Question Number 131823 by mr W last updated on 09/Feb/21 Commented by mr W last updated on 10/Feb/21 $${a}\:{small}\:{sphere}\:{of}\:{mass}\:{m}\:{is}\:{released} \\ $$$${from}\:{rest}\:{at}\:{position}\:{as}\:{shown}. \\ $$$${both}\:{the}\:{sphere}\:{and}\:{the}\:{semi}\:{cylinder} \\ $$$${move}\:{without}\:{friction}.…
Question Number 749 by 123456 last updated on 06/Mar/15 $${x}=\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\sqrt{\mathrm{2}\centerdot\centerdot\centerdot}}}}}} \\ $$$${y}=\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\sqrt{\mathrm{2}+\centerdot\centerdot\centerdot}}}}}} \\ $$$${wich}\:{statment}\:{is}\:{true}? \\ $$$${a}.\:{xy}=\mathrm{4}\vee{xy}=\mathrm{0}\vee{x}+{y}=\mathrm{4}\vee{x}+{y}=\mathrm{2} \\ $$$${b}.\:{x}\notin\mathbb{Z} \\ $$$${c}.{xy}\notin\mathbb{Z} \\ $$$${d}.{x}+{y}\notin\mathbb{Z} \\ $$ Answered…
Question Number 66285 by Rio Michael last updated on 12/Aug/19 $${What}\:{is}\:{the}\:{difference}\:{between} \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{2}^{−} } {{lim}}\:\:{and} \\ $$$$\underset{{x}\rightarrow\mathrm{2}^{+} } {{lim}} \\ $$ Answered by MJS last…
Question Number 131816 by mathmax by abdo last updated on 08/Feb/21 $$\mathrm{calculate}\:\int_{−\infty} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{x}^{\mathrm{n}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{n}} }\mathrm{dx}\:\:\mathrm{with}\:\mathrm{n}\geqslant\mathrm{2}\:\:\mathrm{integr} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 746 by 123456 last updated on 06/Mar/15 $${lets}\:\boxplus:\left(\mathbb{R}^{+} \right)^{\mathrm{2}} \rightarrow\mathbb{R}^{+} \\ $$$${defined}\:{by}\:{x}\boxplus{y}=\sqrt{\lfloor{x}\rfloor\lceil{x}\rceil}+{y} \\ $$$$\mathrm{1}.\:{x}\boxplus{y}\overset{?} {=}{y}\boxplus{x} \\ $$$$\mathrm{2}.{x}\boxplus\left({y}\boxplus{z}\right)\overset{?} {=}\left({x}\boxplus{y}\right)\boxplus{z} \\ $$$$\mathrm{3}.\exists{e},\forall{x}\in\mathbb{R}^{+} ,{x}\boxplus{e}={x}\:? \\ $$$$\mathrm{4}.\exists{e},\forall{x}\in\mathbb{R}^{+}…
Question Number 66279 by gunawan last updated on 12/Aug/19 $$\mathrm{Value}\:\mathrm{of}\:\mathrm{maximum} \\ $$$${f}\left({x}\right)=^{\mathrm{2}} \mathrm{log}\left({x}+\mathrm{5}\right)+^{\mathrm{2}} \mathrm{log}\left(\mathrm{3}−{x}\right) \\ $$$$\mathrm{is}… \\ $$$$\mathrm{a}.\mathrm{4} \\ $$$$\mathrm{b}.\mathrm{8} \\ $$$$\mathrm{c}.\:\mathrm{12} \\ $$$$\mathrm{d}.\:\mathrm{15} \\…
Question Number 66276 by gunawan last updated on 12/Aug/19 $$\mathrm{If}\:{a}\:\mathrm{and}\:{b}\:\mathrm{is}\:\mathrm{root}\:\mathrm{equation} \\ $$$$\mathrm{3}^{\mathrm{log}_{\mathrm{3}} \left(\mathrm{4x}^{\mathrm{2}} +\mathrm{3}\right)} +\mathrm{4}^{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{1}\right)} =\mathrm{49} \\ $$$$\mathrm{then} \\ $$$${a}+{b}=.. \\ $$$${a}.\:\mathrm{3} \\…
Question Number 66274 by mr mondo last updated on 12/Aug/19 Commented by mr W last updated on 12/Aug/19 $${the}\:{answer}\:{is}\:{given}\:{in}\:{Q}\mathrm{66162}! \\ $$ Terms of Service Privacy…
Question Number 739 by malwaan last updated on 08/Mar/15 $${solve}\:{x}^{\mathrm{2}} −\mathrm{7}{y}^{\mathrm{2}} =\mathrm{1}\:{in}\:{Z} \\ $$ Commented by 123456 last updated on 06/Mar/15 $${S}=\left\{\left({x},{y}\right)\in\mathbb{Z}^{\mathrm{2}} \mid{x}^{\mathrm{2}} −\mathrm{7}{y}^{\mathrm{2}} =\mathrm{1}\right\}…
Question Number 66275 by Rasheed.Sindhi last updated on 12/Aug/19 $${Prove}\:{that}\:{for}\:{p},{q},{r}\in\mathbb{N} \\ $$$$\frac{\mathrm{lcm}\left({p},{q},{r}\right)}{\mathrm{gcd}\left({p},{q},{r}\right)}=\frac{{p}×{q}×{r}}{\mathrm{gcd}\left({p},{q}\right)×\mathrm{gcd}\left({q},{r}\right)×\mathrm{gcd}\left({r},{p}\right)} \\ $$ Commented by Prithwish sen last updated on 12/Aug/19 $$\mathrm{p}=\mathrm{nn}_{\mathrm{1}} \mathrm{n}_{\mathrm{2}} \mathrm{x},\mathrm{q}=\mathrm{nn}_{\mathrm{2}}…