Question Number 73399 by mathocean1 last updated on 11/Nov/19 $$\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{65}}\\{\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)=\mathrm{17}}\end{cases} \\ $$$$ \\ $$$${please}\:{help}\:{me}\:{to}\:{solve}\:{it}… \\ $$ Commented by abdomathmax last updated on 11/Nov/19…
Question Number 7861 by Yozzia last updated on 21/Sep/16 $${Prove}\:{that}\:\underset{{i}=\mathrm{0}} {\overset{{n}+\mathrm{1}} {\sum}}\begin{pmatrix}{{n}+\mathrm{1}}\\{{i}}\end{pmatrix}\:{i}^{{n}} \left(−\mathrm{1}\right)^{{i}+\mathrm{1}} =\mathrm{0}\: \\ $$$${for}\:\forall{n}\in\mathbb{N}. \\ $$ Commented by FilupSmith last updated on 22/Sep/16…
Question Number 138916 by mathsuji last updated on 20/Apr/21 $$\underset{\:\mathrm{1}} {\overset{\:\mathrm{4}} {\int}}\:\sqrt{\frac{\sqrt{{z}}−\mathrm{1}}{\:\sqrt{{z}}}}\:{dz}\:=? \\ $$ Answered by bramlexs22 last updated on 20/Apr/21 $$\sqrt{\frac{\sqrt{\mathrm{z}}−\mathrm{1}}{\:\sqrt{\mathrm{z}}}}\:=\:\mathrm{r}\:;\:\frac{\sqrt{\mathrm{z}}\:−\mathrm{1}}{\:\sqrt{\mathrm{z}}}\:=\:\mathrm{r}^{\mathrm{2}} \rightarrow\begin{cases}{\mathrm{z}=\mathrm{1}\rightarrow\mathrm{r}=\mathrm{0}}\\{\mathrm{z}=\mathrm{4}\rightarrow\mathrm{r}=\sqrt{\frac{\mathrm{1}}{\mathrm{2}}}}\end{cases} \\ $$$$\Rightarrow\mathrm{r}^{\mathrm{2}}…
Question Number 73378 by mind is power last updated on 10/Nov/19 $${Hello}\:,{i}\:{shar}\:{withe}\:{you}\:{nice}\:{problem}\: \\ $$$${show}\:{that}\:\forall{k}\in\mathbb{N}^{\ast} \:\exists{n}\in\mathbb{N}\:{such}\:{that} \\ $$$${k}\leqslant\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{j}}<{k}+\mathrm{1} \\ $$$${have}\:{a}\:{very}\:{Nice}\:{day} \\ $$$$ \\ $$…
Question Number 73356 by behi83417@gmail.com last updated on 10/Nov/19 Commented by ajfour last updated on 11/Nov/19 $${I}\:{had}\:{tried}\:{Q}.\mathrm{3}\:.\:{It}\:{did}\:{not}\:{yield} \\ $$$${any}\:{solution},\:{sir}. \\ $$ Commented by behi83417@gmail.com last…
Question Number 7820 by ridwan balatif last updated on 17/Sep/16 $${if}\:\mathrm{2}{x}+\mathrm{1}=\sqrt{\mathrm{111}},\:\mathrm{2}{x}^{\mathrm{5}} +\mathrm{2}{x}^{\mathrm{4}} −\mathrm{53}{x}^{\mathrm{3}} −\mathrm{57}{x}+\mathrm{54}=…? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 138888 by mathdanisur last updated on 19/Apr/21 $${Calculus}: \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\:\left[\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}^{{x}} }\:+\:\frac{\mathrm{2}^{{x}} }{{x}!}\:+\:\frac{{x}!}{{x}^{{x}} }\:\right]\:=\:? \\ $$ Answered by mathmax by abdo last…
Question Number 7815 by Rohit 57 last updated on 17/Sep/16 $${now}\:{wright}\:{the}\:{of}\:{A}.{P}\:{and}\:{G}.{P}\: \\ $$$${wiyh}\:{example}\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7809 by Tawakalitu. last updated on 16/Sep/16 $${x}\:+\:{y}\:+\:{z}\:=\:\mathrm{1}\:\:\:\:\:\:………\:\left({i}\right) \\ $$$${x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \:=\:\mathrm{37}\:\:\:\:\:……..\:\left({ii}\right) \\ $$$${x}^{\mathrm{3}} \:+\:{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{3}} \:=\:\mathrm{91}\:\:\:\:\:……..\:\left({iii}\right) \\ $$$$ \\ $$$${Solve}\:{simultaneously}.\: \\…
Question Number 138879 by peter frank last updated on 19/Apr/21 Answered by Dwaipayan Shikari last updated on 19/Apr/21 $${e}^{{i}\theta\left(\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+..{n}\right)} =\mathrm{1}\Rightarrow{e}^{{i}\theta\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} ={e}^{\mathrm{2}\pi{im}} \:\:\left({m}\in\mathbb{Z}\right) \\ $$$$\Rightarrow\theta=\frac{\mathrm{4}\pi{m}}{{n}\left({n}+\mathrm{1}\right)} \\…