Question Number 138236 by mohammad17 last updated on 11/Apr/21 $${prove}\:{that}\: \\ $$$$ \\ $$$$\frac{{e}^{−\mathrm{2}{y}} }{\mathrm{1}+{e}^{−\mathrm{2}{y}} }<\mid{tan}\left({z}\right)\:−\:{i}\mid<\frac{{e}^{−\mathrm{2}{y}} }{\mathrm{1}−{e}^{−\mathrm{2}{y}} }\:\:\:,{y}>\mathrm{0} \\ $$$$ \\ $$$${how}\:{can}\:{solve}\:{this}\:? \\ $$ Commented…
Question Number 7165 by Tawakalitu. last updated on 15/Aug/16 $$\mathrm{30}\:{teams}\:{participated}\:{in}\:{the}\:{football}\:{tournament}\:.\:{At}\:{the}\: \\ $$$${end}\:{of}\:{the}\:{competition}\:{it}\:{turned}\:{out}\:{that}\:{in} \\ $$$${Any}\:{group}\:{of}\:{three}\:\:{teams}\:{it}\:{is}\:{possible}\:{to}\:{single}\:{out}\:{two} \\ $$$${teams}\:{which}\:{score}\:{equal}\:{point}\:{in}\:{three}\:{games}.\: \\ $$$${within}\:{this}\:{group}\:\left(\mathrm{3}\:{points}\:{are}\:{given}\:{for}\:{the}\:{victory},\:\right. \\ $$$$\left.\mathrm{1}\:{point}\:{for}\:{the}\:{draw}\:,\:\mathrm{0}\:{point}\:{for}\:{the}\:{defeat}\:\right).\: \\ $$$${what}\:{is}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{draws}\:{that}\:{can}\:{occur} \\ $$$${in}\:{such}\:{a}\:{tournament}\:? \\…
Question Number 7164 by aftab ahmad last updated on 14/Aug/16 Answered by Yozzia last updated on 14/Aug/16 $${By}\:{Power}\:{of}\:{a}\:{Point}\:{theorem}, \\ $$$$\left({AB}\right)\left({AC}\right)=\left({AD}\right)\left({AD}\right)=\left({AD}\right)^{\mathrm{2}} \\ $$$$\Rightarrow{AC}=\frac{\left({AD}\right)^{\mathrm{2}} }{{AB}}=\frac{\mathrm{10}^{\mathrm{2}} }{\mathrm{5}}=\mathrm{20}{cm} \\…
Question Number 7163 by Tawakalitu. last updated on 14/Aug/16 Commented by sou1618 last updated on 14/Aug/16 $$\underset{{a}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}\left(\underset{{b}=\mathrm{0}} {\overset{\mathrm{4}} {\sum}}{a}^{{b}} \right)=\underset{{a}=\mathrm{1}} {\overset{\mathrm{4}} {\sum}}\left({a}^{\mathrm{0}} +{a}^{\mathrm{1}}…
Question Number 138235 by mr W last updated on 11/Apr/21 $${for}\:{p},{q}\in\mathbb{R}\:{satisfying}\:{p}^{\mathrm{4}} +{q}^{\mathrm{4}} =\mathrm{4}{pq} \\ $$$${find}\:{the}\:{range}\:{of}\:{p}+{q}\:{when} \\ $$$$\left.\mathrm{1}\right)\:{no}\:{restriction} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{0}\leqslant{p}\leqslant\mathrm{1},\:\mathrm{0}\leqslant{q}\leqslant\mathrm{1} \\ $$ Answered by mr W…
Question Number 7161 by Tawakalitu. last updated on 14/Aug/16 $${If}\:\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0},\:\:{prove}\:{that}. \\ $$$${x}\:=\:\frac{\mathrm{2}{c}}{−\:{b}\:\pm\:\sqrt{{b}^{\mathrm{2}} \:−\:\mathrm{4}{ac}}}\: \\ $$ Commented by sou1618 last updated on 14/Aug/16 $$\left(\ast\right)\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}…
Question Number 72694 by MJS last updated on 31/Oct/19 $$\mathrm{convergent}\:\mathrm{or}\:\mathrm{divergent}? \\ $$$${S}=\frac{\mathrm{2}}{\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{1}}+\frac{\mathrm{2}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{5}}−\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{2}}{\mathrm{7}}−\frac{\mathrm{1}}{\mathrm{7}}… \\ $$ Commented by mathmax by abdo last updated on 31/Oct/19 $${S}=\sum_{{n}=\mathrm{0}} ^{\infty}…
Question Number 7159 by Master Moon last updated on 14/Aug/16 $$\boldsymbol{{log}}_{\mathrm{2}} \underset{\boldsymbol{{x}}=\mathrm{1}} {\overset{\mathrm{2015}} {\prod}}\:\underset{\boldsymbol{{y}}=\mathrm{1}} {\overset{\mathrm{2015}} {\prod}}\left(\mathrm{1}+\boldsymbol{{e}}^{\frac{\mathrm{2}\boldsymbol{\pi{ixy}}}{\mathrm{2015}}} \right)\:=\:? \\ $$ Commented by FilupSmith last updated on…
Question Number 138231 by Bekzod Jumayev last updated on 11/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7157 by Tawakalitu. last updated on 13/Aug/16 $${If}\:{a}\:{and}\:{b}\:{are}\:{positive}\:{numbers} \\ $$$${what}\:{is}\:{the}\:{value}\:{of}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{{ax}} \:−\:{e}^{{bx}} }{\left(\mathrm{1}\:+\:{e}^{{ax}} \right)\left(\mathrm{1}\:+\:{e}^{{bx}} \right)}\:{dx}\: \\ $$ Answered by Yozzia…