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Author: Tinku Tara

I-0-x-a-2-b-2-x-2a-2-x-2-2b-2-dx-a-2-x-2-b-2-2-a-2-b-2-x-a-2-x-2-b-2-

Question Number 141244 by ajfour last updated on 17/May/21 $${I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{x}\left\{\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right){x}−\mathrm{2}{a}^{\mathrm{2}} {x}^{\mathrm{2}} −\mathrm{2}{b}^{\mathrm{2}} \right\}{dx}}{\left({a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}} \right)^{\mathrm{2}} \left\{\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right){x}+{a}^{\mathrm{2}} {x}^{\mathrm{2}} +{b}^{\mathrm{2}}…

y-f-xy-f-x-x-y-R-If-f-4-1006-so-f-2012-

Question Number 10170 by Joel575 last updated on 28/Jan/17 $${y}\:.\:{f}\left({xy}\right)\:=\:{f}\left({x}\right)\:\:\:\:\:\:\:\:{x},\mathrm{y}\:\in\:\mathbb{R} \\ $$$$\mathrm{If}\:{f}\left(\mathrm{4}\right)\:=\:\mathrm{1006},\:\mathrm{so}\:{f}\left(\mathrm{2012}\right)\:=\:? \\ $$ Answered by ridwan balatif last updated on 28/Jan/17 $$\mathrm{f}\left(\mathrm{xy}\right)=\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{y}},\:\:\:\:\mathrm{f}\left(\mathrm{4}\right)=\mathrm{1006} \\ $$$$\mathrm{if}\:\mathrm{x}=\mathrm{1}\:\mathrm{y}=\mathrm{4},\mathrm{then}…

2013-1-2013-1-2-2013-1-2-3-2013-1-2-3-2012-

Question Number 10169 by Joel575 last updated on 28/Jan/17 $$\frac{\mathrm{2013}}{\mathrm{1}}\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+…+\mathrm{2012}}\:=\:? \\ $$ Answered by prakash jain last updated on 29/Jan/17 $$\underset{{i}=\mathrm{1}} {\overset{\mathrm{2012}} {\sum}}\:\frac{\mathrm{2013}}{\underset{{j}=\mathrm{1}} {\overset{{i}} {\sum}}{j}}\:=\:\:\mathrm{2013}\underset{{i}=\mathrm{1}}…

If-the-roots-of-quadratic-equation-ax-2-bx-c-0-were-within-the-interval-0-1-the-maximum-value-from-2a-b-a-b-a-a-b-c-is-

Question Number 10168 by Joel575 last updated on 28/Jan/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0} \\ $$$$\mathrm{were}\:\mathrm{within}\:\mathrm{the}\:\mathrm{interval}\:\left[\mathrm{0},\mathrm{1}\right], \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{from} \\ $$$$\frac{\left(\mathrm{2}{a}−{b}\right)\left({a}−{b}\right)}{{a}\left({a}−{b}+{c}\right)}\:\:\:\:\mathrm{is}\:… \\ $$ Terms of Service Privacy…

Question-10166

Question Number 10166 by Joel575 last updated on 28/Jan/17 Commented by Joel575 last updated on 28/Jan/17 $$\mathrm{Two}\:\mathrm{circles}\:\mathrm{with}\:\mathrm{same}\:\mathrm{center}\:\mathrm{point}\:\mathrm{have} \\ $$$$\mathrm{R}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{R}_{\mathrm{2}} \:\mathrm{with}\:\mathrm{R}_{\mathrm{1}} \:<\:\mathrm{R}_{\mathrm{2}} \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{long}\:\mathrm{of}\:\mathrm{AB}\:\mathrm{bowstring}\:\mathrm{is}\:\mathrm{10}\:\mathrm{cm}, \\…