Question Number 212028 by siva12345 last updated on 27/Sep/24 $${DEFINATION}\:\:\:\:{OF}\:\:\:{QUADRATIC}\:\:{FORM}:\: \\ $$$$\:\:\:\:\:{A}\:\:{Quadratic}\:\:{form}\:\:{is}\:\:{a}\:{homogeneous}\:\:{polynomial}\:\:{of}\:\:{degree}\:{two}\:\:{in}\:\:{multiple}\:\:{variable}.\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{Q}={X}^{{T}} {AX} \\ $$$${Here}\:\:{Q}={Quadratic}\:{form}. \\ $$$${ax}^{\mathrm{2}} +{by}^{\mathrm{2}} +{cz}^{\mathrm{2}} +\mathrm{2}{hxy}+\mathrm{2}{fyz}+\mathrm{2}{gzx}=\mathrm{0} \\ $$$${By}\:\:{using}\:\:{these}\:\:{Q}={X}^{{T}} {AX}\:\:\left[{we}\:\:{can}\:\:{write}\:{matrix}\:{A}\right]…
Question Number 212015 by liuxinnan last updated on 27/Sep/24 $${f}\left(\mathrm{arcsin}\:\frac{{y}}{{x}}\right)={xy}\:\:\:\:\:\:\frac{{dy}}{{dx}}=? \\ $$$$\:\:\:\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212024 by Spillover last updated on 27/Sep/24 Answered by Frix last updated on 27/Sep/24 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{4}}} {\int}}\left(\mathrm{tan}\:{x}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} {dx}\:\overset{\left[{t}=\left(\mathrm{tan}\:{x}\right)^{−\frac{\mathrm{1}}{\mathrm{3}}} \right]} {=}\:\mathrm{3}\underset{\mathrm{1}} {\overset{\infty} {\int}}\frac{{dt}}{{t}^{\mathrm{6}} +\mathrm{1}}…
Question Number 212023 by Spillover last updated on 27/Sep/24 Answered by Frix last updated on 27/Sep/24 $$\int\:\frac{\left({x}+\mathrm{1}\right)\mathrm{tan}\:{x}}{\left(\mathrm{1}+\mathrm{tan}\:{x}\right)^{\mathrm{2}} }{dx}= \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\left({x}+\mathrm{1}−\frac{\mathrm{1}}{\underset{\left[{t}=\mathrm{tan}\:{x}\right]} {\underbrace{\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}}}}−\frac{{x}}{\underset{\left[\mathrm{by}\:\mathrm{parts}\right]} {\underbrace{\mathrm{1}+\mathrm{sin}\:\mathrm{2}{x}}}}\right){dx}= \\ $$$$… \\…
Question Number 212016 by Spillover last updated on 27/Sep/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212033 by RojaTaniya last updated on 27/Sep/24 $$\:{Find}\:{last}\:{two}\:{digit}\:{of}\:\mid\mathrm{33}^{\mathrm{22}} −\mathrm{22}^{\mathrm{33}} \mid \\ $$ Answered by Frix last updated on 27/Sep/24 $$\mathrm{22}^{\mathrm{33}} −\mathrm{33}^{\mathrm{22}} = \\…
Question Number 212017 by Spillover last updated on 27/Sep/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 212018 by Spillover last updated on 27/Sep/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 211992 by ajfour last updated on 26/Sep/24 Commented by ajfour last updated on 26/Sep/24 $${Find}\:{r}\:{in}\:{terms}\:{of}\:{R}\:{and}\:{a}. \\ $$ Commented by ajfour last updated on…
Question Number 211995 by SVMEHTA last updated on 26/Sep/24 $$\int\sqrt{}{tanx}\:{dx} \\ $$ Commented by Frix last updated on 26/Sep/24 $$\mathrm{Use}\:{t}=\sqrt{\mathrm{tan}\:{x}} \\ $$ Commented by BHOOPENDRA…