Question Number 12226 by tawa last updated on 16/Apr/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{this}\:\mathrm{sequence} \\ $$$$\mathrm{3},\:\mathrm{18},\:\mathrm{45},\:\mathrm{84},\:\mathrm{135}\:… \\ $$ Answered by ajfour last updated on 16/Apr/17 $${T}_{{n}} \:=\:\mathrm{3}\boldsymbol{{n}}\left(\mathrm{2}\boldsymbol{{n}}−\mathrm{1}\right)\:. \\ $$…
Question Number 12189 by tawa last updated on 16/Apr/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{to}\:\mathrm{the}\:\mathrm{below}\:\mathrm{deimal} \\ $$$$\mathrm{4}.\mathrm{4444444444444}…….\:\infty \\ $$ Answered by ridwan balatif last updated on 16/Apr/17 $$\mathrm{let}:\:\mathrm{4}.\mathrm{444444}…=\mathrm{a} \\ $$$$\mathrm{4}.\mathrm{4444}…=\mathrm{a}…
Question Number 12190 by tawa last updated on 16/Apr/17 $$\mathrm{Show}\:\mathrm{that},\:\:\mathrm{0}.\mathrm{9999999999999}\:……\:\infty\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1} \\ $$ Answered by ridwan balatif last updated on 16/Apr/17 $$\mathrm{let}\:\mathrm{0}.\mathrm{9999999}….=\mathrm{p} \\ $$$$\mathrm{0}.\mathrm{999999}…=\mathrm{p} \\ $$$$−−−−−−−−×\mathrm{10}…
Question Number 12181 by rish@bh last updated on 15/Apr/17 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{xyz}\:\mathrm{is}\:\mathrm{15}/\mathrm{2}\:\mathrm{or}\:\mathrm{18}/\mathrm{5} \\ $$$$\mathrm{according}\:\mathrm{as}\:\mathrm{the}\:\mathrm{series}\:{a},{x},{y},{z},{b}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}.\:\mathrm{or}\:\mathrm{H}.\mathrm{P}.,\:\mathrm{then}\:'{a}+{b}'\:\mathrm{equals} \\ $$$$\mathrm{where}\:{a},\:{b}\:\mathrm{are}\:+\mathrm{ve}\:\mathrm{integers}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 77687 by jagoll last updated on 09/Jan/20 $${given}\:{function} \\ $$$${f}\left({x}\right)\:={f}\left({x}+\mathrm{2}\right)\:{for}\:\forall{x}\in\mathbb{R} \\ $$$${if}\:\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}{f}\left({x}\right){dx}={B}\:,\:{what}\:{value}\:{of} \\ $$$$\underset{\mathrm{3}} {\overset{\mathrm{7}} {\int}}\:{f}\left({x}+\mathrm{8}\right){dx}\:=\:? \\ $$ Commented by mr…
Question Number 12107 by Joel576 last updated on 13/Apr/17 $$\mathrm{10}^{\mathrm{3}} \:+\:\mathrm{11}^{\mathrm{3}} \:+\:\mathrm{12}^{\mathrm{3}} \:+\:…\:+\:\mathrm{20}^{\mathrm{3}} \\ $$$$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{ways}\:\mathrm{to}\:\mathrm{count}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{of}\:\mathrm{that}\:\mathrm{sequence}\:\mathrm{without}\:\mathrm{sum}\:\mathrm{them}\:\mathrm{manually}? \\ $$ Commented by FilupS last updated on…
Question Number 143134 by help last updated on 10/Jun/21 Answered by liberty last updated on 10/Jun/21 $$\:{y}'=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(\left({x}+{h}\right)^{\mathrm{2}} −\mathrm{4}\left({x}+{h}\right)\right)−\mathrm{cos}\:\left({x}^{\mathrm{2}} −\mathrm{4}{x}\right)}{{h}} \\ $$$$=\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left({x}^{\mathrm{2}} +\mathrm{2}{hx}+{h}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{4}{h}\right)−\mathrm{cos}\:\left({x}^{\mathrm{2}}…
Question Number 12023 by tawa last updated on 09/Apr/17 $$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:−\:\sqrt{\mathrm{xy}}\:=\:\mathrm{3}\:\:\:\:\:……….\:\left(\mathrm{i}\right) \\ $$$$\sqrt{\mathrm{x}\:+\:\mathrm{1}}\:+\:\sqrt{\mathrm{y}\:+\:\mathrm{1}}\:=\:\mathrm{4}\:\:\:\:\:……….\:\left(\mathrm{ii}\right) \\ $$ Answered by Mr Chheang Chantria last updated on 10/Apr/17…
Question Number 11994 by algabara last updated on 09/Apr/17 $$\mathrm{4}{x}=\mathrm{60} \\ $$ Commented by tawa last updated on 09/Apr/17 $$\mathrm{4x}\:\:=\:\mathrm{60} \\ $$$$\mathrm{Divide}\:\mathrm{both}\:\mathrm{side}\:\mathrm{by}\:\mathrm{4} \\ $$$$\frac{\mathrm{4x}}{\mathrm{4}}\:=\:\frac{\mathrm{60}}{\mathrm{4}} \\…
Question Number 142902 by greg_ed last updated on 07/Jun/21 $$\mathrm{I}_{{n}} =\int_{\mathrm{0}} ^{\:_{} \frac{\pi}{\mathrm{2}}} \:\left(\mathrm{sin}\:{x}\right)^{{n}} \:{dx} \\ $$$$\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{integration}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{parts}},\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\::\: \\ $$$$\mathrm{I}_{{n}+\mathrm{2}} \:=\:\frac{{n}+\mathrm{1}}{{n}+\mathrm{2}}\:.\:\mathrm{I}_{{n}} \\ $$ Answered by qaz…