Question Number 22232 by tapan das last updated on 13/Oct/17 $$\mathrm{find}\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\mathrm{where}\:\mathrm{sin}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{y}}\right)=\mathrm{x}+\mathrm{y} \\ $$ Answered by ajfour last updated on 13/Oct/17 $$\:\:\:\:\:{x}={y}\mathrm{sin}\:\left({x}+{y}\right) \\ $$$$\:\:\:\:\mathrm{1}=\frac{{dy}}{{dx}}\mathrm{sin}\:\left({x}+{y}\right)+{y}\left(\mathrm{1}+\frac{{dy}}{{dx}}\right)\mathrm{cos}\:\left({x}+{y}\right) \\…
Question Number 87767 by shshdhdhdhh@gmail.com last updated on 06/Apr/20 Commented by MJS last updated on 06/Apr/20 $$\mathrm{there}'\mathrm{s}\:\mathrm{not}\:\mathrm{a}\:\mathrm{single}\:\mathrm{correct}\:\mathrm{answer}.\:\mathrm{it}'\mathrm{s} \\ $$$$\mathrm{possible}\:\mathrm{to}\:\mathrm{find}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{function}\:\mathrm{satisfying} \\ $$$$\mathrm{a}\:\mathrm{chosen}\:\mathrm{value}\:\mathrm{in}\:\mathrm{the}\:\mathrm{empty}\:\mathrm{field}\:{and}\:\mathrm{all}\:\mathrm{other} \\ $$$$\mathrm{fields}. \\ $$$$\mathrm{an}\:\mathrm{easy}\:\mathrm{example}:\:\mathrm{find}\:\mathrm{the}\:\mathrm{next}\:\mathrm{number}:…
Question Number 87759 by M±th+et£s last updated on 06/Apr/20 Commented by mr W last updated on 06/Apr/20 $$\Delta{DEC}\sim\Delta{ECF}\sim\Delta{PFE} \\ $$$$\frac{{r}_{{z}} }{{EF}}=\frac{{r}_{{y}} }{{FC}}=\frac{{r}_{{x}} }{{CE}}={k},\:{say} \\ $$$$\Rightarrow{CE}=\frac{{r}_{{x}}…
Question Number 22221 by Sahib singh last updated on 13/Oct/17 $$\int\:\:\frac{{a}_{\mathrm{0}} +{b}_{\mathrm{0}} {x}^{\mathrm{2}} }{\left({a}+{x}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by Sahib singh last updated on 16/Oct/17…
Question Number 87757 by john santu last updated on 06/Apr/20 $$\int_{\mathrm{a}} ^{\mathrm{b}} \:\frac{\sqrt{\mathrm{x}−\mathrm{a}}}{\:\sqrt{\mathrm{b}−\mathrm{x}}}\:\mathrm{dx}\:=?\: \\ $$ Commented by john santu last updated on 06/Apr/20 $$\left.\mathrm{let}\:\mathrm{x}\:=\:\mathrm{a}\:+\:\left(\mathrm{b}−\mathrm{a}\right)\:\mathrm{w}\:\right] \\…
Question Number 22220 by Tinkutara last updated on 13/Oct/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integral}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\mathrm{4log}_{{x}/\mathrm{2}} \left(\sqrt{{x}}\right)+\mathrm{2log}_{\mathrm{4}{x}} \left({x}^{\mathrm{2}} \right)= \\ $$$$\mathrm{3log}_{\mathrm{2}{x}} \left({x}^{\mathrm{3}} \right)\:\mathrm{is} \\ $$ Answered by ajfour last…
Question Number 87754 by Rio Michael last updated on 06/Apr/20 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{forces}\:\mathrm{F}_{\mathrm{1}\:} \:\mathrm{and}\:\mathrm{F}_{\mathrm{2}} \:\mathrm{position}\:\mathrm{vectors}\:\mathrm{r}_{\mathrm{1}\:} \mathrm{and}\:\mathrm{r}_{\mathrm{2}} \\ $$$$\:\:\boldsymbol{\mathrm{F}}_{\mathrm{1}} \:=\:\left(\mathrm{2}\boldsymbol{{i}}\:+\:\mathrm{3}\boldsymbol{{j}}\right)\mathrm{N}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{1}} =\:\boldsymbol{\mathrm{i}}\:+\:\mathrm{2}\boldsymbol{\mathrm{j}} \\ $$$$\:\:\:\boldsymbol{\mathrm{F}}_{\mathrm{2}} \:=\:\left(\alpha\boldsymbol{{i}}−\mathrm{7}\boldsymbol{{j}}\right)\:\mathrm{N}\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{r}}_{\mathrm{2}} \:=\:\mathrm{3}\boldsymbol{\mathrm{i}}\:+\:\mathrm{4}\boldsymbol{\mathrm{j}} \\ $$$$\mathrm{Given}\:\mathrm{that}\:\mathrm{these}\:\mathrm{system}\:\mathrm{of}\:\mathrm{forces}\:\mathrm{form}\:\mathrm{a}\:\mathrm{couple} \\…
Question Number 87755 by john santu last updated on 06/Apr/20 $$\mathrm{f}\left(\frac{\mathrm{x}−\mathrm{3}}{\mathrm{x}+\mathrm{1}}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{x}+\mathrm{3}}{\mathrm{1}−\mathrm{x}}\right)\:=\:\mathrm{x} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$ Commented by john santu last updated on 06/Apr/20 $$\left(\mathrm{i}\right)\:\mathrm{let}\:\frac{\mathrm{x}−\mathrm{3}}{\mathrm{x}+\mathrm{1}}\:=\:\mathrm{x}'\:\Rightarrow\mathrm{f}\left(\mathrm{x}'\right)\:+\:\mathrm{f}\left(\frac{\mathrm{x}'−\mathrm{3}}{\mathrm{x}'+\mathrm{1}}\right)\:=\:\frac{\mathrm{x}'+\mathrm{3}}{\mathrm{1}−\mathrm{x}} \\…
Question Number 87752 by Rio Michael last updated on 06/Apr/20 $$\mathrm{A}\:\mathrm{particle}\:\mathrm{exhibits}\:\mathrm{simple}\:\mathrm{hamornic}\:\mathrm{motion}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}} }\:+\:\mathrm{4}{x}\:=\:\mathrm{0} \\ $$$$\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ocsillation}\: \\ $$ Answered by TANMAY PANACEA. last updated…
Question Number 22215 by gopikrishnan005@gmail.com last updated on 13/Oct/17 $${solve}\:{the}\:{inequation}\:−{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{2}>\mathrm{0} \\ $$ Answered by ajfour last updated on 13/Oct/17 $${x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}<\mathrm{0} \\ $$$$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)<\mathrm{0} \\…