Question Number 136739 by Ar Brandon last updated on 25/Mar/21 $$\mathrm{Given}\:\mathrm{0}<\mathrm{a}<\mathrm{b},\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\left(\mathrm{b}−\mathrm{a}\right)^{\mathrm{2}} }{\mathrm{8b}}\leqslant\frac{\mathrm{a}+\mathrm{b}}{\mathrm{2}}−\sqrt{\mathrm{ab}}\leqslant\frac{\left(\mathrm{b}−\mathrm{a}\right)^{\mathrm{2}} }{\mathrm{8a}} \\ $$ Answered by snipers237 last updated on 26/Mar/21 $$\frac{{a}+{b}}{\mathrm{2}}−\sqrt{{ab}\:}=\:\frac{\left(\sqrt{{a}}−\sqrt{{b}}\right)^{\mathrm{2}}…
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Question Number 136733 by Ñï= last updated on 25/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}\frac{\mathrm{1}}{\mathrm{4}^{{n}} \left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} }=\frac{\pi^{\mathrm{3}} }{\mathrm{48}}+\frac{\pi}{\mathrm{4}}{ln}^{\mathrm{2}} \mathrm{2} \\ $$ Answered by mindispower last updated on 25/Mar/21…
Question Number 71198 by Rio Michael last updated on 13/Oct/19 $${A}\:{particle}\:{P}\:{is}\:{projected}\:{from}\:\:{a}\:{point}\:{O}\:{at}\:\:{the}\:{edge}\:{of}\:{a}\:{cliff}\:\mathrm{60}{m} \\ $$$${from}\:{the}\:{sea}\:{with}\:{a}\:{velocity}\:{of}\:\mathrm{30}{ms}^{−\mathrm{1}} .\:{When}\:{P}\:{is}\:{at}\:{a}\:{point}\:{B} \\ $$$${where}\:{OB}\:{is}\:{a}\:{horizontal},\:{another}\:{particle}\:{Qsuch}\:{that}\: \\ $$$${P}\:{and}\:{Q}\:{hit}\:{the}\:{sea}\:{simultaneously}\:{at}\:{thesame}\:{point}\:{A}.\:{Gven}\:{that}\:{they} \\ $$$${strike}\:{the}\:{sea}\:\mathrm{6}{seconds}\:{after}\:{P}\:{was}\:{fired}\bar {\:}\:{calculate} \\ $$$$\left.{a}\right)\:{the}\:{sine}\:{of}\:{the}\:{angle}\:{of}\:{elevation}\:{of}\:{projection}. \\ $$$$\left.{b}\right)\:{the}\:{distance}\:{from}\:{A}\:{to}\:{O}.…
Question Number 71196 by Rio Michael last updated on 12/Oct/19 $${the}\:{curve}\:{y}\:=\:{f}\left({x}\right),\:{when}\:{f}\left({x}\right)\:{is}\:{a}\:{quadratic}\:{expression}\:{has}\: \\ $$$${a}\:{maximum}\:{value}\:{point}\:{at}\:\left(\mathrm{1},\mathrm{4}\right).\:{The}\:{curve}\:{touches}\:{the}\:{line} \\ $$$$\mathrm{6}{x}\:+\:{y}\:=\:\mathrm{13}.\:{Find}\:{the}\:{value}\:{of}\:{x}\:{for}\:{which}\:{y}\:=\:\mathrm{8} \\ $$ Answered by MJS last updated on 12/Oct/19 $${f}\left({x}\right)\:\mathrm{is}\:\mathrm{quadratic}\:\Leftrightarrow\:{y}={ax}^{\mathrm{2}}…
Question Number 136734 by mohammad17 last updated on 25/Mar/21 Answered by Ñï= last updated on 25/Mar/21 $${Q}\mathrm{5}::: \\ $$$${y}_{{p}} =\frac{\mathrm{1}}{{D}^{\mathrm{2}} +\mathrm{3}{D}+\mathrm{12}}\left({e}^{{x}} \mathrm{cos}\:{x}−\mathrm{cos}\:{x}\right) \\ $$$$={e}^{{x}} \frac{\mathrm{1}}{{D}^{\mathrm{2}}…
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Question Number 136724 by mohammad17 last updated on 25/Mar/21 Commented by mohammad17 last updated on 25/Mar/21 $${please}\:{sir}\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 136723 by mnjuly1970 last updated on 25/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….{calculus}\:\:\:\:\:\left({I}\right)….. \\ $$$$\:\:\:\:\:{prove}\:\:\:{that}\::: \\ $$$$\:\:\:\:{f}\left({x}\right)=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}}}\:\overset{???} {=}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:\:{n}}\end{pmatrix}\:{x}^{{n}} \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…
Question Number 71184 by ajfour last updated on 12/Oct/19 Commented by ajfour last updated on 12/Oct/19 $${Each}\:{semicircle}\:{have}\:{radius} \\ $$$${unity}.\:{Find}\:{maximum}\:{value}\:{of}\:{x}. \\ $$ Commented by ajfour last…