Question Number 18704 by gourav~ last updated on 28/Jul/17 Answered by Principal last updated on 28/Jul/17 $$\mathrm{Circumference}\:\mathrm{of}\:\mathrm{circular}\:\mathrm{wire} \\ $$$$=\:\mathrm{2}\pi×\mathrm{7}.\mathrm{5}\:=\:\mathrm{15}\pi\:\mathrm{cm} \\ $$$$\theta\:=\:\frac{{l}}{{r}}\:=\:\frac{\mathrm{15}\pi\:\mathrm{cm}}{\mathrm{120}\:\mathrm{cm}}\:=\:\frac{\pi}{\mathrm{8}}\:\mathrm{rad}\:=\:\mathrm{22}.\mathrm{5}° \\ $$ Terms of…
Question Number 149773 by Samimsultani last updated on 07/Aug/21 Answered by puissant last updated on 07/Aug/21 $${I}=\int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{b}^{\mathrm{2}} }{dx} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{+\infty} \frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}}…
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Question Number 149775 by mathdanisur last updated on 07/Aug/21 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mathrm{5}^{\boldsymbol{\mathrm{x}}} \:=\:\left(\mathrm{3}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{2}^{\boldsymbol{\mathrm{x}}} \right)^{\mathrm{2}} \\ $$ Commented by amin96 last updated on 07/Aug/21 $$\left(\mathrm{9}−\mathrm{4}\right)^{{x}}…
Question Number 84236 by niroj last updated on 10/Mar/20 $$\:\:\mathrm{If}\:\boldsymbol{\mathrm{ax}}^{\mathrm{2}} +\mathrm{2}\boldsymbol{\mathrm{hxy}}\:+\boldsymbol{\mathrm{by}}^{\mathrm{2}} =\:\mathrm{1},\:\mathrm{show}\:\mathrm{that} \\ $$$$\:\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:=\:\frac{\boldsymbol{\mathrm{h}}^{\mathrm{2}} −\boldsymbol{\mathrm{ab}}}{\left(\boldsymbol{\mathrm{hx}}+\boldsymbol{\mathrm{by}}\right)^{\mathrm{3}} }. \\ $$ Answered by TANMAY PANACEA last…
Question Number 84234 by niroj last updated on 10/Mar/20 $$\:\:\boldsymbol{\mathrm{Integrate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}: \\ $$$$\:\:\:\mathrm{1}.\:\int\sqrt{\frac{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$$$\:\:\:\mathrm{2}.\int\:\:\frac{\boldsymbol{\mathrm{dx}}}{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\left(\mathrm{3}+\mathrm{2}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}\right)} \\ $$$$\: \\ $$ Commented by mathmax by abdo last updated…
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Question Number 84232 by niroj last updated on 10/Mar/20 $$\:\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}. \\ $$$$\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }\:+\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}−\:\frac{\boldsymbol{\mathrm{y}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }=\:\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \\ $$ Commented by mind is power last…
Question Number 149770 by mathdanisur last updated on 07/Aug/21 $$\mathrm{6}\boldsymbol{{z}}^{\mathrm{4}} \:=\:\boldsymbol{{z}}^{\boldsymbol{{z}}^{\mathrm{2}} } \:\:\Rightarrow\:\:\mathrm{1}\:+\:\boldsymbol{{z}}^{\mathrm{2}} \:+\:\boldsymbol{{z}}^{\mathrm{4}} \:=\:? \\ $$ Commented by amin96 last updated on 07/Aug/21 $${z}^{\mathrm{2}}…
Question Number 18695 by Arnab Maiti last updated on 27/Jul/17 $$\mathrm{if}\:\:\frac{\mathrm{n}\:\mathrm{tan}\theta}{\mathrm{cos}^{\mathrm{2}} \left(\alpha−\theta\right)}=\frac{\mathrm{m}\:\mathrm{tan}\left(\alpha−\theta\right)}{\mathrm{cos}^{\mathrm{2}} \theta} \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\mathrm{2}\theta=\alpha−\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{n}−\mathrm{m}}{\mathrm{n}+\mathrm{m}}\mathrm{tan}\alpha\right) \\ $$ Answered by Tinkutara last updated…