Question Number 11764 by Peter last updated on 31/Mar/17 $$\mathrm{if}\:\mathrm{x}\:\mathrm{y}\:\mathrm{and}\:\mathrm{z}\:\mathrm{are}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\frac{\mathrm{x}\:+\:\mathrm{xy}}{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{1}}\:=\:\mathrm{2} \\ $$$$\frac{\mathrm{2x}\:+\:\mathrm{xz}}{\mathrm{x}\:+\:\mathrm{z}\:+\mathrm{2}}\:=\:\mathrm{3} \\ $$$$\frac{\mathrm{2}\:+\:\mathrm{2y}+\:\mathrm{z}\:+\:\mathrm{yz}}{\mathrm{y}\:+\:\mathrm{z}\:+\mathrm{3}}\:=\:\mathrm{4} \\ $$$$\mathrm{so},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{y}\:+\:\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{z}\:+\:\mathrm{2}\:}\:=\:….? \\ $$$$ \\ $$ Answered…
Question Number 77296 by mathocean1 last updated on 05/Jan/20 $$\mathrm{Determiner}\:\mathrm{et}\:\mathrm{construire}\:\mathrm{l}.\mathrm{ensemble} \\ $$$$\mathrm{des}\:\mathrm{points}\:\mathrm{M}\:\mathrm{tel}\:\mathrm{que}: \\ $$$$\mathrm{3MA}^{\mathrm{2}} +\mathrm{MB}^{\mathrm{2}} −\mathrm{MC}^{\mathrm{2}} =−\mathrm{42} \\ $$$$\mathrm{Le}\:\mathrm{plan}\:\mathrm{est}\:\mathrm{muni}\:\mathrm{d}.\mathrm{un}\:\mathrm{repere}\: \\ $$$$\mathrm{orthonorme}\:\left(\mathrm{O},\mathrm{I},\mathrm{J}\right) \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{2}\right)\:\:\:\mathrm{B}\left(−\mathrm{2},\mathrm{3}\right)\:\:\mathrm{C}\left(\mathrm{1},\mathrm{9}\right). \\ $$$$\mathrm{on}\:\mathrm{considere}\:\mathrm{que}\:…
Question Number 77297 by vishalbhardwaj last updated on 05/Jan/20 $$\mathrm{If}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{differential} \\ $$$$\mathrm{equation}\:\left(\frac{\mathrm{2}+\mathrm{sinx}}{\mathrm{1}+\mathrm{y}}\right)\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{cosx}\:\mathrm{and} \\ $$$$\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{y}\left(\pi/\mathrm{2}\right)\:\:? \\ $$ Answered by john santu last updated on…
Question Number 142829 by liberty last updated on 06/Jun/21 $$\:{Find}\:{the}\:{simplest}\:{form}\:{for}\: \\ $$$$\:\:{T}\:=\:\sqrt{\mathrm{1}+\sqrt{−\mathrm{3}}}\:+\sqrt{\mathrm{1}−\sqrt{−\mathrm{3}}}\: \\ $$ Answered by EDWIN88 last updated on 06/Jun/21 $$\mathrm{Let}\:\sqrt{\mathrm{a}}\:+\sqrt{−\mathrm{b}}\:=\:\sqrt{\mathrm{1}+\sqrt{−\mathrm{3}}}\:\mathrm{with}\:\mathrm{a}>\mathrm{0}\:,\mathrm{b}>\mathrm{0} \\ $$$$\Rightarrow\mathrm{a}−\mathrm{b}+\mathrm{2}{i}\sqrt{\mathrm{ab}}\:=\:\mathrm{1}+{i}\sqrt{\mathrm{3}}\:\mathrm{we}\:\mathrm{get}\:\begin{cases}{\mathrm{a}−\mathrm{b}=\mathrm{1}}\\{\mathrm{2}\sqrt{\mathrm{ab}}\:=\sqrt{\mathrm{3}}}\end{cases} \\…
