Question Number 106479 by mohammad17 last updated on 05/Aug/20 Answered by Rio Michael last updated on 05/Aug/20 $$\mathrm{c}.\:\mathrm{Let}\:\:{S}\:=\:{a}\:+\:{ar}\:+\:{ar}^{\mathrm{2}} \:+\:…+\:{ar}^{{n}−\mathrm{1}} \:….\left({i}\right) \\ $$$$\:\:\:\mathrm{now}\:{rS}\:=\:{ra}\:+\:{ar}^{\mathrm{2}} \:+\:{ar}^{\mathrm{3}} \:+…+{ar}^{{n}} …..\left({ii}\right)…
Question Number 106469 by ZiYangLee last updated on 05/Aug/20 $$\mathrm{Solve}\:\mathrm{cos}^{\mathrm{2}} \mathrm{x}+\mathrm{3cos}^{\mathrm{2}} \mathrm{2x}=\mathrm{cos}^{\mathrm{2}} \mathrm{3x} \\ $$ Answered by mahdi last updated on 05/Aug/20 $$\mathrm{cos}\left(\mathrm{3x}\right)=\mathrm{cos}\left(\mathrm{2x}\right).\mathrm{cosx}−\mathrm{sin}\left(\mathrm{2x}\right).\mathrm{sinx}= \\ $$$$\left(\mathrm{2cos}^{\mathrm{2}}…
Question Number 106465 by mohammad17 last updated on 05/Aug/20 Answered by Dwaipayan Shikari last updated on 05/Aug/20 $$ \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 106449 by mohammad17 last updated on 05/Aug/20 Answered by Dwaipayan Shikari last updated on 05/Aug/20 $${y}\sqrt{{x}}−{x}\sqrt{{y}}=\mathrm{9} \\ $$$${y}\frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}+\sqrt{{x}}.\frac{{dy}}{{dx}}−\frac{{x}}{\mathrm{2}\sqrt{{y}}}.\frac{{dy}}{{dx}}−\sqrt{{y}}=\mathrm{0} \\ $$$$\frac{{dy}}{{dx}}\left(\sqrt{{x}}−\frac{{x}}{\mathrm{2}\sqrt{{y}}}\right)=\sqrt{{y}}−\frac{{y}}{\mathrm{2}\sqrt{{x}}} \\ $$$$\frac{{dy}}{{dx}}=\frac{\mathrm{2}\sqrt{{xy}}−{y}}{\mathrm{2}\sqrt{{x}}}.\frac{\mathrm{2}\sqrt{{y}}}{\mathrm{2}\sqrt{{xy}}−{x}} \\…
Question Number 106444 by mathdave last updated on 05/Aug/20 Answered by nimnim last updated on 05/Aug/20 $${LHS}:\:\mathrm{3}{tan}^{−\mathrm{1}} \left(\mathrm{2}\right)+{tan}^{−\mathrm{1}} \left(\frac{\mathrm{9}}{\mathrm{13}}\right) \\ $$$$=\:\pi+{tan}\left(\frac{\mathrm{6}−\mathrm{8}}{\mathrm{1}−\mathrm{12}}\right)+{tan}^{−\mathrm{1}} \left(\frac{\mathrm{9}}{\mathrm{13}}\right)\:\:\:\:\:\:\:\left({as}\:\mathrm{2}>\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\right) \\ $$$$=\pi+{tan}^{\mathrm{1}} \left(\frac{\mathrm{2}}{\mathrm{11}}\right)+{tan}^{−\mathrm{1}}…
Question Number 106424 by pandiyan last updated on 05/Aug/20 $$\int{x}^{\mathrm{2}} \\ $$ Answered by Her_Majesty last updated on 05/Aug/20 $${syntax}\:{error};\:{it}\:{must}\:{be}\:\int{x}^{\mathrm{2}} {dx} \\ $$$$\int{x}^{{n}} {dx}=\frac{{x}^{{n}+\mathrm{1}} }{{n}+\mathrm{1}}+{C}…
Question Number 106422 by Algoritm last updated on 05/Aug/20 Commented by mr W last updated on 05/Aug/20 $$\mathrm{73}!=\mathrm{1}×\mathrm{2}×\mathrm{3}×…×\mathrm{49}×\mathrm{50}×…×\mathrm{73} \\ $$$$\mathrm{73}!=\mathrm{0}\:\left({mod}\:\mathrm{2}\right) \\ $$$$\mathrm{73}!=\mathrm{0}\:\left({mod}\:\mathrm{3}\right) \\ $$$$\mathrm{73}!=\mathrm{0}\:\left({mod}\:\mathrm{4}\right) \\…
Question Number 106379 by Algoritm last updated on 04/Aug/20 Answered by mr W last updated on 04/Aug/20 $$\frac{{x}^{\mathrm{2}} }{\mathrm{1}−{x}}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{x}^{{n}+\mathrm{1}} \:\:{for}\:\mid{x}\mid<\mathrm{1} \\ $$$$\frac{\mathrm{2}{x}}{\mathrm{1}−{x}}+\frac{{x}^{\mathrm{2}} }{\left(\mathrm{1}−{x}\right)^{\mathrm{2}}…
Question Number 171906 by ali009 last updated on 23/Jun/22 $${a}\:{fource}\:{f}\:{facts}\:{on}\:{a}\:{body}\:{of}\:{mass} \\ $$$$\left({t}+\mathrm{2}\right){kg}\:{and}\:{it}'{s}\:{momentum}\:{was} \\ $$$$\left({t}^{\mathrm{2}} +\mathrm{6}{t}+\mathrm{8}\right)\:{kg}\:.\:{m}/\:{sec} \\ $$$$\:{what}\:{is}\:{the}\:{average}\:{power}\:{in}\:{the} \\ $$$${first}\:\mathrm{3}\:{seconds} \\ $$ Terms of Service Privacy…
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