Question Number 210974 by bns970 last updated on 25/Aug/24 $$\sqrt{\mathrm{25}} \\ $$ Answered by TonyCWX08 last updated on 25/Aug/24 $$\sqrt{\mathrm{25}} \\ $$$$=\pm\mathrm{5} \\ $$ Commented…
Question Number 210991 by Ismoiljon_008 last updated on 25/Aug/24 Commented by Ismoiljon_008 last updated on 25/Aug/24 $$\:\:\:{DC}=\mathrm{5} \\ $$ Commented by Ismoiljon_008 last updated on…
Question Number 210987 by RojaTaniya last updated on 25/Aug/24 Answered by Frix last updated on 25/Aug/24 $${x}^{\mathrm{6}} −\frac{\mathrm{133}}{\mathrm{78}}{x}^{\mathrm{5}} +\frac{\mathrm{133}}{\mathrm{78}}{x}−\mathrm{1}=\mathrm{0} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}+\mathrm{1}\right)\left({x}−\frac{\mathrm{2}}{\mathrm{3}}\right)\left({x}−\frac{\mathrm{3}}{\mathrm{2}}\right)\left({x}^{\mathrm{2}} +\frac{\mathrm{6}}{\mathrm{13}}{x}+\mathrm{1}\right)=\mathrm{0} \\ $$ Terms…
Question Number 210971 by black_mamba234 last updated on 25/Aug/24 Answered by A5T last updated on 25/Aug/24 $$\left.\mathrm{2}\right)\:\mathrm{2}{x}_{\mathrm{1}} +\mathrm{4}{y}_{\mathrm{1}} −\mathrm{2}{z}_{\mathrm{1}} =\mathrm{2}\left({x}_{\mathrm{1}} +{k}\right)+\mathrm{4}{y}_{\mathrm{1}} −\mathrm{2}\left({z}_{\mathrm{1}} +{k}\right) \\ $$$${f}\left({x}_{\mathrm{1}}…
Question Number 210996 by RojaTaniya last updated on 25/Aug/24 Answered by Frix last updated on 26/Aug/24 $$\mathrm{Only}\:\mathrm{true}\:\mathrm{for}\:\mathrm{the}\:\mathrm{real}\:\mathrm{solution}\:>\mathrm{0}: \\ $$$${x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}−\mathrm{1}=\mathrm{0} \\ $$$${x}^{\mathrm{3}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{9}{x}=\mathrm{4}{x}^{\mathrm{2}}…
Question Number 210958 by RojaTaniya last updated on 24/Aug/24 Commented by Ghisom last updated on 26/Aug/24 $$\mathrm{I}\:\mathrm{get} \\ $$$${x}=\frac{\mathrm{36}}{\mathrm{25}}\wedge{y}=\frac{\mathrm{64}}{\mathrm{25}} \\ $$$${x}=−\frac{\mathrm{7}}{\mathrm{16}}+\frac{\mathrm{3}}{\mathrm{2}}\mathrm{i}\wedge{y}=\frac{\mathrm{63}}{\mathrm{400}}−\frac{\mathrm{27}}{\mathrm{50}}\mathrm{i} \\ $$$${x}=−\frac{\mathrm{7}}{\mathrm{16}}−\frac{\mathrm{3}}{\mathrm{2}}\mathrm{i}\wedge{y}=\frac{\mathrm{63}}{\mathrm{400}}+\frac{\mathrm{27}}{\mathrm{50}}\mathrm{i} \\ $$…
Question Number 210969 by universe last updated on 24/Aug/24 $$\:\:\:\:\mathrm{if}\:\mathrm{a}_{\mathrm{n}} \:=\:\mathrm{n}^{\mathrm{4}} \int_{\mathrm{n}} ^{\mathrm{n}+\mathrm{1}} \:\frac{\mathrm{x}\:\mathrm{dx}}{\mathrm{1}+\mathrm{x}^{\mathrm{5}} }\:\:\mathrm{then} \\ $$$$\:\:\:\:\left(\mathrm{1}\right)\:\Sigma\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\:\mathrm{divergent}?? \\ $$$$\:\:\:\:\left(\mathrm{2}\right)\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{a}_{\mathrm{n}\:} \:=\:?? \\ $$ Terms…
Question Number 210967 by mahdipoor last updated on 24/Aug/24 $${Q}.\mathrm{210956} \\ $$$${im}\:{read}\:{leithold}\:{book}\:{again}\:,\:{in}\:{this}\:{book}\:: \\ $$$$\left.\mathrm{1}\right\}{define}\::\:{ln}\left({x}\right)=\int_{\mathrm{1}} ^{\:{x}} {dx}/{x}\:\:\:\:\:\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right\}{define}\::\:{ln}\left({e}\right)=\mathrm{1}=\int_{\mathrm{1}} ^{\:{e}} {dx}/{x} \\ $$$$\left.\mathrm{3}\right\}{define}\::\:{exp}\left({x}\right)={y}\:\Leftrightarrow\:{ln}\left({y}\right)={x} \\ $$$$\frac{{d}\left({ln}\left({u}\right)\right)}{{du}}=\frac{\mathrm{1}}{{u}}\:\Rightarrow\:\frac{{d}\left({ln}\left({u}\right)\right)}{{dx}}=\frac{{du}/{dx}}{{u}}\:\Rightarrow \\…
Question Number 210961 by RojaTaniya last updated on 24/Aug/24 Answered by A5T last updated on 24/Aug/24 $$\frac{{a}−\mathrm{1}+\mathrm{2}}{{a}−\mathrm{1}}+\frac{{b}−\mathrm{1}+\mathrm{2}}{{b}−\mathrm{1}}+\frac{{c}−\mathrm{1}+\mathrm{2}}{{c}−\mathrm{1}}=\mathrm{10} \\ $$$$\Rightarrow\frac{\mathrm{1}}{{a}−\mathrm{1}}+\frac{\mathrm{1}}{{b}−\mathrm{1}}+\frac{\mathrm{1}}{{c}−\mathrm{1}}=\frac{\mathrm{7}}{\mathrm{2}} \\ $$$${a}+{b}+{c}=\mathrm{0};{ab}+{bc}+{ca}=\frac{{m}−\mathrm{1}}{{m}};{abc}=\frac{−{m}−\mathrm{1}}{{m}} \\ $$$$\Rightarrow\frac{{ab}+{bc}+{ca}−\mathrm{2}\left({a}+{b}+{c}\right)+\mathrm{3}}{{abc}−{ab}−{bc}−{ac}+{a}+{b}+{c}−\mathrm{1}}=\frac{\mathrm{7}}{\mathrm{2}} \\ $$$$\Rightarrow\frac{\frac{{m}−\mathrm{1}+\mathrm{3}{m}}{{m}}}{\frac{−{m}−\mathrm{1}+\mathrm{1}−{m}−{m}}{{m}}}=\frac{\mathrm{7}}{\mathrm{2}}\Rightarrow\frac{\mathrm{4}{m}−\mathrm{1}}{−\mathrm{3}{m}}=\frac{\mathrm{7}}{\mathrm{2}}…
Question Number 210956 by mahdipoor last updated on 23/Aug/24 $${we}\:{define}\::\:{ln}\left({x}\right)=\int_{\mathrm{1}} ^{\:{x}} \frac{{dx}}{{x}} \\ $$$${how}\:{prove}\::\:{ln}\left({x}\right)={log}_{{e}} {x}\:\:\:? \\ $$ Commented by Ghisom last updated on 24/Aug/24 $$\mathrm{an}\:\mathrm{idea}:…