Question Number 135558 by bemath last updated on 14/Mar/21 $$ \\ $$A boy throws a ball at a vertical wall 4 m away. The ball…
Question Number 70021 by naka3546 last updated on 30/Sep/19 $$\sqrt[{\mathrm{3}}]{\sqrt{\sqrt{\mathrm{12345689654321233}\:+\:\mathrm{5333334096}\:\sqrt{\mathrm{12345679}}}}\:−\:\sqrt{\sqrt{\mathrm{12345689654321233}\:−\:\mathrm{5333334096}\:\sqrt{\mathrm{12345679}}}}}\:\:=\:\:… \\ $$ Commented by MJS last updated on 30/Sep/19 $$\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve} \\ $$$$\sqrt{{a}+{b}\sqrt{{c}}}={p}+{q}\sqrt{{c}}\:\Leftrightarrow\:{a}={p}^{\mathrm{2}} +{cq}^{\mathrm{2}} \wedge{b}=\mathrm{2}{pq} \\…
Question Number 70017 by Shamim last updated on 30/Sep/19 $$\mathrm{Solution}- \\ $$$$\mathrm{log}_{\mathrm{8}} \mathrm{x}+\mathrm{log}_{\mathrm{4}} \mathrm{x}+\mathrm{log}_{\mathrm{2}} \mathrm{x}=\mathrm{11} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{x}} \mathrm{8}}+\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{x}} \mathrm{4}}+\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{x}} \mathrm{2}}=\mathrm{11} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{x}} \mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{x}} \mathrm{2}^{\mathrm{2}}…
Question Number 4478 by love math last updated on 30/Jan/16 $${log}_{\mathrm{10}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)=\frac{\mathrm{2}}{{log}_{\mathrm{10}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)}−\mathrm{2} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$ Answered by…
Question Number 4477 by love math last updated on 30/Jan/16 $$\mathrm{2}\:{log}\:\left({x}−\mathrm{2}\right)+{log}\:\left({x}−\mathrm{4}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$$ \\ $$$${Determine}\:{the}\:{domain}\:{of}\:{x}\:{and}\:{find}\:{the}\:{value}\:{of}\:{x}. \\ $$ Answered by Rasheed Soomro last updated on…
Question Number 135544 by 0731619177 last updated on 13/Mar/21 Answered by Olaf last updated on 13/Mar/21 $${f}\left({x}\right)\:=\:\mathrm{sin}{x}+\mathrm{cos}{x}\:=\:\sqrt{\mathrm{2}}\mathrm{cos}\left(\frac{\pi}{\mathrm{4}}−{x}\right) \\ $$$${x}\in\left[\mathrm{0},\frac{\pi}{\mathrm{4}}\right]\:\Rightarrow\:{f}\left({x}\right)\in\left[\mathrm{1},\sqrt{\mathrm{2}}\right] \\ $$$$\Rightarrow\:\forall{x}\in\left[\mathrm{0},\frac{\pi}{\mathrm{4}}\right]\:\lfloor{f}\left({x}\right)\rfloor\:=\:\mathrm{1} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \mathrm{cos}\left(\mathrm{2}{x}\right)×\mathrm{2}^{\mathrm{1}}…
Question Number 70008 by Shamim last updated on 30/Sep/19 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$$$\mathrm{log}_{\mathrm{8}} \mathrm{x}\:+\:\mathrm{log}_{\mathrm{4}} \mathrm{x}\:+\:\mathrm{log}_{\mathrm{2}} \mathrm{x}\:=\:\mathrm{11}. \\ $$ Answered by Maclaurin Stickker last updated on 30/Sep/19…
Question Number 4472 by Yozzii last updated on 30/Jan/16 $${Solve}\:{the}\:{following}\:{differential}\:{equation}: \\ $$$$\:\:\:\:\:\:\:\:\left(\mathrm{2}{xy}^{\mathrm{2}} +\frac{{x}}{{y}^{\mathrm{2}} }\right){dx}+\mathrm{4}{x}^{\mathrm{2}} {ydy}=\mathrm{0} \\ $$ Commented by prakash jain last updated on 01/Feb/16…
Question Number 135540 by mohammad17 last updated on 13/Mar/21 Answered by Olaf last updated on 13/Mar/21 $$\left.\mathrm{Q1a}\right) \\ $$$$\mathrm{1}/\:\:\:\mathrm{S}_{{n}} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left[\frac{\mathrm{1}}{\mathrm{5}^{{k}} }−\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}\right] \\ $$$$\mathrm{S}_{{n}}…
Question Number 135543 by 0731619177 last updated on 13/Mar/21 Answered by Olaf last updated on 13/Mar/21 $$\Omega\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{cos}\left(\mathrm{2}{x}\right)\mathrm{tan}\left(\frac{{x}}{\mathrm{2}}\right){dx} \\ $$$$\Omega\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}−\mathrm{tan}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{tan}^{\mathrm{2}} {x}}\mathrm{tan}\left(\frac{{x}}{\mathrm{2}}\right){dx}…