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Category: Arithmetic

lim-x-x-2-x-x-

Question Number 180106 by cherokeesay last updated on 07/Nov/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{{x}^{\mathrm{2}} +{x}}−{x} \\ $$ Answered by a.lgnaoui last updated on 07/Nov/22 $$\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}}\:−\mathrm{x}=\frac{\left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}}\:−\mathrm{x}\right)\left(\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}}\:+\mathrm{x}\right)}{\:\sqrt{\mathrm{x}^{\mathrm{2}}…

Question-49006

Question Number 49006 by peter frank last updated on 01/Dec/18 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Dec/18 $$\overset{\rightarrow} {{V}}={iV}_{{x}} +{jV}_{{y}} =\mathrm{12}{i}+\mathrm{8}{j} \\ $$$$\mid\overset{\rightarrow} {{V}}\mid=\sqrt{\left(\mathrm{12}\right)^{\mathrm{2}} +\left(\mathrm{8}\right)^{\mathrm{2}}…

Question-48983

Question Number 48983 by peter frank last updated on 30/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Dec/18 $$\left({x}−\mathrm{0}\right)^{\mathrm{2}} +\left({y}−\mathrm{0}\right)^{\mathrm{2}} =\mathrm{4}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}+{y}^{\mathrm{2}} −\mathrm{4}{y}+\mathrm{4}=\mathrm{5} \\…

Question-48981

Question Number 48981 by peter frank last updated on 30/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 01/Dec/18 $$\left.\mathrm{1}\right)\frac{{dy}}{{dx}}={y}\leftarrow{ordinate} \\ $$$$\frac{{dy}}{{y}}={dx}\:\:{so}\:\int\frac{{dy}}{{y}}=\int{dx} \\ $$$${lny}={x}+{lnc} \\ $$$${ln}\left(\frac{{y}}{{c}}\right)={x} \\…

Question-48976

Question Number 48976 by peter frank last updated on 30/Nov/18 Answered by $@ty@m last updated on 01/Dec/18 $${L}=\mathrm{3}{B}−\mathrm{4}\:…\left(\mathrm{1}\right) \\ $$$${b}={B}−\mathrm{2}\:…\left(\mathrm{2}\right) \\ $$$${l}=\mathrm{2}{b}+\mathrm{2}…\left(\mathrm{3}\right) \\ $$$${L}.{B}−{lb}=\mathrm{44}\:…\left(\mathrm{4}\right) \\…

Given-the-position-vectors-v-1-2i-2j-and-v-2-2j-a-show-that-the-unit-vector-in-the-direction-of-v-1-v-2-1-5-i-2j-b-Write-down-the-equation-of-the-line-that-contains-the-position-vectors-

Question Number 48958 by Rio Michael last updated on 30/Nov/18 $${Given}\:{the}\:{position}\:{vectors}\:{v}_{\mathrm{1}} =\:\mathrm{2}\boldsymbol{{i}}−\mathrm{2}\boldsymbol{{j}}\:{and}\:{v}_{\mathrm{2}} =\mathrm{2}\boldsymbol{{j}} \\ $$$$\left.{a}\right)\:{show}\:{that}\:{the}\:{unit}\:{vector}\:{in}\:{the}\:{direction}\:{of}\:{v}_{\mathrm{1}} −{v}_{\mathrm{2}} =\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}\left({i}−\mathrm{2}{j}\right) \\ $$$$\left.{b}\right)\:{Write}\:{down}\:{the}\:{equation}\:{of}\:{the}\:{line}\:{that}\:{contains} \\ $$$${the}\:{position}\:{vectors}\:{v}_{\mathrm{1}} \:{and}\:{v}_{\mathrm{2}} \\ $$$$\left.{c}\right)\:{Find}\:{the}\:{cosine}\:{of}\:{the}\:{angle}\:{between}\:{v}_{\mathrm{1}} \:{and}\:{v}_{\mathrm{2}}…

Question-114461

Question Number 114461 by Jamshidbek2311 last updated on 19/Sep/20 Commented by bemath last updated on 19/Sep/20 $$\mid\left({x}+\mathrm{2}\right)\left({x}+\mathrm{5}\right)\mid\:+\:\mathrm{10}\mid\left({x}−\mathrm{2}\right)\left({x}+\mathrm{2}\right)>\mid\left(\mathrm{2}{x}+\mathrm{3}\right)\left({x}+\mathrm{2}\right)\mid \\ $$$$\mid{x}+\mathrm{2}\mid\:\left\{\mid{x}+\mathrm{5}\mid−\mathrm{10}\mid{x}−\mathrm{2}\mid−\mid\mathrm{2}{x}+\mathrm{3}\mid\right\}>\mathrm{0} \\ $$$${now}\:{its}\:{can}\:{solve} \\ $$$$ \\ $$…