Question Number 157867 by ZiYangLee last updated on 29/Oct/21 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{point}\:{P}\left({a}\:\mathrm{cos}\:\theta,\:{b}\:\mathrm{sin}\:\theta\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{point}\:\mathrm{on} \\ $$$$\mathrm{the}\:\mathrm{ellipse}\:\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}} }=\mathrm{1}. \\ $$$$\mathrm{The}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{at}\:\mathrm{point}\:{P}\:\:\mathrm{is}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{a}\:\mathrm{straight}\:\mathrm{line}\:\mathrm{which}\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{focus}, \\ $$$${F}\:\left({ae},\mathrm{0}\right).\:\mathrm{If}\:{N}\:\mathrm{is}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{point},\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:{N}\:\mathrm{is}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…
Question Number 157829 by Fikret last updated on 28/Oct/21 $$\frac{\sqrt{\mathrm{2}}\:{a}_{{n}} }{{a}_{{n}+\mathrm{1}} }=\sqrt{\mathrm{2}+\left({a}_{{n}} \right)^{\mathrm{2}} }\:\:\:\:\: \\ $$$${a}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\Rightarrow\:\:{a}_{\mathrm{43}} =? \\ $$ Answered by qaz last updated…
Question Number 157813 by MathsFan last updated on 28/Oct/21 $${express}\:\:\mathrm{5}.\mathrm{1}\overset{\bullet} {\mathrm{3}}\overset{\bullet} {\mathrm{4}}\overset{\bullet} {\mathrm{5}}\:\:\:{into}\:{fraction} \\ $$ Answered by Rasheed.Sindhi last updated on 28/Oct/21 $${x}=\mathrm{5}.\mathrm{1}\overline {\mathrm{345}} \\…
Question Number 157815 by mkam last updated on 28/Oct/21 Commented by mkam last updated on 28/Oct/21 $${where}\:{z}={re}^{{i}\theta} \\ $$ Commented by mkam last updated on…
Question Number 92275 by otchereabdullai@gmail.com last updated on 05/May/20 $$\mathrm{Make}\:\mathrm{R}\:\mathrm{the}\:\mathrm{subject}\:\mathrm{of}: \\ $$$$\:\:\mathrm{P}=\:\frac{\mathrm{RE}^{\mathrm{2}} }{\left(\mathrm{R}+\mathrm{b}\right)^{\mathrm{2}} } \\ $$ Answered by MJS last updated on 06/May/20 $${P}\left({R}+{b}\right)^{\mathrm{2}} ={E}^{\mathrm{2}}…
Question Number 157795 by naka3546 last updated on 28/Oct/21 $$\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