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Category: Algebra

what-is-the-cardinality-of-the-set-of-prime-numbers-whose-base-ten-digits-sums-up-to-10-

Question Number 187248 by MWSuSon last updated on 15/Feb/23 $$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{cardinality}\:\mathrm{of}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{prime}\:\mathrm{numbers}\:\mathrm{whose} \\ $$$$\mathrm{base}\:\mathrm{ten}\:\mathrm{digits}\:\mathrm{sums}\:\mathrm{up}\:\mathrm{to}\:\mathrm{10} \\ $$ Commented by Frix last updated on 15/Feb/23 $$\mathrm{Same}\:\mathrm{as}\:\mathbb{N} \\ $$ Terms…

Find-x-if-x-4-a-x-0-lt-a-lt-2-9-

Question Number 187233 by ajfour last updated on 15/Feb/23 $${Find}\:{x}\:{if}\::\:\:\:{x}^{\mathrm{4}} +{a}={x}\:\:\:\:\forall\:\left(\mathrm{0}<{a}<\frac{\mathrm{2}}{\mathrm{9}}\right)\:\:\: \\ $$ Commented by MJS_new last updated on 15/Feb/23 $$\mathrm{maybe}\:\mathrm{off}\:\mathrm{topic}\:\mathrm{but}\:\mathrm{it}\:\mathrm{could}\:\mathrm{be}\:\mathrm{of}\:\mathrm{interest} \\ $$$$\left({x}−\frac{{p}^{\mathrm{2}} }{\mathrm{2}}−\frac{\sqrt{\mathrm{2}−{p}^{\mathrm{6}} }}{\mathrm{2}{p}}\right)\left({x}−\frac{{p}^{\mathrm{2}}…

if-1-2-f-x-dx-2-then-1-4-1-x-f-x-dx-is-please-help-me-Sir-I-ve-been-trying-this-for-2-days-and-getting-stuck-

Question Number 56147 by afachri last updated on 11/Mar/19 $$\mathrm{if}\:\underset{\:\:\mathrm{1}} {\overset{\:\:\mathrm{2}} {\int}}\:{f}\left({x}\right)\:{dx}\:=\:\sqrt{\:\mathrm{2}\:},\:\mathrm{then}\:\underset{\:\:\mathrm{1}} {\overset{\:\:\mathrm{4}} {\int}}\:\frac{\mathrm{1}}{\:\sqrt{\:{x}\:}\:}\:{f}\left({x}\right)\:{dx} \\ $$$$\:\mathrm{is}\:?? \\ $$$$\:\:\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{Sir}.\:\mathrm{I}'\mathrm{ve}\:\mathrm{been}\:\mathrm{trying} \\ $$$$\:\:\mathrm{this}\:\mathrm{for}\:\mathrm{2}\:\mathrm{days}\:\mathrm{and}\:\mathrm{getting}\:\mathrm{stuck}. \\ $$$$ \\ $$$$ \\…

calculate-i-1-49-cos-pi-40-i-sin-pi-40-10-

Question Number 56144 by gunawan last updated on 11/Mar/19 $$\mathrm{calculate}\:\left({i}−\mathrm{1}\right)^{\mathrm{49}} \left(\mathrm{cos}\:\frac{\pi}{\mathrm{40}}+{i}\:\mathrm{sin}\:\frac{\pi}{\mathrm{40}}\right)^{\mathrm{10}} \\ $$ Answered by Smail last updated on 11/Mar/19 $$\left({i}−\mathrm{1}\right)^{\mathrm{49}} =\left[\sqrt{\mathrm{2}}\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}−{i}\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)\right]^{\mathrm{49}} \\ $$$$=\sqrt{\mathrm{2}^{\mathrm{49}} }\left({e}^{{i}\frac{\pi}{\mathrm{4}}}…