Question Number 150963 by EDWIN88 last updated on 17/Aug/21 $${Given}\:{x}\:,{y}\:{real}\:{number}\:{such}\:{that} \\ $$$$\:\mathrm{0}<\frac{{y}}{{x}}<\frac{\mathrm{1}}{\mathrm{2}}.\:{Find}\:{minimum}\:{value} \\ $$$${of}\:\frac{\mathrm{2}{y}}{{x}−{y}}\:+\frac{\mathrm{3}{x}}{{x}+\mathrm{2}{y}}\:.\: \\ $$ Answered by john_santu last updated on 17/Aug/21 $$\:\mathrm{let}\:\frac{\mathrm{y}}{\mathrm{x}}\:=\:\mathrm{t}\:\Rightarrow\mathrm{f}\left(\mathrm{t}\right)=\frac{\mathrm{2t}}{\mathrm{1}−\mathrm{t}}+\frac{\mathrm{3}}{\mathrm{1}+\mathrm{2t}}\: \\…
Question Number 85425 by john santu last updated on 22/Mar/20 $${range}\:{of}\:{function} \\ $$$${y}\:=\:\frac{\mid{x}−\mathrm{1}\mid}{{x}+\mathrm{3}} \\ $$ Answered by john santu last updated on 22/Mar/20 $${for}\:{x}\:\geqslant\mathrm{1}\:\Rightarrow\:{y}\:=\:\frac{{x}−\mathrm{1}}{{x}+\mathrm{3}} \\…
Question Number 19886 by NECC last updated on 17/Aug/17 $${Good}\:{morning}\:{sirs}.{Please}\:{is} \\ $$$${there}\:{any}\:{site}\:{or}\:{pdf}\:{that}\:{really} \\ $$$${explains}\:{motion}\left({from}\:{equation}\right. \\ $$$${of}\:{motion}\:{to}\:{Newton}'{s}\:{laws}\:{of} \\ $$$$\left.{motion}\right)?\: \\ $$$${if}\:{there}\:{is}\:{pls} \\ $$$${mrw}\mathrm{1}\:,{ajfour}\:,\mathrm{123456}\:,{Tinkutara}, \\ $$$${mr}\:{b}.{e}.{h}.{i}\:,{joel}\:{and}\:{others}\:{please} \\…
Question Number 19884 by ajfour last updated on 17/Aug/17 Commented by ajfour last updated on 17/Aug/17 $$\:\:{A}\left({x}_{\mathrm{1}} ,{y}_{\mathrm{1}} \right)\:;\:\:{B}\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} \right)\:\:;\:{C}\left({x}_{\mathrm{3}} ,{y}_{\mathrm{3}} \right)\:\:; \\ $$$$\:\:{D}\left({x}_{\mathrm{4}}…
Question Number 85418 by oustmuchiya@gmail.com last updated on 21/Mar/20 $${Find}\:{the}\:{term}\:{indepent}\:{of}\:{x}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$ Commented by jagoll last updated on 22/Mar/20 $$\mathrm{let}\:\mathrm{2x}=\:\mathrm{u} \\ $$$$\left(\mathrm{u}−\frac{\mathrm{1}}{\mathrm{u}}\right)^{\mathrm{3}} =\:\mathrm{u}^{\mathrm{3}} −\mathrm{3}\left(\mathrm{u}^{\mathrm{2}} \right)\left(\frac{\mathrm{1}}{\mathrm{u}}\right)+\mathrm{3u}\left(\frac{\mathrm{1}}{\mathrm{u}^{\mathrm{2}}…
Question Number 85414 by M±th+et£s last updated on 21/Mar/20 $$\int\frac{\mathrm{1}}{\mathrm{1}+\sqrt{{cos}\left({x}\right)}\:}\:{dx} \\ $$ Commented by M±th+et£s last updated on 21/Mar/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\mathrm{1}+\sqrt{{cos}\left({x}\right)}}\:{dx}\:\:\:{typo}….\: \\ $$ Answered…
Question Number 85412 by Power last updated on 21/Mar/20 Commented by jagoll last updated on 22/Mar/20 $$\mathrm{by}\:\mathrm{observe} \\ $$$$\mathrm{x}\:=\:\mathrm{y} \\ $$$$\left(\mathrm{2x}\right)^{\mathrm{3}} \:=\:\mathrm{3}^{\mathrm{3}} \:\Rightarrow\:\mathrm{y}\:=\:\mathrm{x}=\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\left(\mathrm{2x}\right)^{\mathrm{2}}…
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Question Number 19875 by ajfour last updated on 16/Aug/17 Commented by ajfour last updated on 17/Aug/17 $${Find}\:{z}_{\mathrm{0}} \:,\:\frac{{p}}{{p}+{q}}\:,\:\frac{{r}}{{r}+{s}}\:;\:{in}\:{terms}\:{of} \\ $$$$\:\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:{z}_{\mathrm{3}} ,\:{and}\:{z}_{\mathrm{4}} \:. \\…