Question Number 141525 by hgrocks last updated on 20/May/21 $$\mathrm{Let}\:<\mathrm{x}_{\mathrm{n}} >\:\mathrm{be}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{defined}\:\mathrm{by} \\ $$$$\mathrm{x}_{\mathrm{n}+\mathrm{1}} \:=\:\frac{\mathrm{1}}{\mathrm{k}}\left(\mathrm{x}_{\mathrm{n}} +\frac{\mathrm{k}}{\mathrm{x}_{\mathrm{n}} }\right)\:\forall\:\mathrm{n}\:\in\:\mathbb{N} \\ $$$$\mathrm{Show}\:\mathrm{that}\:<\mathrm{x}_{\mathrm{n}} >\:\mathrm{converges}\:\mathrm{to}\:\sqrt{\frac{\mathrm{k}}{\mathrm{k}−\mathrm{1}}} \\ $$$$\mathrm{x}_{\mathrm{1}} >\mathrm{0}\:,\:\mathrm{k}>\mathrm{1} \\ $$ Answered…
Question Number 141521 by 7770 last updated on 19/May/21 $$\begin{cases}{\sqrt[{\mathrm{3}}]{\boldsymbol{{x}}+\boldsymbol{{y}}}+\sqrt{\boldsymbol{{x}}−\mathrm{3}\boldsymbol{{y}}}=\mathrm{4}}\\{\mathrm{2}\boldsymbol{{x}}+\mathrm{3}\boldsymbol{{y}}=\mathrm{17}}\end{cases} \\ $$$$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}. \\ $$ Answered by MJS_new last updated on 20/May/21 $$\mathrm{let}'\mathrm{s}\:\mathrm{try}\:{x}+{y}={a}^{\mathrm{3}} \:\wedge\:{x}−\mathrm{3}{y}={b}^{\mathrm{2}} \\ $$$$\Leftrightarrow…
Question Number 75940 by Rio Michael last updated on 21/Dec/19 $${Given}\:{that}\:{a}\in\mathbb{Z}\:{and}\:{k}\in\mathbb{Z}\:{and}\:\left[{a}+{x}\right]\:=\:{a}\:+\left[{x}\right]\:=\:{k} \\ $$$$\left.{a}\right)\:{show}\:{that}\:\:{k}−{a}\leqslant\:{x}\leqslant\:{k}−{a}\:+\mathrm{1} \\ $$$$\left.{b}\left.\right)\:{Deduce}\:{from}\:\left({a}\right)\right)\:{that}\:\left[{x}+{a}\right]\:=\:\left[{x}\right]\:+{a} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 75938 by Rio Michael last updated on 21/Dec/19 $${solve}\:{the}\:{inequality} \\ $$$$\:{ln}\left({x}^{\mathrm{2}} −\mathrm{4}{e}^{\mathrm{2}} \right)<\:\mathrm{1}\:+\:{ln}\mathrm{3}{x} \\ $$ Commented by turbo msup by abdo last updated…
Question Number 75937 by Rio Michael last updated on 21/Dec/19 $${find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{x}\:{for}\:{which}\: \\ $$$$\:\:\frac{{ln}\:{x}\:+\:\mathrm{2}}{{lnx}−\mathrm{2}}\:>\:\frac{\mathrm{1}−{lnx}}{\mathrm{1}+{lnx}} \\ $$ Answered by benjo last updated on 21/Dec/19 Commented by Rio…
Question Number 75936 by Rio Michael last updated on 21/Dec/19 $${prove}\:{that}\:{if}\:\left[\frac{{x}\:+\:\mathrm{1}}{{x}}\right]\:=\:\mathrm{0}\:{then}\:{x}\:\leqslant\:−\mathrm{1} \\ $$ Commented by turbo msup by abdo last updated on 21/Dec/19 $$\left[\frac{{x}+\mathrm{1}}{{x}}\right]=\mathrm{0}\:\Rightarrow\left[\mathrm{1}+\frac{\mathrm{1}}{{x}}\right]=\mathrm{0}\:\Rightarrow \\…
Question Number 75934 by Rio Michael last updated on 21/Dec/19 $${how}\:{do}\:{i}\:{sketch}\:{the}\:{curve}\: \\ $$$${y}\:=\:{x}−\left[{x}\right]\:,{for}\:\mathrm{0}\leqslant{x}<\mathrm{6} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 141469 by otchereabdullai@gmail.com last updated on 19/May/21 $$\mathrm{simplify} \\ $$$$\left(\mathrm{log}_{\mathrm{3}} \mathrm{11}\right)\left(\mathrm{log}_{\mathrm{11}} \mathrm{13}\right)\left(\mathrm{log}_{\mathrm{13}} \mathrm{15}\right)\left(\mathrm{log}_{\mathrm{15}} \mathrm{27}\right)\left(\mathrm{log}_{\mathrm{27}} \mathrm{81}\right) \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{need}\:\mathrm{help} \\ $$ Answered by bramlexs22 last…
Question Number 10391 by 314159 last updated on 06/Feb/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\mathrm{through}\:\left(\mathrm{2},\mathrm{3}\right)\: \\ $$$$\left(\mathrm{i}\right)\mathrm{parallel}\:\mathrm{to} \\ $$$$\left(\mathrm{ii}\right)\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{2x}−\mathrm{3y}+\mathrm{6}=\mathrm{0} \\ $$ Answered by mrW1 last updated on 06/Feb/17…
Question Number 141453 by Khalmohmmad last updated on 19/May/21 Commented by PRITHWISH SEN 2 last updated on 19/May/21 $$\mathrm{let} \\ $$$$\mathrm{ab}=\mathrm{t}\:\:\:\mathrm{a}+\mathrm{b}=\mathrm{u} \\ $$$$\mathrm{then} \\ $$$$\mathrm{tu}=\mathrm{880}…