Question Number 109303 by peter frank last updated on 22/Aug/20 Commented by som(math1967) last updated on 23/Aug/20 $$\mathrm{Acute}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{y}=\mathrm{x}+\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{x}−\mathrm{axis}\:\mathrm{istan}^{−\mathrm{1}} \mathrm{1}=\frac{\pi}{\mathrm{4}} \\ $$$$\therefore\mathrm{angle}\:\mathrm{between}\:\mathrm{bisector} \\ $$$$\mathrm{and}\:\mathrm{x}−\mathrm{axis}\:=\frac{\pi}{\mathrm{8}}…
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Question Number 109246 by peter frank last updated on 22/Aug/20 Answered by Ar Brandon last updated on 22/Aug/20 $$\mathrm{a}.\:\mathrm{I}=\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{4x}+\mathrm{2}}}=\int\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} −\mathrm{2}}} \\ $$$$\:\:\:\:\mathrm{x}+\mathrm{2}=\sqrt{\mathrm{2}}\mathrm{ch}\theta\Rightarrow\mathrm{dx}=\sqrt{\mathrm{2}}\mathrm{sh}\theta\mathrm{d}\theta \\ $$$$\:\:\:\mathrm{I}=\int\frac{\mathrm{sh}\theta\mathrm{d}\theta}{\left(\sqrt{\mathrm{2}}\mathrm{ch}\theta−\mathrm{1}\right)\sqrt{\mathrm{sh}^{\mathrm{2}}…
Question Number 174677 by pluton last updated on 08/Aug/22 Commented by Rasheed.Sindhi last updated on 08/Aug/22 $$\mathrm{See}\:\mathrm{Q}#\mathrm{174591} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 109075 by Rio Michael last updated on 20/Aug/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{twe}\:\mathrm{circles}\: \\ $$$${C}_{\mathrm{1}} \::\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:−\mathrm{6}{x}−\mathrm{4}{y}\:+\:\mathrm{9}\:=\:\mathrm{0}\:\mathrm{and}\:{C}_{\mathrm{2}} \::\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{6}{y}\:+\:\mathrm{9}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}\:{C}_{\mathrm{3}} \:\mathrm{which}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{centre} \\ $$$$\mathrm{of}\:{C}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\mathrm{of}\:\mathrm{intersection}\:\mathrm{of}\:{C}_{\mathrm{1}}…
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Question Number 108913 by Rasheed.Sindhi last updated on 20/Aug/20 $$\mathcal{IF}\:{F}\:\:{varies}\:{directly}\:{as}\:{A}\:{and}\:{N}, \\ $$$${find}\:\:{the}\:{constant}\:{of} \\ $$$${proportionality}\:{when}\:{A}=\mathrm{182}, \\ $$$${F}=\mathrm{365}\:{and}\:{N}=\mathrm{80}. \\ $$ Answered by Don08q last updated on 20/Aug/20…
Question Number 43350 by peter frank last updated on 10/Sep/18 Commented by maxmathsup by imad last updated on 10/Sep/18 $${let}\:\:{S}\:\left({x}\right)={x}\:+\mathrm{2}{x}^{\mathrm{2}} \:+\mathrm{3}{x}^{\mathrm{3}} \:+…{nx}^{{n}} \:\Rightarrow\:\frac{{S}\left({x}\right)}{{x}}=\mathrm{1}+\mathrm{2}{x}\:+\mathrm{3}{x}^{\mathrm{2}} \:+….{nx}^{{n}−\mathrm{1}} \:{but}…