Question Number 4760 by malwaan last updated on 06/Mar/16 $${the}\:{number}\:\mathrm{27000001} \\ $$$${has}\:\mathrm{4}\:{prime}\:{factors}. \\ $$$${find}\:{thier}\:{sum} \\ $$ Commented by prakash jain last updated on 06/Mar/16 $$\mathrm{7},\mathrm{43},\mathrm{271},\mathrm{331}…
Question Number 135718 by liberty last updated on 15/Mar/21 Answered by dhgt last updated on 04/May/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 135692 by liberty last updated on 15/Mar/21 $$ \\ $$Solve the system of congruences 2x≡1(mod5) 3x≡2(mod7) 4x≡1(mod11) Answered by floor(10²Eta[1]) last updated on…
Question Number 70145 by Scientist0000001 last updated on 01/Oct/19 $${prove}\:{that}\:;\:{arg}\left(\boldsymbol{{z}}\mathrm{1}\boldsymbol{{z}}\mathrm{2}\right)={arg}\left({z}\mathrm{1}\right)+{arg}\left({z}\mathrm{2}\right). \\ $$$${arg}\left({z}\mathrm{1}/{z}\mathrm{2}\right)={arg}\left({z}\mathrm{1}\right)−{arg}\left({z}\mathrm{2}\right). \\ $$ Answered by MJS last updated on 01/Oct/19 $${z}_{\mathrm{1}} ={r}_{\mathrm{1}} \mathrm{e}^{\mathrm{i}\theta_{\mathrm{1}} }…
Question Number 70138 by Scientist0000001 last updated on 01/Oct/19 $${prove}\:{that}\:\:\:{e}^{{i}\theta} ={e}^{{i}\left(\theta+\mathrm{2}{k}\Pi\right)} \:\:{given}\:{that}\:{k}=\mathrm{0},\pm\mathrm{1},\pm\mathrm{2}… \\ $$ Answered by mind is power last updated on 01/Oct/19 $${e}^{{ix}} ={cos}\left({x}\right)+{isin}\left({x}\right)…
Question Number 4540 by Yozzii last updated on 06/Feb/16 $${Let}\:{us}\:{define}\:{the}\:{positive}\:{number}\:{n}\:{with}\:{four} \\ $$$${digits}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}}\:{and}\:\boldsymbol{\mathrm{d}}\:{such}\:{that}\:{n}=\boldsymbol{\mathrm{abcd}} \\ $$$${with}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}},\boldsymbol{\mathrm{c}},\boldsymbol{\mathrm{d}}\in\mathbb{Z},\:\mathrm{1}\leqslant\boldsymbol{\mathrm{a}}\leqslant\mathrm{9},\:\mathrm{0}\leqslant\boldsymbol{\mathrm{b}}\leqslant\mathrm{9}, \\ $$$$\mathrm{0}\leqslant\boldsymbol{\mathrm{c}}\leqslant\mathrm{9}\:{and}\:\mathrm{0}\leqslant\boldsymbol{\mathrm{d}}\leqslant\mathrm{9}.\:{Let}\:{us}\:{then}\:{say} \\ $$$${that}\:{a}\:{cool}\:{number}\:{is}\:{a}\:{four}\:{digit}\:{number}, \\ $$$${say}\:{n},\:{such}\:{that}\:{the}\:{two}\:{digit}\:{numbers}\:{written}\:{as} \\ $$$$\boldsymbol{\mathrm{ab}}\:{and}\:\boldsymbol{\mathrm{cd}}\:{are}\:{given}\:{by}\:\boldsymbol{\mathrm{ab}}={r}×{s}\:{and} \\ $$$$\boldsymbol{\mathrm{cd}}=\left({r}−\mathrm{1}\right)×\left({s}+\mathrm{1}\right)\:{for}\:{some}\:{non}−{negative}\:{integers} \\…
Question Number 135566 by bemath last updated on 14/Mar/21 $${Let}\:{p},{q}\:{and}\:{r}\:{be}\:{the}\:{distinct}\:{roots} \\ $$$${of}\:{the}\:{polynomial}\:{x}^{\mathrm{3}} −\mathrm{22}{x}^{\mathrm{2}} +\mathrm{80}{x}−\mathrm{67}. \\ $$$${There}\:{exist}\:{real}\:{number}\:{A},{B}\:{and} \\ $$$${C}\:{such}\:{that}\:\frac{\mathrm{1}}{{s}^{\mathrm{3}} −\mathrm{22}{s}^{\mathrm{2}} +\mathrm{80}{s}−\mathrm{67}}\:= \\ $$$$\frac{{A}}{{s}−{p}}\:+\:\frac{{B}}{{s}−{q}}\:+\:\frac{{C}}{{s}−{r}}\:{for}\:{all}\:{real}\:{numbers} \\ $$$${s}\:{with}\:{s}\:\notin\:\left\{{p},{q},{r}\right\}.{What}\:{is}\: \\…
Question Number 135557 by bemath last updated on 14/Mar/21 $$\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\:\theta−{i}\:\mathrm{sin}\:\theta}\:=? \\ $$$${i}=\sqrt{−\mathrm{1}} \\ $$ Answered by mathmax by abdo last updated on 14/Mar/21 $$\frac{\mathrm{1}}{\mathrm{1}−\mathrm{cos}\theta−\mathrm{isin}\theta}=\frac{\mathrm{1}}{\mathrm{2sin}^{\mathrm{2}} \left(\frac{\theta}{\mathrm{2}}\right)−\mathrm{2isin}\left(\frac{\theta}{\mathrm{2}}\right)\mathrm{cos}\left(\frac{\theta}{\mathrm{2}}\right)}…
Question Number 4362 by Rasheed Soomro last updated on 13/Jan/16 $$\mathrm{Determine}\:\mathrm{integers}\:\mathrm{x},\mathrm{y},\mathrm{z}\:\mathrm{satisfying}: \\ $$$$\mathrm{ax}^{\mathrm{b}} +\mathrm{by}^{\mathrm{c}} =\mathrm{cz}^{\mathrm{a}} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\:\mathrm{fixed}\:\mathrm{integers}. \\ $$ Commented by Yozzii last updated on…
Question Number 4358 by Rasheed Soomro last updated on 12/Jan/16 $$\mathrm{Determine}\:\mathrm{integer}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{bx}^{\mathrm{a}} +\mathrm{ay}^{\mathrm{b}} =\mathrm{cz}^{\mathrm{c}} \\ $$$$\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\:\mathrm{fixed}\:\mathrm{integers}. \\ $$ Commented by Filup last updated on…