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Author: Tinku Tara

Question-85105

Question Number 85105 by naka3546 last updated on 19/Mar/20 Answered by MJS last updated on 19/Mar/20 $${x}=\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{8}}{\mathrm{9}}+\mathrm{1}+\frac{\mathrm{64}}{\mathrm{81}}+\frac{\mathrm{125}}{\mathrm{243}}+…={S}_{\infty} \\ $$$${S}_{{n}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{{k}^{\mathrm{3}} }{\mathrm{3}^{{k}} }\:=\frac{\mathrm{33}}{\mathrm{8}}−\left(\frac{{n}^{\mathrm{3}} }{\mathrm{2}}+\frac{\mathrm{9}{n}^{\mathrm{2}}…

pi-pi-x-2020-sin-x-cos-x-dx-8-find-pi-pi-x-2020-cos-x-dx-

Question Number 85097 by jagoll last updated on 19/Mar/20 $$\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{x}^{\mathrm{2020}} \:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{8} \\ $$$$\mathrm{find}\:\underset{−\pi} {\overset{\pi} {\int}}\:\mathrm{x}^{\mathrm{2020}} \:\mathrm{cos}\:\mathrm{x}\:\mathrm{dx}\:=\:? \\ $$ Answered by john santu last…

Question-150628

Question Number 150628 by aupo14 last updated on 14/Aug/21 Answered by som(math1967) last updated on 14/Aug/21 $$\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}.\boldsymbol{{x}}.\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{4}}=\mathrm{4}+\frac{\mathrm{1}}{\mathrm{4}}−\mathrm{4}\boldsymbol{{y}} \\ $$$$\left(\boldsymbol{{x}}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} =\left(\frac{\mathrm{17}}{\mathrm{4}}−\mathrm{4}\boldsymbol{{y}}\right) \\ $$$$\left(\boldsymbol{{x}}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} =−\mathrm{4}\left(\boldsymbol{{y}}−\frac{\mathrm{17}}{\mathrm{16}}\right) \\…

Question-19557

Question Number 19557 by ajfour last updated on 12/Aug/17 Commented by ajfour last updated on 12/Aug/17 $$\mathrm{If}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{line}\:\mathrm{through}\:\:\mathrm{z}=\:\mathrm{z}_{\mathrm{0}} \\ $$$$\mathrm{and}\:\:\mathrm{z}=\mathrm{c}\:\:\:\mathrm{be}\:\:\bar {\mathrm{a}z}+\mathrm{a}\bar {\mathrm{z}}+\mathrm{k}=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{z}=\mathrm{a}\:\mathrm{and}\:\mathrm{scalar}\:\mathrm{k}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{z}_{\mathrm{0}}…

Find-center-and-radius-of-circle-having-equation-zz-1-i-z-1-i-z-1-0-

Question Number 19555 by Tinkutara last updated on 12/Aug/17 $$\mathrm{Find}\:\mathrm{center}\:\mathrm{and}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{circle}\:\mathrm{having} \\ $$$$\mathrm{equation}\:{z}\bar {{z}}\:+\:\left(\mathrm{1}\:−\:{i}\right){z}\:+\:\left(\mathrm{1}\:+\:{i}\right)\bar {{z}}\:−\:\mathrm{1}\:=\:\mathrm{0}. \\ $$ Answered by ajfour last updated on 12/Aug/17 $$\mathrm{Equation}\:\mathrm{of}\:\mathrm{circle}: \\…