Question Number 48919 by vajpaithegrate@gmail.com last updated on 30/Nov/18 $$\mathrm{if}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{lengrhs}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:\mathrm{segment} \\ $$$$\mathrm{of}\:\mathrm{any}\:\mathrm{focal}\:\mathrm{chord}\:\mathrm{of}\:\mathrm{parabola}\:\mathrm{y}^{\mathrm{2}} =\mathrm{4ax}. \\ $$$$\mathrm{where}\:\mathrm{p},\mathrm{q}\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\left(\mathrm{5}+^{} \sqrt{}\mathrm{2}\:\right)\mathrm{x}^{\mathrm{2}} −\left(\mathrm{4}+\sqrt{\mathrm{5}}\right)\mathrm{x}+\left(\mathrm{4}+\sqrt{}\mathrm{5}\right)=\mathrm{0}\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{semi}\:\mathrm{letusrectum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parabola} \\ $$$$\mathrm{is} \\ $$$$\mathrm{ans}:\mathrm{2}…
Question Number 48918 by vajpaithegrate@gmail.com last updated on 30/Nov/18 $$\mathrm{if}\:\mathrm{r}_{\mathrm{1}} \mathrm{andr}_{\mathrm{2}\:} \mathrm{are}\:\mathrm{the}\:\mathrm{radii}\:\mathrm{of}\:\mathrm{smallest}\:\mathrm{and}\: \\ $$$$\mathrm{largest}\:\mathrm{circles}\:\mathrm{which}\:\mathrm{passes}\:\mathrm{through}\: \\ $$$$\left(\mathrm{5},\mathrm{6}\right)\mathrm{and}\:\mathrm{touches}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{4x}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{r}_{\mathrm{1}} \mathrm{r}_{\mathrm{2}} = \\ $$$$\mathrm{ans}:\frac{\mathrm{41}}{\mathrm{4}} \\…
Question Number 179972 by mr W last updated on 05/Nov/22 Commented by mr W last updated on 05/Nov/22 $${find}\:{the}\:{number}\:{of}\:{days}\:{since}\:{an} \\ $$$${essential}\:{member}\:{of}\:{the}\:{forum}\:{is} \\ $$$${missed}. \\ $$…
Question Number 48897 by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18 $${find}\:{the}\:{highest}\:{power}\:{of}\:\mathrm{5}\:{contained}\:{in}\mathrm{158}!\:\: \\ $$ Answered by mr W last updated on 29/Nov/18 $$\mathrm{155}=\mathrm{31}×\mathrm{5} \\ $$$$\mathrm{5},\mathrm{2}×\mathrm{5},\mathrm{3}×\mathrm{5},…,\mathrm{31}×\mathrm{5}\Rightarrow\mathrm{31}\:{times} \\ $$$$\mathrm{1}×\mathrm{5},\mathrm{2}×\mathrm{5},\mathrm{3}×\mathrm{5},…,\mathrm{6}×\mathrm{5}\Rightarrow\mathrm{6}\:{times}…
Question Number 179961 by yaojunon2t last updated on 05/Nov/22 $${f}\left({x}\right)\in\left[\mathrm{0},\mathrm{1}\right],\mathrm{1}\leqslant{f}\left({x}\right)\leqslant\mathrm{3} \\ $$$${how}\:{to}\:{prove}\:\mathrm{1}\leqslant\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{{f}\left({x}\right)}\leqslant\frac{\mathrm{4}}{\mathrm{3}}? \\ $$ Answered by Frix last updated on 06/Nov/22…
Question Number 114433 by bemath last updated on 19/Sep/20 $${find}\:{sum}\:{of}\:{the}\:{series}\: \\ $$$$\mathrm{1}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} +…+\left(\mathrm{4}{n}−\mathrm{3}\right)^{\mathrm{2}} −\left(\mathrm{4}{n}−\mathrm{1}\right)^{\mathrm{2}} \\ $$ Answered by 1549442205PVT last…
Question Number 48884 by tanmay.chaudhury50@gmail.com last updated on 29/Nov/18 $${find}\:{last}\:{digit}\:{of} \\ $$$$\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!+…+\mathrm{23}! \\ $$$${and}\:\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+…+\mathrm{134}! \\ $$ Answered by mr W last updated on 29/Nov/18 $${last}\:{digit}\:{of}\:{n}!\:{is}\:\mathrm{0}\:{for}\:{n}\geqslant\mathrm{5}.…
Question Number 48877 by absa last updated on 29/Nov/18 Commented by absa last updated on 29/Nov/18 $${find}\:{the}\:{inverse}\:{laplace}\:{transformation}? \\ $$ Answered by Abdulhafeez Abu qatada last…
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Question Number 179908 by Acem last updated on 04/Nov/22 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Some}}\:\boldsymbol{{Important}}\:\boldsymbol{{notes}} \\ $$$$\:\mathrm{1}\boldsymbol{{st}}\:{Someone}\:{has}\:{solved}\:{a}\:{question}\:{as}\:{wrong}, \\ $$$$\:{and}\:{after}\:{he}\:{see}\:{other}\:{people}\:{have}\:{solved}\:{it} \\ $$$$\:{correctly}\:{he}\:{delete}\:{his}\:{poste}!\:{hmmm}\:{by}\:{the}\:{way}, \\ $$$$\:{i}\:{have}\:{some}\:{lapses},\:{i}'{ve}\:{never}\:{deleted}\:{any}. \\ $$$$\:{My}\:{mistakes}\:{keep}\:{you}\:{from}\:{making}\:{like}\:{them}. \\ $$$$\:{There}\:{is}\:{no}\:{embarrassment},\:{so}\:{please},\:{leave} \\ $$$$\:{things}\:{as}\:{they}\:{are}. \\…