Question Number 193247 by mokys last updated on 08/Jun/23 $${if}\:{f}\left({x}\right)\:=\:\frac{{ax}+\mathrm{1}}{{x}+{b}}\:{find}\:{f}^{\:\mathrm{100}} \left({x}\right)\:{and}\:{f}^{\mathrm{101}} \left({x}\right)\:? \\ $$ Answered by aba last updated on 08/Jun/23 $$\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}+\mathrm{1}}{\mathrm{x}+\mathrm{b}}=\mathrm{a}+\frac{\mathrm{1}−\mathrm{ab}}{\mathrm{x}+\mathrm{b}} \\ $$$$\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{f}{o}\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{a}+\frac{\mathrm{1}−\mathrm{ab}}{\mathrm{x}+\mathrm{b}}\right)=\mathrm{a}+\frac{\mathrm{1}−\mathrm{ab}}{\mathrm{f}\left(\mathrm{x}\right)+\mathrm{b}}…
Question Number 193237 by CrispyXYZ last updated on 08/Jun/23 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{In}\:\mathrm{any}\:\mathrm{acute}\:\bigtriangleup{ABC},\:\mathrm{cot}^{\mathrm{2}} {A}+\mathrm{cot}^{\mathrm{2}} {B}+\mathrm{cot}^{\mathrm{2}} {C}\geqslant\mathrm{1}. \\ $$$$\mathrm{Equality}\:\mathrm{is}\:\mathrm{possible}\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:{A}={B}={C}=\frac{\pi}{\mathrm{3}}. \\ $$ Answered by MM42 last updated on…
Question Number 193236 by Mingma last updated on 08/Jun/23 Answered by MM42 last updated on 09/Jun/23 $${if}\:\:“{p}''\:{is}\:{prime}\:{number}\:\Rightarrow\:\left({p}−\mathrm{1}\right)!\overset{{p}} {\equiv}−\mathrm{1}\:\:\left({wilson}'{d}\:{theorem}\right) \\ $$$${h}=\mathrm{17}{k}+\mathrm{5}\Rightarrow{h}\overset{\mathrm{17}} {\equiv}\:\mathrm{5}\:\: \\ $$ Answered by…
Question Number 193239 by Mingma last updated on 08/Jun/23 Answered by a.lgnaoui last updated on 08/Jun/23 $$\measuredangle\mathrm{B}=\mathrm{180}−\mathrm{110}=\mathrm{70} \\ $$$$\bigtriangleup\mathrm{ABE}\:\:\:\:\measuredangle\mathrm{AEB}=\mathrm{180}−\mathrm{120}=\mathrm{60} \\ $$$$\bigtriangleup\mathrm{ACE}\:\:\:\:\measuredangle\mathrm{AEC}=\mathrm{180}−\mathrm{60}=\mathrm{120} \\ $$$$ \\ $$$$\bigtriangleup\mathrm{ABC}\:\:\:\frac{\mathrm{sin}\:\mathrm{40}}{\mathrm{AB}}=\frac{\mathrm{sin}\:\mathrm{70}}{\mathrm{BC}}…
Question Number 193238 by lmcp1203 last updated on 08/Jun/23 $${s}={a}+{b}+{c}+{d}+….. \\ $$$${number}\:{terms}\::{n} \\ $$$$\left\{{a};{b};{c};{d}…..\right\}>\mathrm{0} \\ $$$$\left.{then}\:{E}={s}/\left({s}−{a}\right)+{s}/\left({s}−{b}\right)+{s}/{s}−{c}\right)+…. \\ $$$$\left.{a}\left.\right)\:{E}>={n}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:{b}\right){E}>={n}^{\mathrm{2}} /\left({n}−\mathrm{1}\right) \\ $$$$\left.{c}\left.\right)\:{E}>={n}/\left({n}+\mathrm{1}\right)\:\:\:\:\:\:{d}\right)\:{E}>={n}^{\mathrm{2}} /\left({n}+\mathrm{1}\right) \\ $$$$\left.{e}\right)\:{E}>={n}^{\mathrm{2}}…
Question Number 193235 by mathlove last updated on 08/Jun/23 Answered by a.lgnaoui last updated on 08/Jun/23 $$\boldsymbol{\mathrm{T}}\mathrm{otale}\:\mathrm{Area}=\mathrm{22}+\mathrm{A}\:\:\:\:\:\:\left(\mathrm{A}=\boldsymbol{\mathrm{xy}}\right) \\ $$$$\mathrm{22}+\boldsymbol{\mathrm{xy}}=\mathrm{6}\boldsymbol{\mathrm{x}}+\left(\mathrm{8}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{y}} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{xy}}=\mathrm{8}\boldsymbol{\mathrm{y}}+\mathrm{6}\boldsymbol{\mathrm{x}}−\mathrm{22} \\ $$$$ \\ $$$$\boldsymbol{\mathrm{xy}}=\mathrm{4}\boldsymbol{\mathrm{y}}+\mathrm{3}\boldsymbol{\mathrm{x}}−\mathrm{11}\:\:\:\left(\mathrm{1}\right)…
Question Number 193256 by cherokeesay last updated on 08/Jun/23 Answered by som(math1967) last updated on 09/Jun/23 Commented by som(math1967) last updated on 09/Jun/23 $${DE}=\sqrt{\mathrm{5}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}}…
Question Number 193253 by MATHEMATICSAM last updated on 08/Jun/23 $$\boldsymbol{\mathrm{Select}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}\:\boldsymbol{\mathrm{with}}\: \\ $$$$\boldsymbol{\mathrm{explaination}}: \\ $$$$\mathrm{If}\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{log}_{\mathrm{3}} {M}\:+\:\mathrm{3log}_{\mathrm{3}} {N}\:=\:\mathrm{1}\:+\:\mathrm{log}_{\mathrm{0}.\mathrm{008}} \mathrm{5}\:\mathrm{then} \\ $$$$\mathrm{a}.\:{M}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{N}} \\ $$$$\mathrm{b}.\:{N}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{M}} \\ $$$$\mathrm{c}.\:{M}^{\mathrm{3}}…
Question Number 193248 by mnjuly1970 last updated on 08/Jun/23 $$ \\ $$$$\:\mathrm{L}=\:\mathrm{lim}_{\:{x}\rightarrow\mathrm{0}} \:\frac{\:\mathrm{sin}\left({x}\:\right)−\mathrm{arcsin}\left({x}\right)}{\mathrm{tan}\left({x}\right)−\:\mathrm{arctan}\left({x}\right)}=?\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\: \\ $$ Answered by MM42 last updated on…
Question Number 193250 by mathocean1 last updated on 08/Jun/23 $${Solve}: \\ $$$${y}'\left({x}\right)={y}^{\mathrm{2}} \left({t}\right)+{t}^{\mathrm{2}} \: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com