Question Number 70874 by Mr. K last updated on 09/Oct/19 $${If}\:\mathrm{4}−\mathrm{2}\sqrt{\mathrm{5}}\:{and}\:\mathrm{4}+\mathrm{2}\sqrt{\mathrm{5}\:}\:{are}\:{solutions} \\ $$$${of}\:{x}^{\mathrm{2}} +\left(\mathrm{5}{a}−{b}\right){x}+\left(\mathrm{3}{b}−{a}\right)=\mathrm{0} \\ $$$${whete}\:{a}\:{and}\:{b}\:{are}\:{real}\:{numbers},\: \\ $$$${determine}\:{the}\:{product}\:{of}\:\boldsymbol{{ab}}. \\ $$ Answered by tw000001 last updated…
Question Number 136408 by nimnim last updated on 21/Mar/21 $$\:\:\:\:\:\:{S}=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{3}{k}^{\mathrm{2}} }{\mathrm{2}{k}^{\mathrm{3}} +\mathrm{2}}\:\:=? \\ $$$$\:\:\:\:\:\:\:\:\:=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{3}{k}^{\mathrm{2}} }{{k}^{\mathrm{3}} +\mathrm{1}}\right)=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{\mathrm{1}}{{k}+\mathrm{1}}+\frac{\mathrm{2}{k}−\mathrm{1}}{{k}^{\mathrm{2}} −{k}+\mathrm{1}}\right] \\ $$$$\:\:\:\:\:\:\:\:\:{I}\:{dont}\:{know}\:{how}\:{to}\:{continue}…{Please}\:{Help}.…
Question Number 5338 by FilupSmith last updated on 09/May/16 Commented by FilupSmith last updated on 09/May/16 $$\mathrm{I}\:\mathrm{have}\:{n}\:\mathrm{lines}\:\mathrm{inside}\:\mathrm{the}\:\mathrm{interior}\:\mathrm{of}\:\mathrm{a} \\ $$$$\mathrm{semi}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{radius}\:{r}.\:\mathrm{All}\:\mathrm{lines}\:\mathrm{are} \\ $$$$\mathrm{of}\:\mathrm{length}\:{a}. \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{lines}\:\mathrm{is}\:\mathrm{less}\:\mathrm{than}…
Question Number 70872 by Abdo msup. last updated on 09/Oct/19 $${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:{e}^{−{x}−{y}} \:{ln}\left(\mathrm{2}{x}+{y}\right){dxdy} \\ $$ Commented by Abdo msup. last updated on 11/Oct/19 $${let}\:{I}=\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}}…
Question Number 5337 by Junaid Mirza last updated on 09/May/16 Commented by prakash jain last updated on 09/May/16 $$\mathrm{4}\:\mathrm{is}\:\mathrm{correct}. \\ $$$$\mathrm{Relative}\:\mathrm{refractive}\:\mathrm{index}\:\:_{\mathrm{1}} \mu_{\mathrm{2}} =\frac{\mu_{\mathrm{2}} }{\mu_{\mathrm{1}} }…
Question Number 70873 by Abdo msup. last updated on 09/Oct/19 $${calculate}\:\int\int_{\left[\mathrm{1},\mathrm{3}\right]^{\mathrm{2}} } \:\:\:{e}^{−{x}−{y}} \:{ln}\left(\mathrm{2}{x}+{y}\right){dxdy} \\ $$ Answered by mind is power last updated on 09/Oct/19…
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Question Number 136405 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} −\mathrm{3x}+\mathrm{2}\:\:\mathrm{determine}\:\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{and}\:\int\:\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{nf}\left(\mathrm{x}\right)\right)\mathrm{dx}\:\:\mathrm{with} \\ $$$$\mathrm{n}\:\mathrm{integr} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 70870 by Abdo msup. last updated on 09/Oct/19 $${let}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+{x}^{\mathrm{2}} \right)^{\mathrm{4}} }\:\:{with}\:\:\mid{x}\mid>\mathrm{1} \\ $$$${and}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right){find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\:\frac{{dt}}{\left({t}^{\mathrm{2}} −\mathrm{2}{t}\:+{x}^{\mathrm{2}}…
Question Number 136404 by mathmax by abdo last updated on 21/Mar/21 $$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{n}\left(−\mathrm{1}\right)^{\mathrm{n}} }{\left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{n}+\mathrm{3}\right)} \\ $$ Answered by mindispower last updated on 21/Mar/21…