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Category: Number Theory

find-the-laplace-invesrse-for-I-s-I-s-2000s-2-s-2-200-2-s-2-400s-2-10-5-

Question Number 183678 by ali009 last updated on 28/Dec/22 $${find}\:{the}\:{laplace}\:{invesrse}\:{for}\:{I}\left({s}\right) \\ $$$${I}\left({s}\right)=\frac{\mathrm{2000}{s}^{\mathrm{2}} }{\left({s}^{\mathrm{2}} +\mathrm{200}^{\mathrm{2}} \right)\left({s}^{\mathrm{2}} +\mathrm{400}{s}+\mathrm{2}×\mathrm{10}^{\mathrm{5}} \right)} \\ $$ Terms of Service Privacy Policy Contact:…

Determine-all-functions-f-R-R-such-that-the-equality-f-x-y-f-x-f-y-holds-for-all-x-y-R-Here-by-x-we-denote-the-greatest-integer-not-exceeding-x-

Question Number 117848 by john santu last updated on 14/Oct/20 $${Determine}\:{all}\:{functions}\:{f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${such}\:{that}\:{the}\:{equality}\:{f}\left(\left[{x}\right]\:{y}\right)=\:{f}\left({x}\right)\:\left[{f}\left({y}\right)\:\right] \\ $$$${holds}\:{for}\:{all}\:{x},{y}\:\in\mathbb{R}\:.\:{Here}\:\:{by}\:\left[{x}\right]\:{we}\: \\ $$$${denote}\:{the}\:{greatest}\:{integer}\:{not}\:{exceeding}\:{x}. \\ $$$$ \\ $$ Terms of Service Privacy…

Find-the-units-digit-of-2013-1-2013-2-2013-3-2013-2013-

Question Number 117369 by bemath last updated on 11/Oct/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{2013}^{\mathrm{1}} +\mathrm{2013}^{\mathrm{2}} +\mathrm{2013}^{\mathrm{3}} +…+\mathrm{2013}^{\mathrm{2013}} \\ $$ Answered by JDamian last updated on 11/Oct/20 $${S}=\mathrm{2013}^{\mathrm{1}} +\mathrm{2013}^{\mathrm{2}} +\:\centerdot\centerdot\centerdot\:+\:\mathrm{2013}^{\mathrm{2013}}…

If-x-is-a-complex-number-satisfying-x-2-x-1-0-what-is-the-value-of-x-53-x-52-x-51-x-50-x-49-

Question Number 117045 by bobhans last updated on 09/Oct/20 $$\mathrm{If}\:\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{satisfying}\: \\ $$$$\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\:=\:\mathrm{0}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{x}^{\mathrm{53}} +\mathrm{x}^{\mathrm{52}} +\mathrm{x}^{\mathrm{51}} +\mathrm{x}^{\mathrm{50}} +\mathrm{x}^{\mathrm{49}} \:? \\ $$ Answered by john…

739-is-a-prime-number-and-its-reversed-number-937-is-also-prime-Determine-4-digit-prime-numbers-whose-reversed-be-also-prime-If-number-of-such-primes-is-a-function-of-number-of-digits-determ

Question Number 51507 by Rasheed.Sindhi last updated on 27/Dec/18 $$\:^{\bullet} \mathrm{739}\:{is}\:{a}\:\:{prime}\:{number}\:{and} \\ $$$${its}\:{reversed}\:{number}\:\mathrm{937}\:{is}\:{also} \\ $$$${prime}. \\ $$$${Determine}\:\mathrm{4}-{digit}\:{prime}\:{numbers} \\ $$$${whose}\:{reversed}\:{be}\:{also}\:{prime}. \\ $$$$\:^{\bullet} {If}\:{number}\:{of}\:{such}\:{primes}\:{is}\:{a} \\ $$$${function}\:{of}\:{number}\:{of}\:{digits}, \\…

Let-S-1-2-3-4-5-6-7-If-we-multiply-atleast-2-numbers-from-this-set-with-each-other-what-are-the-chances-of-the-product-to-turn-out-to-be-divisible-by-3-

Question Number 182199 by depressiveshrek last updated on 05/Dec/22 $${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{7}\right\} \\ $$$${If}\:{we}\:{multiply}\:{atleast}\:\mathrm{2}\:{numbers} \\ $$$${from}\:{this}\:{set}\:{with}\:{each}\:{other},\:{what} \\ $$$${are}\:{the}\:{chances}\:{of}\:{the}\:{product}\:{to} \\ $$$${turn}\:{out}\:{to}\:{be}\:{divisible}\:{by}\:\mathrm{3}? \\ $$ Answered by Acem last updated…

4-3-2-5-3-1-1-6-1-2-8-1-find-numbers-of-each-

Question Number 50960 by kaivan.ahmadi last updated on 22/Dec/18 $$\mathrm{4}\:\:\:\left(\mathrm{3}\right)\:\:\:\:\mathrm{2} \\ $$$$\mathrm{5}\:\:\:\:\mathrm{3}\:\:\:\left(?\right)\:\:\mathrm{1}\:\:\:\:\mathrm{1} \\ $$$$\mathrm{6}\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{2}\:\:\left(\mathrm{8}\right)\:\:\:\:?\:\:\:\:\:?\:\:\:\:\:\mathrm{1} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{each}\:\:\:? \\ $$ Terms of Service Privacy Policy…