrm{x}. \\ $$ Commented by dioph last updated on 02/Aug/17…
Question Number 84477 by jagoll last updated on 13/Mar/20 $$\left(\mathrm{ycos}\:\mathrm{x}+\mathrm{2xe}^{\mathrm{y}} \right)\mathrm{dx}+\left(\mathrm{sin}\:\mathrm{x}+\mathrm{x}^{\mathrm{2}} \mathrm{e}^{\mathrm{y}} −\mathrm{1}\right)\mathrm{dy}=\mathrm{0} \\ $$ Answered by john santu last updated on 13/Mar/20 $$\frac{\partial\mathrm{M}}{\partial\mathrm{y}}\:=\:\mathrm{cos}\:\mathrm{x}+\mathrm{2xe}^{\mathrm{y}} \\…
Question Number 18940 by Tinkutara last updated on 01/Aug/17 $$\mathrm{A}\:\mathrm{light}\:\mathrm{rope}\:\mathrm{is}\:\mathrm{passed}\:\mathrm{over}\:\mathrm{a}\:\mathrm{pulley}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{at}\:\mathrm{its}\:\mathrm{one}\:\mathrm{end}\:\mathrm{a}\:\mathrm{block}\:\mathrm{is}\:\mathrm{attached}, \\ $$$$\mathrm{and}\:\mathrm{on}\:\mathrm{the}\:\mathrm{other}\:\mathrm{end}\:\mathrm{a}\:\mathrm{boy}\:\mathrm{is}\:\mathrm{climbing} \\ $$$$\mathrm{up}\:\mathrm{with}\:\mathrm{acceleration}\:\frac{{g}}{\mathrm{2}}\:\mathrm{relative}\:\mathrm{to}\:\mathrm{rope}. \\ $$$$\mathrm{Mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{block}\:\mathrm{is}\:\mathrm{30}\:\mathrm{kg}\:\mathrm{and}\:\mathrm{that}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{boy}\:\mathrm{is}\:\mathrm{40}\:\mathrm{kg}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{tension}\:\mathrm{and} \\ $$$$\mathrm{acceleration}\:\mathrm{of}\:\mathrm{the}\:\mathrm{rope}. \\ $$ Commented…
Question Number 150009 by mathdanisur last updated on 08/Aug/21 Answered by alcoho last updated on 09/Aug/21 $${iymc}\:{queztion} \\ $$$${ur}\:{identity}\:{is}\:{noted}\: \\ $$ Terms of Service Privacy…
Question Number 150007 by mathdanisur last updated on 08/Aug/21 $$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}}{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$ Answered by Ar Brandon last updated on 08/Aug/21 $${I}=\int\frac{{x}^{\mathrm{2}} +{x}}{{x}^{\mathrm{6}} +\mathrm{1}}{dx}=\int\frac{{x}^{\mathrm{2}}…
Question Number 150006 by mathdanisur last updated on 08/Aug/21 $$\mathrm{If}\:\:\mathrm{x}\:+\:\mathrm{y}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\mathrm{which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{cannot}\:\mathrm{be}\:\:\mathrm{xy}.? \\ $$ Answered by dumitrel last updated on 08/Aug/21 $${xy}={k}\Rightarrow{x}+\frac{{k}}{{x}}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow\mathrm{2}{x}^{\mathrm{2}} −{x}+\mathrm{2}{k}=\mathrm{0}\Rightarrow\bigtriangleup\geqslant\mathrm{0}\Rightarrow \\ $$$$\mathrm{1}−\mathrm{16}{k}\geqslant\mathrm{0}\Rightarrow{k}\in\left(−\infty;\frac{\mathrm{1}}{\mathrm{16}}\right]\Rightarrow{k}\notin\left(\frac{\mathrm{1}}{\mathrm{16}};\infty\right)…
Question Number 84469 by jagoll last updated on 13/Mar/20 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{sin}\:\mathrm{3b}\:+\:\left(\mathrm{cos}\:\mathrm{b}+\mathrm{sin}\:\mathrm{b}\right)\left(\mathrm{1}−\mathrm{2sin}\:\mathrm{2b}\right) \\ $$$$=\:\mathrm{cos}\:\mathrm{3b} \\ $$ Answered by som(math1967) last updated on 13/Mar/20 $${sin}\mathrm{3}{b}+{cosb}−\mathrm{2}{sin}\mathrm{2}{bcosb}+\mathrm{sin}\:{b}−\mathrm{2sin}\:{b}\mathrm{sin}\:\mathrm{2}{b} \\…
Question Number 84467 by jagoll last updated on 13/Mar/20 $$\int\:\mathrm{ln}\left(\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)\:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 149996 by tabata last updated on 08/Aug/21 $$\left(\mathrm{1}\right)\:\int\:\:\frac{{dx}}{\mathrm{1}+{tanx}} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\int\:\:\frac{\sqrt{{tanx}}}{{sinx}\:{cosx}}{dx} \\ $$ Answered by mindispower last updated on 08/Aug/21 $$=\int\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \left({x}\right)}.\frac{\sqrt{{tg}\left({x}\right)}}{{tg}\left({x}\right)}{dx}=\int\frac{\mathrm{1}}{{cos}^{\mathrm{2}}…
Question Number 84460 by jagoll last updated on 13/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{2}+\mathrm{x}\right)−\mathrm{sin}\:\left(\mathrm{2}−\mathrm{x}\right)}{\mathrm{x}} \\ $$ Commented by jagoll last updated on 13/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(\mathrm{2}+\mathrm{x}\right)+\mathrm{cos}\:\left(\mathrm{2}−\mathrm{x}\right)}{\mathrm{1}} \\ $$$$=\:\mathrm{2cos}\:\mathrm{2} \\…