Question Number 21100 by ibraheem160 last updated on 12/Sep/17 $$\mathrm{if}\:\mathrm{3}^{\mathrm{2n}+\mathrm{3}} =\mathrm{m},\mathrm{find}\:\mathrm{3}^{−\mathrm{n}} \\ $$ Commented by chernoaguero@gmail.com last updated on 13/Sep/17 $$\mathrm{3}^{\mathrm{2}{n}} ×\mathrm{2}^{\mathrm{3}} ={m} \\ $$$$\mathrm{27}\left(\mathrm{3}^{{n}}…
Question Number 21097 by Tinkutara last updated on 12/Sep/17 $$\mathrm{Suppose}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{10}\:\mathrm{pairwise} \\ $$$$\mathrm{nonparallel}\:\mathrm{lines}\:\mathrm{intersect}\:\mathrm{one}\:\mathrm{another}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{possible}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{polygons}\:\left(\mathrm{with}\:\mathrm{finite}\:\mathrm{areas}\right)\:\mathrm{that}\:\mathrm{can} \\ $$$$\mathrm{be}\:\mathrm{formed}? \\ $$ Answered by Tinkutara last updated…
Question Number 21071 by Tinkutara last updated on 12/Sep/17 $$\mathrm{The}\:\mathrm{values}\:\mathrm{of}\:'{k}'\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mid{x}\mid^{\mathrm{2}} \left(\mid{x}\mid^{\mathrm{2}} \:−\:\mathrm{2}{k}\:+\:\mathrm{1}\right)\:=\:\mathrm{1}\:−\:{k}^{\mathrm{2}} ,\:\mathrm{has} \\ $$$$\mathrm{repeated}\:\mathrm{roots},\:\mathrm{when}\:{k}\:\mathrm{belongs}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\left\{\mathrm{1},\:−\mathrm{1}\right\} \\ $$$$\left(\mathrm{2}\right)\:\left\{\mathrm{0},\:\mathrm{1}\right\} \\ $$$$\left(\mathrm{3}\right)\:\left\{\mathrm{0},\:−\mathrm{1}\right\} \\ $$$$\left(\mathrm{4}\right)\:\left\{\mathrm{2},\:\mathrm{3}\right\}…
Question Number 21070 by Tinkutara last updated on 11/Sep/17 $$\mathrm{Let}\:\mathrm{us}\:\mathrm{consider}\:\mathrm{an}\:\mathrm{equation}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \\ $$$$−\:\mathrm{3}{x}\:+\:{k}\:=\:\mathrm{0}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:{k}\:\mathrm{for} \\ $$$$\mathrm{which}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has} \\ $$$$\mathrm{1}.\:\mathrm{Exactly}\:\mathrm{one}\:\mathrm{root}\:\mathrm{which}\:\mathrm{is}\:\mathrm{positive}, \\ $$$$\mathrm{then}\:{k}\:\mathrm{belongs}\:\mathrm{to} \\ $$$$\mathrm{2}.\:\mathrm{Exactly}\:\mathrm{one}\:\mathrm{root}\:\mathrm{which}\:\mathrm{is}\:\mathrm{negative}, \\ $$$$\mathrm{then}\:{k}\:\mathrm{belongs}\:\mathrm{to} \\ $$$$\mathrm{3}.\:\mathrm{One}\:\mathrm{negative}\:\mathrm{and}\:\mathrm{two}\:\mathrm{positive}\:\mathrm{root} \\…
Question Number 86598 by Rio Michael last updated on 29/Mar/20 $$\:\mathrm{write}\:\mathrm{out}\:\mathrm{the}\:\mathrm{general}\:\mathrm{summation}\:\mathrm{formula}\:\mathrm{for} \\ $$$$\:\mathrm{the}\:\mathrm{maclaurin}\:\mathrm{series}\:\mathrm{expansion}\:\mathrm{for}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\left(\mathrm{cos}\:{x}\:+\:\mathrm{cosh}\:{x}\right) \\ $$ Commented by mathmax by abdo last updated on 31/Mar/20 $${cosx}\:=\sum_{{n}=\mathrm{0}}…
Question Number 21048 by Tinkutara last updated on 10/Sep/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{2cos2}{x}\:−\:\left({a}\:+\:\mathrm{7}\right)\mathrm{cos}{x}\:+ \\ $$$$\mathrm{3}{a}\:−\:\mathrm{13}\:=\:\mathrm{0}\:\mathrm{possesses}\:\mathrm{atleast}\:\mathrm{one}\:\mathrm{real} \\ $$$$\mathrm{solution},\:\mathrm{then}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{integral} \\ $$$$\mathrm{value}\:\mathrm{of}\:'{a}'\:\mathrm{can}\:\mathrm{be} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 21012 by Tinkutara last updated on 10/Sep/17 $$\mathrm{A}\:\mathrm{spring}\:\mathrm{with}\:\mathrm{one}\:\mathrm{end}\:\mathrm{attached}\:\mathrm{to}\:\mathrm{a} \\ $$$$\mathrm{mass}\:\mathrm{and}\:\mathrm{the}\:\mathrm{other}\:\mathrm{to}\:\mathrm{a}\:\mathrm{rigid}\:\mathrm{support}\:\mathrm{is} \\ $$$$\mathrm{stretched}\:\mathrm{and}\:\mathrm{released}. \\ $$$$\left({a}\right)\:\mathrm{Magnitude}\:\mathrm{of}\:\mathrm{acceleration},\:\mathrm{when} \\ $$$$\mathrm{just}\:\mathrm{released}\:\mathrm{is}\:\mathrm{maximum}. \\ $$$$\left({b}\right)\:\mathrm{Magnitude}\:\mathrm{of}\:\mathrm{acceleration},\:\mathrm{when} \\ $$$$\mathrm{at}\:\mathrm{equilibrium}\:\mathrm{position},\:\mathrm{is}\:\mathrm{maximum}. \\ $$$$\left({c}\right)\:\mathrm{Speed}\:\mathrm{is}\:\mathrm{maximum}\:\mathrm{when}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{at} \\…
Question Number 20992 by NECx last updated on 09/Sep/17 Commented by NECx last updated on 09/Sep/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{guys} \\ $$ Answered by $@ty@m last updated on…
Question Number 20989 by Tinkutara last updated on 09/Sep/17 $$\mathrm{In}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{shown}\:\mathrm{below},\:\mathrm{the}\:\mathrm{block}\:\mathrm{of} \\ $$$$\mathrm{mass}\:\mathrm{2}\:\mathrm{kg}\:\mathrm{is}\:\mathrm{at}\:\mathrm{rest}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{spring}\:\mathrm{constant} \\ $$$$\mathrm{of}\:\mathrm{both}\:\mathrm{the}\:\mathrm{springs}\:{A}\:\mathrm{and}\:{B}\:\mathrm{is}\:\mathrm{100}\:\mathrm{N}/\mathrm{m} \\ $$$$\mathrm{and}\:\mathrm{spring}\:{B}\:\mathrm{is}\:\mathrm{cut}\:\mathrm{at}\:{t}\:=\:\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{magnitude}\:\mathrm{of}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{block} \\ $$$$\mathrm{immediately}\:\mathrm{is} \\ $$ Commented by Tinkutara…