Question Number 157795 by naka3546 last updated on 28/Oct/21 $$\left\{{a}_{{n}} \right\}\:{is}\:{a}\:\:{natural}\:\:{number}\:\:{sequence}\:\:{for}\:\:{n}\:\geqslant\:\mathrm{0}\:\:{that}\:\:{satisfy} \\ $$$${recurrence}\:\:{relation}\:\:{a}_{{m}+{n}} \:+\:{a}_{{m}−{n}} \:−{m}+{n}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({a}_{\mathrm{2}{m}} \:+{a}_{\mathrm{2}{n}} \right)\:,\:\: \\ $$$${for}\:\:\forall\:{m},{n}\:\:{nonnegative}\:\:{integers}\:. \\ $$$${Find}\:\:{a}_{\mathrm{2016}} \:. \\ $$ Answered…
Question Number 157788 by joki last updated on 27/Oct/21 $$\mathrm{look}\:\mathrm{for}\:\mathrm{a}\:\mathrm{simpler}\:\mathrm{boolean}\:\mathrm{function}\:\mathrm{in} \\ $$$$\mathrm{POS}\:\mathrm{form}\:\mathrm{of}: \\ $$$$\mathrm{a}.\mathrm{f}\left(\mathrm{r},\mathrm{s},\mathrm{t},\mathrm{u}\right)=\Pi\left(\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{9},\mathrm{10},\mathrm{12},\mathrm{14}\right) \\ $$$$\mathrm{b}.\mathrm{g}\left(\mathrm{w},\mathrm{x},\mathrm{y},\mathrm{z}\right)=\Sigma\left(\mathrm{4},\mathrm{8},\mathrm{13},\mathrm{14}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92248 by naka3546 last updated on 05/May/20 Commented by MJS last updated on 06/May/20 $${x}=\frac{\mathrm{126}}{\:\sqrt{\mathrm{85}}} \\ $$$${EA}=\frac{\mathrm{69}}{\:\sqrt{\mathrm{85}}},\:{AF}=\frac{\mathrm{57}}{\:\sqrt{\mathrm{85}}},\:{DB}=\frac{\mathrm{28}}{\:\sqrt{\mathrm{85}}},\:{BE}=\frac{\mathrm{98}}{\:\sqrt{\mathrm{85}}} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{just}\:\mathrm{solving}\:\mathrm{the}\:\mathrm{3}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{3}\:\mathrm{triangles}\:{ABE},\:{AFC},\:{BCD} \\ $$…
Question Number 92247 by askask last updated on 05/May/20 $$\mathrm{How}\:\mathrm{to}\:\mathrm{convert}\:\mathrm{the}\:\mathrm{non}−\mathrm{linear}\:\mathrm{equation}{s} \\ $$$$\mathrm{to}\:\mathrm{linear}\:\mathrm{form}? \\ $$$$ \\ $$$${y}=\frac{{x}}{{c}+{mx}} \\ $$$$ \\ $$$${y}={ce}^{{mx}} \\ $$ Commented by Joel578…
Question Number 157770 by Oberon last updated on 27/Oct/21 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{proof}\:\mathrm{this}\:\mathrm{intresting}\:\mathrm{identity}? \\ $$$$\mathrm{ln}\:\mathrm{x}\:=\:\left(\mathrm{x}−\mathrm{1}\right)\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\left(\frac{\mathrm{2}}{\mathrm{1}+\sqrt[{\mathrm{2}^{\mathrm{n}} }]{\mathrm{x}}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 157749 by naka3546 last updated on 27/Oct/21 $${a}^{\mathrm{2}} +\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:+\:{d}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$$${a},{b},{c},{d}\:\in\:\mathbb{R} \\ $$$${max}\left\{{a}^{\mathrm{3}} \:+\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}} \:+\:{d}^{\mathrm{3}} \right\}\:\:=\:\:? \\ $$ Commented…
Question Number 157725 by joki last updated on 27/Oct/21 $$\mathrm{form}\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\left(\left(\mathrm{xy}\right)'\mathrm{c}\right)'\left(\left(\mathrm{x}'+\mathrm{c}\right)\left(\mathrm{y}'+\mathrm{z}'\right)\right)'\: \\ $$$$\mathrm{in}\:\mathrm{standard}\:\mathrm{SOP}\:\mathrm{form}\:\mathrm{and}\:\mathrm{canonical}\:\mathrm{SOP}\:\mathrm{form} \\ $$ Answered by Kunal12588 last updated on 27/Oct/21 $$\left[\left({xy}\right)'{c}\right]'\left[\left({x}'+{c}\right)\left({y}'+{z}'\right)\right]' \\ $$$$=\left[\left(\left({xy}\right)'\right)'+{c}'\right]\left[\left({x}'+{c}\right)'+\left({y}'+{z}'\right)'\right] \\…
Question Number 26649 by Mr eaay last updated on 27/Dec/17 $${Solve}\:{the}\:{equation}:{x}+{y}=\mathrm{5}−−−{i} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}^{{x}} +\:{y}^{{y}} =\mathrm{31}−−−{ii} \\ $$$${No}\:{trial}\:{and}\:{error} \\ $$$$ \\ $$ Commented by mrW1 last…
Question Number 92179 by otchereabdullai@gmail.com last updated on 05/May/20 $$\left(\frac{\mathrm{x}}{\mathrm{12}}\right)^{\mathrm{log}_{\sqrt{\mathrm{3}}} \mathrm{x}} =\left(\frac{\mathrm{x}}{\mathrm{18}}\right)^{\mathrm{log}_{\sqrt{\mathrm{2}}} \mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$ Commented by john santu last updated on 05/May/20…
Question Number 157706 by Oberon last updated on 26/Oct/21 Answered by mr W last updated on 26/Oct/21 $$\mathrm{2}{a}_{{n}} =\sqrt{\frac{\mathrm{2}{a}_{{n}−\mathrm{1}} +\mathrm{1}}{\mathrm{2}}} \\ $$$${let}\:{b}_{{n}} =\mathrm{2}{a}_{{n}} \\ $$$${b}_{{n}}…