Question Number 165375 by mathlove last updated on 31/Jan/22 Answered by Rasheed.Sindhi last updated on 31/Jan/22 $$\underset{−} {{a}+{b}+{c}=\mathrm{7}\:\wedge\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} =\mathrm{9}\:\wedge\:{abc}=\mathrm{5}\:\:\:\:} \\ $$$$\left({a}+{b}+{c}\right)^{\mathrm{2}} =\left(\mathrm{7}\right)^{\mathrm{2}} \\…
Question Number 165364 by mathlove last updated on 31/Jan/22 Answered by Ar Brandon last updated on 31/Jan/22 $${S}=\frac{\mathrm{1}}{\mathrm{1}+{e}^{−\mathrm{99}} }+\frac{\mathrm{1}}{\mathrm{1}+{e}^{−\mathrm{98}} }+\centerdot\centerdot\centerdot+\frac{\mathrm{1}}{\mathrm{1}+{e}^{\mathrm{98}} }+\frac{\mathrm{1}}{\mathrm{1}+{e}^{\mathrm{99}} } \\ $$$$\:\:\:\:=\frac{{e}^{\mathrm{99}} }{\mathrm{1}+{e}^{\mathrm{99}}…
Question Number 99827 by MWSuSon last updated on 23/Jun/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{days}\:\mathrm{after}\:\mathrm{12}/\mathrm{7}/\mathrm{1941} \\ $$$$\left(\mathrm{pearl}\:\mathrm{harbour}\:\mathrm{bombed}\right)\:\mathrm{was}\:\mathrm{9}/\mathrm{11}/\mathrm{2001} \\ $$$$\left(\mathrm{the}\:\mathrm{september}\:\mathrm{11}\:\mathrm{terrorist}\:\mathrm{attack}?\right. \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help},\:\mathrm{i}'\mathrm{m}\:\mathrm{having}\:\mathrm{27175days},\: \\ $$$$\mathrm{which}\:\mathrm{apparently}\:\mathrm{isn}'\mathrm{t}\:\mathrm{correct}. \\ $$ Terms of Service…
Question Number 165362 by HongKing last updated on 31/Jan/22 Answered by aleks041103 last updated on 01/Feb/22 $${if}\:{gcd}\left({a},{b}\right)=\mathrm{1}\:{and}\:{b}>{a},\:{then}: \\ $$$${for}\:\forall{r}=\mathrm{0},\mathrm{1},\mathrm{2},…,{b}−\mathrm{1},\:\exists{k}\in\mathbb{N}\:{such}\:{that} \\ $$$${ka}\equiv{r}\left({mod}\:{b}\right). \\ $$$$ \\ $$$${In}\:{our}\:{case},\:{gcd}\left(\mathrm{19},\mathrm{360}\right)=\mathrm{1}…
Question Number 165355 by Ari last updated on 31/Jan/22 Answered by Ar Brandon last updated on 31/Jan/22 $$\begin{cases}{{x}+{y}−{z}=\mathrm{170}}\\{{z}+{y}−{x}=\mathrm{130}}\end{cases}\:\:\Rightarrow\mathrm{2}{y}=\mathrm{300}\Rightarrow{y}=\mathrm{150} \\ $$ Terms of Service Privacy Policy…
Question Number 99807 by PengagumRahasiamu last updated on 23/Jun/20 Answered by ajfour last updated on 23/Jun/20 $${x}=\mathrm{54},\:{y}=\mathrm{24},\:{z}=\mathrm{6} \\ $$$${x}+{y}+{z}=\mathrm{84}. \\ $$$$ \\ $$ Commented by…
Question Number 99803 by student work last updated on 23/Jun/20 $$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }\right)=? \\ $$$$\mathrm{helpe}\:\mathrm{me} \\ $$ Answered by smridha last updated on 23/Jun/20…
Question Number 99796 by harckinwunmy last updated on 23/Jun/20 Answered by 1549442205 last updated on 30/Jun/20 $$\mathrm{Our}\:\mathrm{problem}\:\mathrm{is}\:\mathrm{equivalent}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the} \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equations}:\begin{cases}{\mathrm{y}^{\mathrm{2}} =\mathrm{4}^{\mathrm{x}} \:\left(\mathrm{1}\right)}\\{\mathrm{y}^{\mathrm{x}} =\mathrm{16}\:\left(\mathrm{2}\right)}\end{cases}\:\left(\ast\right) \\ $$$$\left(\mathrm{1}\right)\Leftrightarrow\mathrm{y}^{\mathrm{2}} =\left(\mathrm{2}^{\mathrm{x}}…
Question Number 99789 by bemath last updated on 23/Jun/20 $$\begin{cases}{\mathrm{2}^{{x}} .\mathrm{3}^{{y}} \:=\:\mathrm{6}}\\{\mathrm{3}^{{x}} .\mathrm{4}^{{y}} \:=\:\mathrm{12}}\end{cases} \\ $$ Commented by john santu last updated on 23/Jun/20 $$\begin{cases}{\mathrm{3}^{{y}−\mathrm{1}}…
Question Number 165322 by Ari last updated on 29/Jan/22 $${who}\:{can}\:{prove}\:{that}\:\mathrm{2}^{{n}} −\mathrm{1}{produces} \\ $$$${a}\:{prime}\:{number}\:{when}\:\:{n}\:\:{is}\:{a}\: \\ $$$${prime}\:{number} \\ $$ Commented by mr W last updated on 30/Jan/22…