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 $$\mathrm{p}=\mathrm{nn}_{\mathrm{1}} \mathrm{n}_{\mathrm{2}} \mathrm{x},\mathrm{q}=\mathrm{nn}_{\mathrm{2}}…
Question Number 737 by 123456 last updated on 08/Mar/15 $$\frac{\mathrm{1}}{{T}}\underset{{t}_{\mathrm{1}} } {\overset{{t}_{\mathrm{2}} } {\int}}{V}\mathrm{sin}\:\omega{t}−{V}_{\gamma} \:{dt}=? \\ $$$${t}_{\mathrm{1}} \:{and}\:{t}_{\mathrm{2}} \:{are}\:{solution}\:{to} \\ $$$${V}\mathrm{sin}\:\omega{t}={V}_{\gamma} \\ $$$${V}\geqslant{V}_{\gamma} \\ $$$${V}_{\gamma}…
Question Number 131810 by Fikret last updated on 08/Feb/21 $${f}\left({x}\right)=\begin{cases}{−\mathrm{2}{x}\:\:\:\:\:\:\:\:\:\:;\:\:{x}\leqslant\mathrm{0}}\\{{f}\left({x}−\mathrm{1}\right)\:\:\:;\:\:{x}>\mathrm{0}}\end{cases} \\ $$$$ \\ $$$$\:\:\underset{\mathrm{0}} {\overset{\mathrm{100}} {\int}}{f}\left({x}\right){dx}\:=? \\ $$ Answered by mr W last updated on…
Question Number 131805 by Engr_Jidda last updated on 08/Feb/21 $${obtain}\:{the}\:{series}\:{solution}\:{of}\:{the}\:{differential}\: \\ $$$${equation}:\:{y}^{{II}} +{xy}^{{I}} −{y}={x}^{\mathrm{2}} +\mathrm{1} \\ $$$${y}\left(\mathrm{0}\right)=\mathrm{1}\:{and}\:{y}^{{I}} \left(\mathrm{0}\right)=\mathrm{2} \\ $$ Answered by physicstutes last updated…
Question Number 131807 by Fikret last updated on 08/Feb/21 $${f}\left({x}\right)=\mathrm{2}−{x}\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{f}\left({x}\right){dx}\:\:\Rightarrow\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{f}\left({x}\right){dx}=? \\ $$$$ \\ $$$$ \\ $$ Commented by Fikret last updated…