Question Number 62844 by alphaprime last updated on 25/Jun/19 $${Let}\:{p}\left({x}\right)\:=\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:\:{be}\:{such}\:{that}\:{p}\left({x}\right)\:{takes}\:{real}\:{values} \\ $$$${for}\:{real}\:{values}\:{of}\:{x}\:{and}\:{non}−{real}\:{values}\:{for}\:{non}−{real} \\ $$$${values}\:{of}\:{x}\:.\:{Prove}\:{that}\:{a}\:=\:\mathrm{0}\:{and}\:{find}\:{all} \\ $$$${possible}\:{values}\:{of}\:{c}. \\ $$ Answered by ajfour last updated on…
Question Number 128371 by aliibrahim1 last updated on 06/Jan/21 Commented by MJS_new last updated on 06/Jan/21 $${A}_{{n}} =\frac{\mathrm{752}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{2}{k}−\mathrm{1}}\:−\mathrm{752}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{2}{k}}}{\mathrm{2}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{n}+{k}}} \\…
Question Number 128368 by I want to learn more last updated on 06/Jan/21 $$\mathrm{If}\:\:\:\:\mathrm{a}_{\mathrm{1}} \:=\:\:\mathrm{2},\:\:\:\:\mathrm{a}_{\mathrm{2}} \:\:=\:\:\mathrm{3},\:\:\:\:\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{2}} \:\:=\:\:\mathrm{a}_{\mathrm{n}\:\:+\:\:\mathrm{1}} \:\:+\:\:\frac{\mathrm{a}}{\mathrm{2}},\:\:\:\:\:\:\mathrm{find}\:\:\mathrm{a}_{\mathrm{n}} \\ $$ Answered by mr W last…
Question Number 128369 by I want to learn more last updated on 06/Jan/21 $$\mathrm{If}\:\:\:\mathrm{u}_{\mathrm{1}} \:\:+\:\:\mathrm{u}_{\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{3}} \:\:+\:\:…\:\:+\:\:\mathrm{u}_{\mathrm{n}} \:\:\:=\:\:\:\mathrm{2n}^{\mathrm{2}} \:\:+\:\:\mathrm{n}\:\:\:\mathrm{is}\:\mathrm{an}\:\mathrm{AP}. \\ $$$$\mathrm{Find}\:\:\:\:\:\:\:\:\mathrm{u}_{\mathrm{1}} \:\:+\:\:\mathrm{u}_{\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{3}} \:\:+\:\:…\:\:+\:\:\mathrm{u}_{\mathrm{2n}\:\:−\:\:\mathrm{2}} \:\:+\:\:\mathrm{u}_{\mathrm{2n}\:\:−\:\:\mathrm{1}}…
Question Number 128341 by liberty last updated on 06/Jan/21 $$\mathrm{Which}\:\mathrm{is}\:\mathrm{larger}\:\mathrm{Z}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{6}−\frac{\mathrm{4}}{\mathrm{11}}}}\:\mathrm{or}\:\mathrm{S}\:=\:\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{3}}{\mathrm{6}−\frac{\mathrm{5}}{\mathrm{11}}}}\:? \\ $$ Commented by mr W last updated on 06/Jan/21 $${without}\:{calculation}: \\ $$$${Z}:\:{larger}\nearrow{smaller}\nearrow{larger} \\ $$$$\Rightarrow{Z}\:{is}\:{larger}\:{than}\:{S}.…
Question Number 62798 by ANTARES VY last updated on 25/Jun/19 $$\boldsymbol{\mathrm{Calculate}} \\ $$$$\boldsymbol{\mathrm{tg}}\left(\mathrm{20}°\right)+\mathrm{4}\boldsymbol{\mathrm{sin}}\left(\mathrm{20}°\right)+\mathrm{1} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 128329 by bramlexs22 last updated on 06/Jan/21 $$\left(\mathrm{2}\right)\mathrm{Solution}\:\mathrm{set}\::\:{x}\:\mid\mathrm{2}{x}−\mathrm{6}\:\mid\:<\:\mathrm{3}{x}\: \\ $$$$\mathrm{is}\:\_ \\ $$$$\left(\mathrm{2}\right)\:\mathrm{If}\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{2}−\sqrt{{a}+{bx}^{\mathrm{3}} }}{{x}−\mathrm{2}}\:=\:{H}\:,\:{then} \\ $$$$\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{{x}^{\mathrm{2}} −\mathrm{4}}{\:\sqrt{{a}+{bx}^{\mathrm{3}} }−\mathrm{1}}\:=\:\_ \\ $$ Answered by…
Question Number 128290 by mr W last updated on 06/Jan/21 $${find}\:\mathrm{10}−\frac{\mathrm{1}}{\mathrm{10}−\frac{\mathrm{1}}{\mathrm{10}−\frac{\mathrm{1}}{\mathrm{10}−\frac{\mathrm{1}}{\mathrm{10}−……}}}}=? \\ $$$$\left({A}\right)\:\:\:\:\:\mathrm{5}−\mathrm{2}\sqrt{\mathrm{6}} \\ $$$$\left({B}\right)\:\:\:\:\:\mathrm{5}+\mathrm{2}\sqrt{\mathrm{6}} \\ $$$$\left({C}\right)\:\:\:\:\:\mathrm{5}\pm\mathrm{2}\sqrt{\mathrm{6}} \\ $$$$\left({D}\right)\:\:\:\:\:{none}\:{of}\:{above} \\ $$$$ \\ $$$${please}\:{give}\:{your}\:{answer}\:{and}\:{explain} \\ $$$${why}!…
Question Number 128264 by bobhans last updated on 06/Jan/21 $$\sqrt[{\mathrm{8}\:\:\:\:}]{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−\frac{\mathrm{1}}{\mathrm{2207}−…}}}}} \\ $$ Commented by MJS_new last updated on 06/Jan/21 $$\frac{\mathrm{3}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$ Commented by bobhans…
Question Number 128232 by math35 last updated on 05/Jan/21 $$\mathrm{1}.\mathrm{For}\:\mathrm{n}\in\mathbb{N},\mathrm{define}\:\:\mathrm{s}_{\mathrm{n}} =\mathrm{1}+\mathrm{2}^{\mathrm{2}^{\mathrm{n}} } +\mathrm{2}^{\mathrm{2}^{\mathrm{n}+\mathrm{1}} } .\mathrm{Which}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{is}\:\mathrm{false}\:\mathrm{for}\:\mathrm{some}\:\mathrm{values}\:\mathrm{of}\:\mathrm{n}\in\mathbb{N}? \\ $$$$\mathrm{A}.\mathrm{3}\mid\mathrm{s}_{\mathrm{n}} \\ $$$$\mathrm{B}.\mathrm{7}\mid\mathrm{s}_{\mathrm{n}} \\ $$$$\mathrm{C}.\mathrm{s}_{\mathrm{n}} \mid\mathrm{s}_{\mathrm{n}+\mathrm{1}} \\…