Question Number 77473 by BK last updated on 06/Jan/20 Commented by mr W last updated on 06/Jan/20 $${y}=\frac{{dy}}{{dx}}+\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\frac{{d}^{\mathrm{3}} {y}}{{dy}^{\mathrm{3}} }+… \\ $$$$\frac{{dy}}{{dx}}=\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}}…
Question Number 11935 by uni last updated on 05/Apr/17 $$\frac{\mathrm{7}!}{\mathrm{6}!}+\frac{\mathrm{8}!}{\mathrm{7}!}+\frac{\mathrm{9}!}{\mathrm{8}!}+…\frac{\mathrm{n}!}{\left(\mathrm{n}−\mathrm{1}\right)!}=\mathrm{84}\:\Rightarrow\mathrm{n}=? \\ $$ Answered by bahmanfeshki1 last updated on 06/Apr/17 $${n}=\mathrm{14} \\ $$ Answered by ajfour…
Question Number 143006 by mathdanisur last updated on 08/Jun/21 $$\mathrm{1}.\:{y}\frac{\partial{z}}{\partial{x}}\:+\:{z}\frac{\partial{z}}{\partial{y}}\:=\:\frac{{y}}{{x}} \\ $$$$\mathrm{2}.\:{x}^{\mathrm{2}} \frac{\partial{z}}{\partial{x}}\:−\:{xy}\frac{\partial{z}}{\partial{y}}\:+\:{y}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$\mathrm{3}.\:\begin{cases}{\frac{\partial{z}}{\partial{x}}\:=\:\frac{{z}}{{x}}}\\{\frac{\partial{z}}{\partial{y}}\:=\:\frac{\mathrm{2}{z}}{{y}}}\end{cases} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 11930 by 786786AM last updated on 05/Apr/17 $$\mathrm{Let}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{be}\:\mathrm{two}\:\mathrm{numbers},\:\mathrm{x}\:\mathrm{be}\:\mathrm{the}\:\mathrm{single}\:\mathrm{arithmetic}\:\mathrm{mean}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{arithmetic}\:\mathrm{means}\:\mathrm{between}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{nx}. \\ $$ Answered by ajfour last updated on 05/Apr/17 $${A}_{{r}} =\:{a}+\frac{\left({b}−{a}\right)}{\left({n}+\mathrm{1}\right)}{r} \\ $$$$\underset{{r}=\mathrm{1}}…
Question Number 143003 by bramlexs22 last updated on 08/Jun/21 Answered by EDWIN88 last updated on 08/Jun/21 $$\left(\mathrm{1}\right)\:\mathrm{Since}\:\Delta\mathrm{ACE}\:\mathrm{and}\:\Delta\mathrm{ACB}\:\mathrm{share}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{altitude},\mathrm{and}\:\mathrm{AE}=\frac{\mathrm{1}}{\mathrm{3}}\mathrm{AB}\:,\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\Delta\mathrm{ACE}= \\ $$$$\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\Delta\mathrm{ACB}\:.\: \\ $$$$\mathrm{By}\:\mathrm{Heron}\:\mathrm{formula}\: \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{3}}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\Delta\mathrm{ACB}\:=\:\frac{\mathrm{1}}{\mathrm{3}}\sqrt{\frac{\mathrm{15}}{\mathrm{2}}\left(\frac{\mathrm{7}}{\mathrm{2}}\right)\left(\frac{\mathrm{5}}{\mathrm{2}}\right)\left(\frac{\mathrm{3}}{\mathrm{2}}\right)}\:=\frac{\mathrm{5}\sqrt{\mathrm{7}}}{\mathrm{4}}…
Question Number 77464 by naka3546 last updated on 06/Jan/20 $$\underset{\:\:\mathrm{0}} {\int}\:\overset{\frac{\pi}{\mathrm{2}}} {\:}\mathrm{ln}\:\left(\mathrm{2}\:\mathrm{cos}\:{x}\right)\:{dx}\:\:=\:\:? \\ $$ Commented by kaivan.ahmadi last updated on 06/Jan/20 $${u}={ln}\left(\mathrm{2}{cosx}\right)\Rightarrow{du}=−{tgxdx} \\ $$$${dv}={dx}\Rightarrow{v}={x} \\…
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Question Number 142992 by otchereabdullai@gmail.com last updated on 08/Jun/21 Commented by otchereabdullai@gmail.com last updated on 08/Jun/21 $$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{understand}\:\mathrm{why}\:\mathrm{we}\: \\ $$$$\mathrm{have}\:\mathrm{S}=−\mathrm{20m}\:\mathrm{in}\:\mathrm{option}\:\left(\mathrm{b}\right) \\ $$ Commented by Olaf_Thorendsen last…
Question Number 77459 by jagoll last updated on 06/Jan/20 $$ \\ $$$$ \\ $$$${the}\:{greatest}\:{value}\:{of}\:{n}\:{so}\:{that}\: \\ $$$${only}\:{one}\:{value}\:{of}\:{k}\:{satisfies}\: \\ $$$$\frac{\mathrm{8}}{\mathrm{15}}<\frac{{n}}{{n}+{k}}<\frac{\mathrm{7}}{\mathrm{13}}\:{is}\: \\ $$ Answered by MJS last updated…
Question Number 11921 by carrot last updated on 05/Apr/17 $${given}\:{that}\:{y}={Acos}\mathrm{5}{x}\:+\:{Bsin}\mathrm{5}{x}, \\ $$$${show}\:{that}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{25}{y}=\mathrm{0} \\ $$ Answered by sandy_suhendra last updated on 05/Apr/17 $$\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{5Asin5x}\:+\:\mathrm{5Bcos5x} \\…