Question Number 21867 by Tinkutara last updated on 05/Oct/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{points}\:\mathrm{in}\:\mathrm{the}\:\mathrm{cartesian} \\ $$$$\mathrm{plane}\:\mathrm{with}\:\mathrm{integral}\:\mathrm{coordinates} \\ $$$$\mathrm{satisfying}\:\mathrm{the}\:\mathrm{inequalities}\:\mid{x}\mid\:\leqslant\:\mathrm{4},\:\mid{y}\mid\:\leqslant \\ $$$$\mathrm{4}\:\mathrm{and}\:\mid{x}\:−\:{y}\mid\:\leqslant\:\mathrm{4}\:\mathrm{is} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 87398 by jagoll last updated on 04/Apr/20 $$\mathrm{dear}\:\mathrm{mr}\:\mathrm{w} \\ $$$$\mathrm{a}_{\mathrm{n}+\mathrm{2}} \:=\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:−\:\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{find}\:\mathrm{a}_{\mathrm{n}} \\ $$ Commented by mr W last updated on…
Question Number 87382 by mathocean1 last updated on 04/Apr/20 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{tan}\frac{\mathrm{5}\pi}{\mathrm{12}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{this}\: \\ $$$$\mathrm{equation}:\:{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{1}=\mathrm{0} \\ $$ Answered by ajfour last updated on 04/Apr/20 $${x}^{\mathrm{3}} +\mathrm{1}=\mathrm{3}{x}\left({x}+\mathrm{1}\right)…
Question Number 87379 by john santu last updated on 04/Apr/20 $$\underset{\mathrm{k}\:=\:\mathrm{2}} {\overset{\mathrm{2010}} {\prod}}\:\frac{\mathrm{k}^{\mathrm{2}} −\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\:=\:? \\ $$ Commented by jagoll last updated on 04/Apr/20 $$\underset{\mathrm{k}\:=\:\mathrm{2}}…
Question Number 152912 by mathdanisur last updated on 03/Sep/21 Answered by ghimisi last updated on 03/Sep/21 $$\Sigma\frac{{a}}{\mathrm{2}{b}+\mathrm{3}{c}}=\Sigma\frac{{a}^{\mathrm{2}} }{\mathrm{2}{ab}+\mathrm{3}{ac}}\geqslant\frac{\left({a}+{b}+{c}\right)^{\mathrm{2}} }{\mathrm{5}\left({ab}+{bc}+{ac}\right)}\geqslant\frac{\mathrm{3}\left({ab}+{bc}+{ca}\right)}{\mathrm{5}\left({ab}+{bc}+{ac}\right)}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$ Commented by ghimisi last…
Question Number 152907 by mathdanisur last updated on 03/Sep/21 $$\mathrm{Find}\:\mathrm{a}\:\mathrm{closed}\:\mathrm{form}: \\ $$$$\Omega=\left(\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{29}} −\mathrm{x}^{\mathrm{9}} }{\mathrm{x}^{\mathrm{40}} +\mathrm{1}}\:\mathrm{dx}\right)\left(\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{29}} −\mathrm{2x}^{\mathrm{9}} }{\mathrm{x}^{\mathrm{40}} +\mathrm{4}}\mathrm{dx}\right) \\ $$ Answered…
Question Number 152901 by ajfour last updated on 03/Sep/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 152898 by bobhans last updated on 02/Sep/21 Commented by mathdanisur last updated on 03/Sep/21 $$\mathrm{5x}^{\mathrm{5}} −\mathrm{23x}^{\mathrm{4}} +\mathrm{39x}^{\mathrm{3}} −\mathrm{33x}^{\mathrm{2}} +\mathrm{24x}=\mathrm{4}\:\Rightarrow\:=\mathrm{2} \\ $$ Commented by…
Question Number 152892 by mathdanisur last updated on 02/Sep/21 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{yz}\:=\:\mathrm{3}}\\{\mathrm{y}^{\mathrm{2}} \:-\:\mathrm{xz}\:=\:\mathrm{1}}\\{\mathrm{z}^{\mathrm{2}} \:-\:\mathrm{xy}\:=\:-\:\mathrm{1}}\end{cases} \\ $$ Commented by MJS_new last updated on…
Question Number 152881 by mathdanisur last updated on 02/Sep/21 $$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{Li}_{\mathrm{2}} \:\left(\frac{\mathrm{x}}{\mathrm{1}\:-\:\mathrm{x}}\right)\:\mathrm{log}\left(\mathrm{x}\right)\:\mathrm{log}\left(\mathrm{1}\:-\:\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com