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1-2002-4-2002-7-2002-2002-2002-Thank-you-so-much-

Question Number 157546 by naka3546 last updated on 24/Oct/21 $$\left(\underset{\mathrm{1}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\left(\underset{\mathrm{4}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\left(\underset{\mathrm{7}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\ldots+\:\left(\underset{\mathrm{2002}} {\overset{\mathrm{2002}} {\:}}\right)\:\:=\:? \\ $$$${Thank}\:\:{you}\:\:{so}\:\:{much}\:. \\ $$ Commented by mr…

Question-26438

Question Number 26438 by San Sophanethsan069 last updated on 25/Dec/17 Answered by mrW1 last updated on 25/Dec/17 $${A}=\mathrm{999}…\mathrm{9}\:\left({n}\:{digits}\:\mathrm{9}\right) \\ $$$${S}\left({A}\right)={sum}\:{of}\:{digits}\:{of}\:{A}=\mathrm{9}{n} \\ $$$${A}=\mathrm{10}^{{n}} −\mathrm{1} \\ $$$${A}^{\mathrm{2}}…

Find-the-equation-of-the-tangents-drawn-from-the-point-1-3-to-the-parabola-y-2-16x-

Question Number 157487 by ZiYangLee last updated on 23/Oct/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{drawn} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{3}\right)\:\mathrm{to}\:\mathrm{the}\:\mathrm{parabola} \\ $$$${y}^{\mathrm{2}} =−\mathrm{16}{x}. \\ $$ Answered by mr W last updated on 23/Oct/21…

Sir-Tinku-Tara-I-ve-been-facing-some-difficulties-eversince-I-changed-my-device-1-I-can-t-save-my-work-as-images-to-my-new-device-In-case-I-have-to-upload-my-work-to-another-plateform-such-as-

Question Number 157478 by Ar Brandon last updated on 23/Oct/21 $$\mathrm{Sir}\:\mathrm{Tinku}-\mathrm{Tara}, \\ $$$$\mathrm{I}'\mathrm{ve}\:\mathrm{been}\:\mathrm{facing}\:\mathrm{some}\:\mathrm{difficulties}\:\mathrm{eversince}\:\mathrm{I}\:\mathrm{changed}\:\mathrm{my}\:\mathrm{device} \\ $$$$\mathrm{1}\bullet\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{save}\:\mathrm{my}\:\mathrm{work}\:\mathrm{as}\:\mathrm{images}\:\mathrm{to}\:\mathrm{my}\:\mathrm{new}\:\mathrm{device}. \\ $$$$\:\:\:\:\:\mathrm{In}\:\mathrm{case}\:\mathrm{I}\:\mathrm{have}\:\mathrm{to}\:\mathrm{upload}\:\mathrm{my}\:\mathrm{work}\:\mathrm{to}\:\mathrm{another}\:\mathrm{plateform}\:\mathrm{such}\:\mathrm{as}\:\mathrm{a}\: \\ $$$$\:\:\:\:\:\mathrm{whatsapp}\:\mathrm{group},\:\mathrm{I}'\mathrm{ll}\:\mathrm{just}\:\mathrm{have}\:\mathrm{to}\:\mathrm{send}\:\mathrm{it}\:\mathrm{directly}\:\mathrm{from}\:\mathrm{app}.\:\mathrm{Whereas} \\ $$$$\:\:\:\:\:\mathrm{with}\:\mathrm{my}\:\mathrm{previous}\:\mathrm{device}\:\mathrm{I}\:\mathrm{could}\:\mathrm{save}\:\mathrm{it}\:\mathrm{as}\:\mathrm{an}\:\mathrm{image}\:\mathrm{then}\:\mathrm{send}\:\mathrm{it}\:\mathrm{from} \\ $$$$\:\:\:\:\:\mathrm{gallery}\:\mathrm{while}\:\mathrm{on}\:\mathrm{another}\:\mathrm{plateforme}. \\ $$$$\mathrm{2}\bullet\:\mathrm{It}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{for}\:\mathrm{me}\:\mathrm{to}\:\mathrm{send}\:\mathrm{images}\:\mathrm{after}\:\mathrm{inserting}\:\mathrm{page}\:\mathrm{breaks}.\:\mathrm{It}\:\mathrm{has}…

1-u-4-1-u-4-du-

Question Number 157420 by Gbenga last updated on 23/Oct/21 $$\int\frac{\mathrm{1}}{\boldsymbol{{u}}^{\mathrm{4}} +\left(\mathrm{1}−\boldsymbol{{u}}\right)^{\mathrm{4}} }\boldsymbol{{du}} \\ $$ Answered by EvaNelle00 last updated on 23/Oct/21 $$\int\:\frac{{du}}{{u}^{\mathrm{4}} \left(\mathrm{1}\:+\:\left(\frac{\mathrm{1}−{u}}{{u}}\right)^{\mathrm{4}} \right)} \\…

If-m-tan-30-n-tan-12-cos-2-

Question Number 157388 by naka3546 last updated on 22/Oct/21 $${If}\:\:{m}\:\mathrm{tan}\:\left(\theta\:−\:\mathrm{30}°\right)\:=\:{n}\:\mathrm{tan}\:\left(\theta\:+\:\mathrm{12}°\right) \\ $$$$\mathrm{cos}\:\mathrm{2}\theta\:\:=\:? \\ $$ Commented by cortano last updated on 22/Oct/21 $$\:{m}\mathrm{tan}\:\left(\theta−\mathrm{30}°\right)={n}\mathrm{tan}\:\left(\mathrm{30}°+\theta−\mathrm{18}°\right) \\ $$$$\Rightarrow{m}\left(\frac{\mathrm{3tan}\:\theta−\sqrt{\mathrm{3}}}{\mathrm{3}+\sqrt{\mathrm{3}}\:\mathrm{tan}\:\theta}\right)={n}\left(\frac{\mathrm{tan}\:\left(\mathrm{30}°+\theta\right)−\mathrm{tan}\:\mathrm{18}°}{\mathrm{1}+\mathrm{tan}\:\left(\mathrm{30}°+\theta\right)\:\mathrm{tan}\:\mathrm{18}°}\right) \\…

1-n-1-5-n-2-5-n-3-2-n-1-1-4n-2-1-3-n-1-3n-5n-1-n-1-n-n-1-

Question Number 91837 by zainal tanjung last updated on 03/May/20 $$\left.\mathrm{1}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{5}}{\mathrm{n}+\mathrm{2}}−\frac{\mathrm{5}}{\mathrm{n}+\mathrm{3}}\:\right)=… \\ $$$$ \\ $$$$\left.\mathrm{2}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\mathrm{4n}^{\mathrm{2}} −\mathrm{1}}\right)=… \\ $$$$ \\ $$$$\left.\mathrm{3}\right).\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty}…