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Author: Tinku Tara

Show-that-for-any-arbitary-constants-A-and-B-y-A-sinx-1-x-cosx-B-cosx-1-x-sinx-satisfy-the-differential-equation-d-2-y-dx-2-1-2-x-2-y-0-

Question Number 9011 by tawakalitu last updated on 13/Nov/16 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{for}\:\mathrm{any}\:\mathrm{arbitary}\:\mathrm{constants}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B} \\ $$$$\mathrm{y}\:=\:\mathrm{A}\left(\mathrm{sinx}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\mathrm{cosx}\right)\:+\:\mathrm{B}\left(\mathrm{cosx}\:−\:\frac{\mathrm{1}}{\mathrm{x}}\mathrm{sinx}\right)\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}\:\:\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\:+\:\left(\mathrm{1}\:−\:\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }\right)\mathrm{y}\:=\:\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact:…

If-x-3y-6z-7z-2-and-y-1-2-z-6y-3-2-z-6y-Find-x-3-y-3-

Question Number 9009 by tawakalitu last updated on 13/Nov/16 $$\mathrm{If}\::\:\:\mathrm{x}\:=\:\frac{\mathrm{3y}\:+\:\mathrm{6z}}{\mathrm{7z}\:−\:\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}}{\frac{\mathrm{3}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}} \\ $$$$\mathrm{Find}\::\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \\ $$ Answered by Rasheed Soomro last updated on 14/Nov/16 $$\mathrm{If}\::\:\:\mathrm{x}\:=\:\frac{\mathrm{3y}\:+\:\mathrm{6z}}{\mathrm{7z}\:−\:\mathrm{2}}\:\:\mathrm{and}\:\:\mathrm{y}\:=\:\frac{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}}{\frac{\mathrm{3}}{\mathrm{2}}\mathrm{z}\:+\:\mathrm{6y}}=\frac{\mathrm{z}+\mathrm{12y}}{\mathrm{3z}+\mathrm{12y}} \\…

Question-140076

Question Number 140076 by bobhans last updated on 04/May/21 Commented by mr W last updated on 05/May/21 $${eqn}.\:\mathrm{2}{x}−\mathrm{3}{y}+{a}=\mathrm{0}\:{fixes}\:{only}\:{the} \\ $$$${inclination}\:{of}\:{the}\:{line}.\:{the}\:{vertical} \\ $$$${position}\:{will}\:{be}\:{determined}\:{by}\:{the} \\ $$$${value}\:{of}\:{a}.\:{the}\:{distance}\:{from}\:{point} \\…

prove-1-2-3-4-5-6-2n-1-2n-1-3n-1-

Question Number 9004 by mrW last updated on 12/Nov/16 $$\mathrm{prove} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\centerdot\frac{\mathrm{3}}{\mathrm{4}}\centerdot\frac{\mathrm{5}}{\mathrm{6}}\centerdot\centerdot\centerdot\centerdot\centerdot\frac{\mathrm{2n}−\mathrm{1}}{\mathrm{2n}}\leqslant\frac{\mathrm{1}}{\:\sqrt{\mathrm{3n}+\mathrm{1}}} \\ $$ Answered by mrW last updated on 15/Nov/16 $$\mathrm{Using}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\mathrm{prove}\:{P}\left(\mathrm{n}\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}}…

Let-f-x-3x-2-1-x-lt-0-cx-d-0-x-1-x-8-x-gt-1-find-the-value-of-c-amp-d-such-that-f-x-continous-everywhere-

Question Number 140073 by EDWIN88 last updated on 04/May/21 $$\mathrm{Let}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{3x}^{\mathrm{2}} −\mathrm{1}\:;\:\mathrm{x}<\mathrm{0}}\\{\mathrm{cx}+\mathrm{d}\:;\:\mathrm{0}\leqslant\mathrm{x}\leqslant\mathrm{1}}\\{\sqrt{\mathrm{x}+\mathrm{8}}\:;\:\mathrm{x}>\mathrm{1}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{c}\:\&\:\mathrm{d}\:\mathrm{such}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{continous} \\ $$$$\mathrm{everywhere} \\ $$ Answered by bobhans last updated on 04/May/21 $$\mathrm{since}\:\underset{{x}\rightarrow\mathrm{0}^{\:−}…