Question Number 77294 by Rabnawaz last updated on 05/Jan/20 $${f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{27}{x} \\ $$$${Find}\:{intervals}\:{where}\:{given}\:{fuction}\:{ii} \\ $$$${is} \\ $$$$\mathrm{1}.{increasing} \\ $$$$\mathrm{2}.{decreasing} \\ $$$$\mathrm{3}\:{concave}\:{up}\:{and}\:{down} \\ $$$$\mathrm{4}\:{point}\:{of}\:{inflection} \\ $$…
Question Number 11759 by Joel576 last updated on 31/Mar/17 $$\mathrm{A}\:\mathrm{quadrilateral}\:\mathrm{with}\:\mathrm{consecutive}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{7},\:\mathrm{15},\:\mathrm{15},\:\mathrm{and}\:{d} \\ $$$$\mathrm{is}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{its}\:\mathrm{diameter}\:{d}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{circle} \\ $$ Answered by ajfour last updated on 31/Mar/17 Commented by…
Question Number 77290 by TawaTawa last updated on 05/Jan/20 $$\int\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} }\:\:\mathrm{dx} \\ $$ Commented by mathmax by abdo last updated on 05/Jan/20 $${let}\:{I}\:=\int\sqrt{{x}^{\mathrm{3}} \:+{x}^{\mathrm{4}}…
Question Number 11754 by Joel576 last updated on 31/Mar/17 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{between}\:\mathrm{1}\:−\:\mathrm{2017} \\ $$$$\mathrm{that}\:\mathrm{aren}'\mathrm{t}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5},\:\mathrm{6},\:\mathrm{7},\:\mathrm{8}\:? \\ $$ Answered by mrW1 last updated on 31/Mar/17 $${let}\:{a}={count}\:{of}\:{numbers}\:{which}\:{are}\:{multiple}\:{of}\:\mathrm{5} \\ $$$${let}\:{b}={count}\:{of}\:{numbers}\:{which}\:{are}\:{multiple}\:{of}\:\mathrm{6} \\…
Question Number 11753 by Joel576 last updated on 31/Mar/17 $${a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{from}\:\mathrm{equation}\:{x}^{\mathrm{3}} \:−\:\mathrm{5}{x}^{\mathrm{2}} \:−\:\mathrm{9}{x}\:+\:\mathrm{10}\:=\:\mathrm{0} \\ $$$$\mathrm{If}\:{P}\left({x}\right)\:=\:{Ax}^{\mathrm{3}} \:+\:{Bx}^{\mathrm{2}} \:+\:{Cx}\:−\:\mathrm{2015}\:\mathrm{and} \\ $$$${P}\left({a}\right)\:=\:{b}\:+\:{c}\: \\ $$$${P}\left({b}\right)\:=\:{a}\:+\:{c} \\ $$$${P}\left({c}\right)\:=\:{a}\:+\:{b} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{A}\:+\:{B}\:+\:{C}\:? \\…
Question Number 11751 by tawa last updated on 31/Mar/17 $$\mathrm{Simplify}:\:\mathrm{sin}\left(\mathrm{6}\theta\right) \\ $$ Answered by mrW1 last updated on 31/Mar/17 $$\mathrm{sin}\:\left(\mathrm{6}\theta\right)=\mathrm{sin}\:\left(\mathrm{4}\theta+\mathrm{2}\theta\right)=\mathrm{sin}\:\left(\mathrm{4}\theta\right)\mathrm{cos}\:\left(\mathrm{2}\theta\right)+\mathrm{sin}\:\left(\mathrm{2}\theta\right)\mathrm{cos}\:\left(\mathrm{4}\theta\right) \\ $$$$=\mathrm{2sin}\:\left(\mathrm{2}\theta\right)\mathrm{cos}^{\mathrm{2}} \:\left(\mathrm{2}\theta\right)+\mathrm{sin}\:\left(\mathrm{2}\theta\right)\left[\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:\left(\mathrm{2}\theta\right)\right] \\…