Question Number 173902 by mnjuly1970 last updated on 20/Jul/22 $$ \\ $$$$\:\:{Q}:\:{How}\:{many}\:{common}\:{three}−{digit}\:{numbers} \\ $$$$\:\:\:\:{are}\:{there}\:{in}\:{the}\:{following} \\ $$$$\:\:\:\:\:{two}\:{sequences}? \\ $$$$\:\:\:\:\:\begin{cases}{\:\:{a}_{{n}} \:=\:\mathrm{1}\:\:,\:\mathrm{5}\:,\:\mathrm{9}\:,\mathrm{13}\:,\:…}\\{\:\:{b}_{\:{m}} \:=\:\mathrm{4}\:,\:\mathrm{7}\:,\:\mathrm{10}\:,\:\mathrm{13}\:,…}\end{cases} \\ $$ Answered by mr…
Question Number 173768 by BaliramKumar last updated on 17/Jul/22 $${Total}\:{factors}\:\:{of}\:\:\mathrm{20}!\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 42672 by Tawa1 last updated on 31/Aug/18 $$\mathrm{Simplify}:\:\:\:\left(\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\right)\left(\mathrm{x}^{−\mathrm{1}} \:+\:\mathrm{y}^{−\mathrm{1}} \:+\:\mathrm{z}^{−\mathrm{1}} \right)\:=\:\left(\mathrm{x}^{−\mathrm{1}} \:\mathrm{y}^{−\mathrm{1}} \:\mathrm{z}^{−\mathrm{1}} \right)\left(\mathrm{x}\:+\:\mathrm{y}\right)\left(\mathrm{y}\:+\:\mathrm{z}\right)\left(\mathrm{z}\:+\:\mathrm{x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 108082 by ismoilov last updated on 14/Aug/20 Answered by Her_Majesty last updated on 14/Aug/20 $${x}={tan}^{−\mathrm{1}} {t} \\ $$$$\frac{\left({t}+\mathrm{1}\right)\left({t}−\mathrm{2}\right)}{{t}^{\mathrm{2}} +\mathrm{1}}\geqslant\mathrm{0}\:\Rightarrow\:−\mathrm{1}\leqslant{t}\leqslant\mathrm{2} \\ $$$$\Rightarrow\:{for}\:\mathrm{0}\leqslant{x}<\mathrm{2}\pi \\ $$$$\frac{\pi}{\mathrm{2}}−{tan}^{−\mathrm{1}}…
Question Number 42495 by Tawa1 last updated on 26/Aug/18 $$\mathrm{In}\:\mathrm{the}\:\mathrm{sequence}\:\:\mathrm{1},\:\mathrm{22},\:\mathrm{333},\:…\:\mathrm{10101010101010101010},\:\mathrm{1111111111111111111111},\:… \\ $$$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{in}\:\mathrm{the}\:\mathrm{200th}\:\mathrm{term}\:\mathrm{is}\:?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 107974 by Ar Brandon last updated on 13/Aug/20 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{k}\right)^{\mathrm{2}} }} \\ $$ Answered by Dwaipayan Shikari last updated on 14/Aug/20…
Question Number 173178 by pete last updated on 07/Jul/22 $$\mathrm{When}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}\:\left(\mathrm{G}.\mathrm{P}.\right) \\ $$$$\mathrm{with}\:\mathrm{r}=\mathrm{2}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{the}\:\mathrm{corresponding} \\ $$$$\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{progression}\:\left(\mathrm{A}.\mathrm{P}.\right), \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{formed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{first}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{and}\:\mathrm{AP}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}\:\mathrm{and}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{three}\:\mathrm{termsof}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence}\:\mathrm{are} \\ $$$$\mathrm{3},\:\mathrm{7}\:\mathrm{and}\:\mathrm{11}\:\mathrm{respectively},\:\mathrm{find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{new}\:\mathrm{sequence} \\…
Question Number 173165 by mr W last updated on 07/Jul/22 $${what}'{s}\:{the}\:{largest}\:{number}\:{you}\:{can} \\ $$$${form}\:{only}\:{using}\:{the}\:{digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}? \\ $$ Answered by pnuvu last updated on 07/Jul/22 $$\mathrm{4}^{\mathrm{3}^{\left(\mathrm{2}+\mathrm{1}\right)} } \\…
Question Number 42019 by Tawa1 last updated on 16/Aug/18 $$\mathrm{find}\:\mathrm{x}:\:\:\:\:\:\mathrm{2}^{\mathrm{x}} \:+\:\mathrm{3}^{\mathrm{x}} \:=\:\mathrm{13} \\ $$ Commented by math khazana by abdo last updated on 17/Aug/18 $${let}\:{f}\left({x}\right)=\mathrm{2}^{{x}}…
Question Number 41958 by 123456780 last updated on 15/Aug/18 $$\begin{cases}{\mathrm{x}^{\sqrt{\mathrm{y}}} +\mathrm{y}^{\sqrt{\mathrm{x}}} =\frac{\mathrm{49}}{\mathrm{48}}}\\{\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=\frac{\mathrm{7}}{\mathrm{2}}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\mathrm{k}.\mathrm{k} \\ $$ Answered by MJS last updated on 16/Aug/18…