Menu Close

Category: Algebra

x-1-y-2-y-2-x-1-1-gt-x-

Question Number 111008 by Khanacademy last updated on 01/Sep/20 $$\frac{\sqrt{\boldsymbol{{x}}+\mathrm{1}}}{\boldsymbol{{y}}+\mathrm{2}}\:+\:\frac{\sqrt{\boldsymbol{{y}}+\mathrm{2}}}{\boldsymbol{{x}}+\mathrm{1}}\:=\mathrm{1}\:\:\:\:\:\:=>\:\:\boldsymbol{{x}}=? \\ $$ Commented by Rasheed.Sindhi last updated on 01/Sep/20 $${x}\:{in}\:{terms}\:{of}\:{y}? \\ $$ Commented by Khanacademy…

Question-45451

Question Number 45451 by Tinkutara last updated on 13/Oct/18 Answered by tanmay.chaudhury50@gmail.com last updated on 13/Oct/18 $$\mid\left({x}+{iy}−\mathrm{3}−\mathrm{2}{i}\right)\mid=\mid\left({x}+{iy}\right){cos}\left(\frac{\pi}{\mathrm{4}}−{tan}^{−\mathrm{1}} \frac{{y}}{{x}}\right)\mid \\ $$$$\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({y}−\mathrm{2}\right)^{\mathrm{2}} }\:=\mid\left({x}+{iy}\right)\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}.\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\:}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}.\frac{{y}}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}}…

z-C-z-3i-z-i-R-z-3-z-1-I-find-z-

Question Number 176513 by CrispyXYZ last updated on 20/Sep/22 $${z}\in\mathbb{C},\:\frac{{z}−\mathrm{3i}}{{z}+\mathrm{i}}\in\mathbb{R}^{−} \:,\:\:\frac{{z}−\mathrm{3}}{{z}+\mathrm{1}}\in\mathbb{I} \\ $$$$\mathrm{find}\:{z}. \\ $$ Answered by a.lgnaoui last updated on 20/Sep/22 $$\mathrm{Posons}\:\:\:\mathrm{z}=\mathrm{x}+\mathrm{iy} \\ $$$$\frac{\mathrm{z}−\mathrm{3i}}{\mathrm{z}+\mathrm{i}}=\frac{\mathrm{x}+\left(\mathrm{y}−\mathrm{3}\right)\mathrm{i}}{\mathrm{x}+\left(\mathrm{y}+\mathrm{1}\right)\mathrm{i}}=\frac{\left[\mathrm{x}+\left(\mathrm{y}−\mathrm{3}\right)\mathrm{i}\right]\left[\mathrm{x}−\left(\mathrm{y}+\mathrm{1}\right)\mathrm{i}\right]}{\mathrm{x}^{\mathrm{2}}…

ABC-sinA-cosB-tanC-find-the-value-of-cos-3-A-cos-2-A-cosA-

Question Number 176514 by CrispyXYZ last updated on 20/Sep/22 $$\bigtriangleup{ABC},\:\mathrm{sin}{A}=\mathrm{cos}{B}=\mathrm{tan}{C} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}^{\mathrm{3}} {A}+\mathrm{cos}^{\mathrm{2}} {A}−\mathrm{cos}{A}. \\ $$ Answered by mr W last updated on 21/Sep/22 $$\mathrm{sin}\:{A}=\mathrm{cos}\:{B}\:\Rightarrow{B}={A}−\frac{\pi}{\mathrm{2}}…

Three-consecutive-terms-of-a-G-P-are-the-3rd-5th-and-8th-term-of-an-A-P-Find-the-common-ratio-

Question Number 45422 by Tawa1 last updated on 12/Oct/18 $$\mathrm{Three}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}\:\mathrm{are}\:\mathrm{the}\:\mathrm{3rd},\:\mathrm{5th}\:\mathrm{and}\:\mathrm{8th}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 12/Oct/18 $${A}+\left(\mathrm{3}−\mathrm{1}\right){D}={a} \\ $$$${A}+\left(\mathrm{5}−\mathrm{1}\right){D}={ar} \\…

L-E-est-l-algebre-des-endomorphisme-continus-d-un-espace-de-Banach-E-muni-de-la-norme-d-application-lineaire-GL-E-est-le-sous-ensemble-des-elements-inversibles-de-L-E-a-Montrer-que-GL-E-est-ouv

Question Number 176482 by Vynho last updated on 19/Sep/22 $${L}\left({E}\right)\:{est}\:{l}'{algebre}\:{des}\:{endomorphisme} \\ $$$${continus}\:{d}'{un}\:{espace}\:{de}\:{Banach}\:{E}, \\ $$$${muni}\:{de}\:{la}\:{norme}\:{d}'{application}\:{lineaire} \\ $$$$;\:{GL}\left({E}\right)\:{est}\:{le}\:{sous}\:{ensemble}\:{des} \\ $$$${elements}\:{inversibles}\:{de}\:{L}\left({E}\right) \\ $$$$\left.{a}\right){Montrer}\:{que}\:{GL}\left({E}\right)\:{est}\:{ouvert}\:{dans} \\ $$$${L}\left({E}\right) \\ $$$$\left.{b}\right){montrer}\:{que}\:{l}'{application}\: \\…