Question Number 56641 by ajfour last updated on 20/Mar/19 $$\mathrm{x}^{\mathrm{5}} +\mathrm{ax}^{\mathrm{4}} +\mathrm{cx}^{\mathrm{2}} +\mathrm{dx}+\mathrm{e}=\mathrm{0} \\ $$$$\mathrm{let}\:\mathrm{x}=\frac{\mathrm{rt}+\mathrm{s}}{\mathrm{t}+\mathrm{p}}\:\:.\:\mathrm{Find}\:\mathrm{r},\mathrm{s},\mathrm{p}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{equation}\:\mathrm{gets}\:\mathrm{transformed} \\ $$$$\mathrm{to}\:\:\:\:\:\lambda\mathrm{t}^{\mathrm{5}} +\mathrm{Dt}+\mathrm{E}=\mathrm{0}. \\ $$ Commented by ajfour…
Question Number 122174 by AbdullahMohammadNurusSafa last updated on 14/Nov/20 $${If}\:\:\boldsymbol{{x}}\:=\:\sqrt{\mathrm{5}\:}\:+\:\sqrt{\mathrm{3}},{then}\:\boldsymbol{{x}}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\boldsymbol{{x}}^{\mathrm{3}} }\:=\:? \\ $$$$\boldsymbol{{or}},\:\boldsymbol{{is}}\:\boldsymbol{{it}}\:\boldsymbol{{possible}}\:\boldsymbol{{at}}\:\boldsymbol{{all}}? \\ $$ Answered by behi83417@gmail.com last updated on 14/Nov/20 $$\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}}…
Question Number 122166 by physicstutes last updated on 14/Nov/20 $$\mathrm{Given}\:\mathrm{that}\:{I}_{{n}} \:=\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}\left(\mathrm{1}−{x}\right)^{{n}} {dx} \\ $$$$\mathrm{obtain}\:\mathrm{a}\:\mathrm{reduction}\:\mathrm{formulae}\:\mathrm{for}\:{I}_{{n}\:} \:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:{I}_{{n}−\mathrm{2}} \:\mathrm{Hence}\:\mathrm{evaluate}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{x}\left(\mathrm{1}−{x}\right)^{\mathrm{5}} {dx}. \\ $$…
Question Number 187695 by mnjuly1970 last updated on 20/Feb/23 $$ \\ $$$$\:\:\:{If}\:,\:\:{f}\left(\:{x}\:\right)=\:\frac{\:\:{si}\underset{} {{n}}\:\left({cos}\:\left({x}\right)\:\right)}{\overset{} {\:}\sqrt{\:\frac{\pi}{{x}}}} \\ $$$$\:\:\:\:\Rightarrow\:\:\:{f}\:'\:\left(\frac{\:\pi}{\mathrm{2}}\:\right)\:=\:? \\ $$ Answered by horsebrand11 last updated on 20/Feb/23…
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Question Number 56602 by Tawa1 last updated on 19/Mar/19 $$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{sin}^{\mathrm{2}} \left(\alpha\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{2}\alpha\right)\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{3}\alpha\right)\:+\:…\:+\:\mathrm{sin}^{\mathrm{2}} \left(\mathrm{n}\alpha\right) \\ $$ Commented by maxmathsup by imad last updated…
Question Number 56575 by Sr@2004 last updated on 18/Mar/19 Commented by Sr@2004 last updated on 18/Mar/19 $${please}\:{solve}\:\mathrm{12}\:{er}\:\mathrm{1}\:{no}. \\ $$ Commented by Sr@2004 last updated on…
Question Number 122095 by Anuragkar last updated on 14/Nov/20 $${Find}\:{the}\:\:{number}\:{of}\:{triplets}\left({x}/{a}/{b}\right)\:{where}\:{x} \\ $$$${is}\:{a}\:{real}\:{number}\:{and}\:\left({a}/{b}\right)\:{belongs}\:{to}\:{the}\:{set} \\ $$$$\left\{\mathrm{1}/\mathrm{2}/\mathrm{3}/\mathrm{4}/\mathrm{5}/\mathrm{6}/\mathrm{7}/\mathrm{8}/\mathrm{9}\right\}\:{such}\:{that}\: \\ $$$$ \\ $$$${x}^{\mathrm{2}} −{a}\left\{{x}\right\}+{b}\:=\mathrm{0} \\ $$$${where}\:\left\{{x}\right\}\:{denotes}\:{the}\:{fractional}\:{part}\:{of}\:{real}\:{number}\:{x} \\ $$$$ \\ $$$$…
Question Number 122081 by bobhans last updated on 14/Nov/20 $$\:{solve}\:\begin{cases}{\mid{x}−\mathrm{1}\mid+\mid{y}−\mathrm{1}\mid=\mathrm{1}}\\{\mid{x}−\mathrm{1}\mid−{y}=−\mathrm{5}}\end{cases} \\ $$ Answered by mathmax by abdo last updated on 14/Nov/20 $$\Rightarrow\begin{cases}{\mid\mathrm{x}−\mathrm{1}\mid=\mathrm{y}−\mathrm{5}}\\{\mid\mathrm{y}−\mathrm{1}\mid+\mathrm{y}\:=\mathrm{6}\:\:\:\:\:\mathrm{let}\:\mathrm{solve}\:\mid\mathrm{y}−\mathrm{1}\mid+\mathrm{y}\:=\mathrm{6}\:\:\mathrm{withy}\geqslant\mathrm{5}}\end{cases} \\ $$$$\Rightarrow\mid\mathrm{y}−\mathrm{1}\mid+\mathrm{y}−\mathrm{6}=\mathrm{0} \\…
Question Number 122075 by peter frank last updated on 13/Nov/20 Answered by MJS_new last updated on 14/Nov/20 $$\mathrm{seriously}??? \\ $$$$=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\mid{x}+\mathrm{1}\mid{dx}=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left({x}+\mathrm{1}\right){dx}=\left[\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+{x}\right]_{\mathrm{0}}…