Question Number 47394 by gunawan last updated on 09/Nov/18 $${f}\left({z}\right)=\frac{\mathrm{3}{z}+\mathrm{1}}{\mathrm{2}−\mathrm{4}{z}} \\ $$$${f}\left({f}\left({z}\right)\right)=… \\ $$ Commented by maxmathsup by imad last updated on 10/Nov/18 $${fof}\left({z}\right)\:=\frac{\mathrm{3}{f}\left({z}\right)+\mathrm{1}}{\mathrm{2}−\mathrm{4}{f}\left({z}\right)}=\:\frac{\mathrm{3}\frac{\mathrm{3}{z}+\mathrm{1}}{\mathrm{2}−\mathrm{4}{z}}\:+\mathrm{1}}{\mathrm{2}−\mathrm{4}\:\frac{\mathrm{3}{z}+\mathrm{1}}{\mathrm{2}−\mathrm{4}{z}}}\:=\frac{\mathrm{9}{z}+\mathrm{3}+\mathrm{2}−\mathrm{4}{z}}{\mathrm{4}−\mathrm{8}{z}−\mathrm{12}{z}−\mathrm{4}}\:=\frac{\mathrm{5}{z}+\mathrm{5}}{−\mathrm{20}{z}} \\…
Question Number 47391 by gunawan last updated on 09/Nov/18 $${z}_{\mathrm{1}} =\mathrm{3}+{i} \\ $$$${z}_{\mathrm{2}} =\mathrm{1}−\mathrm{2}{i} \\ $$$$\begin{vmatrix}{\frac{\mathrm{2}{z}_{\mathrm{2}} +{z}_{\mathrm{1}} −\mathrm{5}−{i}}{\mathrm{2}{z}_{\mathrm{1}} −{z}_{\mathrm{2}} +\mathrm{3}−{i}}}\end{vmatrix}^{\mathrm{2}} =.. \\ $$ Commented by…
Question Number 47389 by gunawan last updated on 09/Nov/18 $$\left(\sqrt{\mathrm{3}}−{i}\right)^{\mathrm{1}+\mathrm{2}{i}} =… \\ $$ Commented by maxmathsup by imad last updated on 09/Nov/18 $${we}\:{have}\:\mid\sqrt{\mathrm{3}}−{i}\mid=\mathrm{2}\:\Rightarrow\sqrt{\mathrm{3}}−{i}\:=\mathrm{2}\left(\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}}\right)=\mathrm{2}\left({cos}\left(−\frac{\pi}{\mathrm{6}}\right)+{isin}\left(−\frac{\pi}{\mathrm{6}}\right)\right) \\ $$$$=\mathrm{2}{e}^{−\frac{{i}\pi}{\mathrm{6}}}…
Question Number 178452 by cortano1 last updated on 16/Oct/22 $$\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\left(\left(\mathrm{p}\wedge\mathrm{q}\right)\Rightarrow\mathrm{r}\right)\Rightarrow\left(\left(\mathrm{p}\wedge\sim\mathrm{r}\right)\Rightarrow\sim\mathrm{q}\right) \\ $$$$\:\:\:\mathrm{is}\:\mathrm{tautology}\: \\ $$ Answered by Spillover last updated on 17/Oct/22 Commented by…
Question Number 178448 by Spillover last updated on 16/Oct/22 $$\mathrm{Using}\:\mathrm{the}\:\mathrm{algebra}\:\mathrm{propositions} \\ $$$$\mathrm{simplify} \\ $$$$\left(\mathrm{p}\leftrightarrow\mathrm{q}\right)\rightarrow\left(\mathrm{p}\rightarrow\mathrm{q}\right) \\ $$ Answered by greougoury555 last updated on 16/Oct/22 $$\left[\left({p}\rightarrow{q}\right)\wedge\left({q}\rightarrow{p}\right)\right]\rightarrow\left({p}\rightarrow{q}\right) \\…
Question Number 178434 by Spillover last updated on 16/Oct/22 $$\mathrm{Simplify}\:\mathrm{by}\:\mathrm{using}\:\mathrm{law}\:\mathrm{of}\:\mathrm{algebra} \\ $$$$\left(\mathrm{a}\right)\:\left[\mathrm{p}\vee\left(\mathrm{p}\wedge\mathrm{q}\right)\right]\rightarrow\sim\mathrm{p} \\ $$$$\left(\mathrm{b}\right)\left(\mathrm{p}\wedge\mathrm{q}\right)\rightarrow\mathrm{q} \\ $$ Answered by Spillover last updated on 16/Oct/22 Answered by…
Question Number 178433 by Spillover last updated on 16/Oct/22 $$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{proposition}\:\mathrm{is}\:\mathrm{true}\:\mathrm{or}\:\mathrm{not} \\ $$$$\left[\left(\mathrm{p}\rightarrow\sim\mathrm{q}\right)\wedge\left(\mathrm{q}\vee\mathrm{r}\right)\wedge\mathrm{p}\right]\rightarrow\mathrm{r} \\ $$ Answered by Spillover last updated on 18/Oct/22 Terms of…
Question Number 178423 by Shrinava last updated on 16/Oct/22 $$\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{k}}{\mathrm{p}}\:\:\:\mathrm{and}\:\:\:\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{k}}{\mathrm{p}}\:=\:\mathrm{1},\mathrm{5} \\ $$$$\mathrm{Find}\:\:\:\frac{\mathrm{m}}{\mathrm{n}}\:+\:\frac{\mathrm{k}}{\mathrm{p}}\:=\:? \\ $$ Answered by haladu last updated on 16/Oct/22 $$\:\: \\ $$$$\:\:\frac{\boldsymbol{\mathrm{m}}}{\boldsymbol{\mathrm{n}}}\:+\:\frac{\boldsymbol{\mathrm{k}}}{\boldsymbol{\mathrm{p}}}\:\:=\:\mathrm{2}\:\frac{\boldsymbol{\mathrm{m}}}{\boldsymbol{\mathrm{n}}}\:\:=\:\mathrm{2}×\:\mathrm{1}.\mathrm{5}\:\:=\:\mathrm{3}\: \\…
Question Number 178413 by mathlove last updated on 16/Oct/22 $$\left(\mathrm{2}{x}^{\mathrm{3}} {y}+\mathrm{3}{xy}−\mathrm{5}{x}^{\mathrm{2}} {y}^{\mathrm{2}} +\mathrm{12}\right)\boldsymbol{\div}\left(\mathrm{2}{x}−\mathrm{4}\right) \\ $$$$ \\ $$Divide it using compound division Commented by Rasheed.Sindhi last…
Question Number 178412 by Spillover last updated on 16/Oct/22 $$\mathrm{Express}\:\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}−\mathrm{ln}\:\mathrm{x}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of} \\ $$$$\mathrm{natural}\:\mathrm{logarithms}.\mathrm{Hence}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{limit}\:\mathrm{as}\:\mathrm{x}\rightarrow\infty \\ $$ Answered by Ar Brandon last updated on 16/Oct/22…