Question Number 68422 by ajfour last updated on 10/Sep/19 Answered by ajfour last updated on 10/Sep/19 $${C}=\mathrm{10}{m}^{\mathrm{3}} {p}^{\mathrm{2}} +{b}\left({m}^{\mathrm{3}} +\mathrm{6}{m}^{\mathrm{2}} {p}+\mathrm{3}{mp}^{\mathrm{2}} \right) \\ $$$$\:+{c}\left(\mathrm{3}{m}^{\mathrm{2}} +\mathrm{6}{mp}+{p}^{\mathrm{2}}…
Question Number 68414 by behi83417@gmail.com last updated on 10/Sep/19 $$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{find}\:\mathrm{any}\:\mathrm{value}\:\mathrm{for} \\ $$$$\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\:\mathrm{from}\:\mathrm{below}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equetions}? \\ $$$$\begin{cases}{\boldsymbol{\mathrm{sina}}+\boldsymbol{\mathrm{sinb}}=\boldsymbol{\mathrm{sinc}}}\\{\boldsymbol{\mathrm{cosa}}+\boldsymbol{\mathrm{cosb}}=\boldsymbol{\mathrm{cosc}}}\end{cases} \\ $$ Commented by kaivan.ahmadi last updated on 10/Sep/19 $$\begin{cases}{{sinacosa}+{sinbcosa}={sinccosa}}\\{−{sinacosa}−{sinacosb}=−{sinacosc}}\end{cases}\Rightarrow \\…
Question Number 2874 by RasheedAhmad last updated on 29/Nov/15 $${What}\:{is}\:{the}\:{meaning}\:{of} \\ $$$$\left({i}\right)\:{z}\rightarrow\mathrm{0}\:\:\:\left({ii}\right)\:{z}\rightarrow{z}_{\mathrm{0}} \:\:\:{z},{z}_{\mathrm{0}} \in\mathbb{C} \\ $$ Answered by Filup last updated on 29/Nov/15 $$\left(\mathrm{1}\right) \\…
Question Number 2845 by Rasheed Soomro last updated on 28/Nov/15 $$\mathcal{W}{hile}\:{you}\:{are}\:{in}\:{between}\:{the}\:{project} \\ $$$$\mathcal{I}\:{am}\:{trying}\:{to}\:{improve}\:{my}\:{digestiblity}\:{to} \\ $$$${digest}\:{the}\:{concept}\:{of}\:'{analytical}\:{continuation}'. \\ $$$$ \\ $$$${First}\:{we}\:{make}\:{aformula}\:{to}\:{sum}\:{n}\:{terms}\:{of}\:{a}\:{powe}\:{series}: \\ $$$$\frac{{x}^{{n}} −\mathrm{1}}{{x}−\mathrm{1}}=\mathrm{1}+{x}+{x}^{\mathrm{2}} +…+{x}^{{n}} \\ $$$${latter}\:{we}\:{change}\:{it}\:{for}\:\mid{x}\mid<\mathrm{1}\:{and}\:{n}\rightarrow\infty\:\left[{x}^{{n}}…
Question Number 2843 by prakash jain last updated on 28/Nov/15 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$${n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)…\left({n}+{r}−\mathrm{1}\right)\:\mathrm{is}\:\mathrm{divible}\:\mathrm{by}\:{r}! \\ $$$$ \\ $$$${n},{r}\in\mathbb{N}. \\ $$ Commented by 123456 last updated on…
Question Number 133903 by shaker last updated on 25/Feb/21 Commented by mr W last updated on 25/Feb/21 $${what}\:{do}\:{mean}\:{with}\:{argth}\left({x}\right)?\:{is}\:{it} \\ $$$${the}\:{same}\:{as}\:{arctanh}\left({x}\right)\:{in}\:{your} \\ $$$${country}? \\ $$ Commented…
Question Number 133885 by bemath last updated on 25/Feb/21 $$\:\mathrm{Consider}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{two} \\ $$$$\mathrm{intersecting}\:\mathrm{straight}\:\mathrm{lines} \\ $$$$\begin{cases}{{ax}+{by}+{c}=\mathrm{0}}\\{{a}_{\mathrm{1}} {x}+{b}_{\mathrm{1}} {y}+{c}_{\mathrm{1}} =\mathrm{0}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{straight}\:\mathrm{line} \\ $$$$\mathrm{passing}\:\mathrm{through}\:\mathrm{a}\:\mathrm{given}\:\mathrm{point} \\ $$$$\left(\mathrm{x}_{\mathrm{0}} ,\mathrm{y}_{\mathrm{0}} \right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{intersection}\:\mathrm{point}…
Question Number 2796 by Rasheed Soomro last updated on 27/Nov/15 $${Prove}\:{that} \\ $$$$\left({i}\right)\:\zeta\left(\mathrm{2}\right)=\frac{\pi^{\mathrm{2}} }{\mathrm{6}}\:\:\:\:\:\:\:\:\:\:\:\:\:\left({ii}\right)\:\:\zeta\left(\mathrm{4}\right)=\frac{\pi^{\mathrm{4}} }{\mathrm{90}} \\ $$ Answered by prakash jain last updated on 28/Nov/15…
Question Number 68336 by pete last updated on 09/Sep/19 $$\mathrm{A}\:\mathrm{man}\:\mathrm{gave}\:\$\mathrm{5},\mathrm{720}.\mathrm{00}\:\mathrm{to}\:\mathrm{be}\:\mathrm{shared}\:\mathrm{among} \\ $$$$\mathrm{his}\:\mathrm{son}\:\mathrm{and}\:\mathrm{three}\:\mathrm{daughters}.\:\mathrm{If}\:\mathrm{each}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{daughter}'\mathrm{s}\:\mathrm{share}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{of}\:\mathrm{the}\:\mathrm{son}'\mathrm{s}\:\mathrm{share}, \\ $$$$\mathrm{how}\:\mathrm{much}\:\mathrm{did}\:\mathrm{the}\:\mathrm{son}\:\mathrm{receive}? \\ $$ Commented by Rasheed.Sindhi last updated on 09/Sep/19…
Question Number 2762 by Rasheed Soomro last updated on 26/Nov/15 $${Without}\:{using}\:\underset{−} {{induction}}\:{o}\underset{−} {{r}\:\:{arithmatic}\:{series}−{concept}\:\:\:} \\ $$$$\:{prove}\:{the}\:{following}: \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}=\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$ Answered by prakash jain last updated…