Question Number 58622 by mr W last updated on 26/Apr/19 $${solve} \\ $$$${x}+{y}=\mathrm{2}{xy} \\ $$$${y}+{z}=\mathrm{3}{yz} \\ $$$${z}+{x}=\mathrm{7}{zx} \\ $$ Commented by rahul 19 last updated…
Question Number 124149 by I want to learn more last updated on 01/Dec/20 $$\mathrm{Two}\:\mathrm{men}\:\mathrm{and}\:\mathrm{four}\:\mathrm{women}\:\mathrm{line}\:\mathrm{up}\:\mathrm{at}\:\mathrm{a}\:\mathrm{checkout}\:\mathrm{counter}\:\mathrm{in}\:\mathrm{a}\:\mathrm{store}. \\ $$$$\left(\mathrm{a}\right)\:\:\:\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{they}\:\mathrm{line}\:\mathrm{up}??? \\ $$$$\left(\mathrm{b}\right)\:\:\:\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{they}\:\mathrm{line}\:\mathrm{up}\:\mathrm{if}\:\mathrm{the}\:\mathrm{first}\:\mathrm{person}\:\mathrm{line}\:\mathrm{is} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{a}\:\mathrm{woman}\:\mathrm{and}\:\mathrm{the}\:\mathrm{line}\:\mathrm{changes}\:\mathrm{by}\:\mathrm{gender}.\:\left(\mathrm{w},\:\:\mathrm{m},\:\:\mathrm{w},\:\:\mathrm{w},\:\:\mathrm{m},\:\:\mathrm{w}\right)?? \\ $$ Commented by I…
Question Number 58592 by rahul 19 last updated on 25/Apr/19 $${If}\:\mid{z}−\mathrm{1}\mid=\mathrm{1},\:{then}\:{prove}\:{that}\:{arg}\left({z}\right)\:=\: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{arg}\left({z}−\mathrm{1}\right). \\ $$ Answered by tanmay last updated on 26/Apr/19 $${z}={re}^{{i}\theta} ={rcos}\theta+{irsin}\theta \\…
Question Number 124110 by mathocean1 last updated on 30/Nov/20 $$ \\ $$$${N}=\left(\mathrm{3548}\right)^{\mathrm{9}} ×\left(\mathrm{2537}\right)^{\mathrm{31}} \\ $$$${Determinate}\:{the}\:{last}\:{digit}\:{of}\:{N}. \\ $$ Answered by floor(10²Eta[1]) last updated on 24/Dec/20 $$\mathrm{N}=\left(\mathrm{3548}\right)^{\mathrm{9}}…
Question Number 124109 by mathocean1 last updated on 30/Nov/20 $$ \\ $$$$ \\ $$$${N}={x}\mathrm{32}{y}\:{in}\:{base}\:\mathrm{5}. \\ $$$${determinate}\:{x}\:{and}\:{y}\:{such}\:{that}\:{N}\:{is} \\ $$$${divisible}\:{by}\:\mathrm{3}\:{and}\:\mathrm{4}. \\ $$ Answered by floor(10²Eta[1]) last updated…
Question Number 124108 by mathocean1 last updated on 30/Nov/20 $${N}={x}\mathrm{43}{y}\:{in}\:{base}\:\mathrm{7}. \\ $$$${determinate}\:{x}\:{and}\:{y}\:{such}\:{that}\:{N}\:{is} \\ $$$${divisible}\:{by}\:\mathrm{6}. \\ $$$$ \\ $$ Answered by floor(10²Eta[1]) last updated on 01/Dec/20…
Question Number 124107 by mathocean1 last updated on 30/Nov/20 $${n}\:\in\:\mathbb{N}\:{and}\:{p}\:{is}\:{a}\:{prime}\:{number}\:\left({p}\geqslant\mathrm{3}\right). \\ $$$${a}\:{and}\:{b}\:{are}\:{defined}\:{by}:\:{a}=\mathrm{2}^{{n}} \:{and} \\ $$$${b}={a}×{b}.\:\:{S}\left({a}\right)\:{is}\:{the}\:{sum}\:{of}\:{divisors}\: \\ $$$${of}\:{a}\:{and}\:{S}\left({b}\right)\:\:{is}\:{the}\:{sum}\:{of}\:{divisors} \\ $$$${of}\:{b}. \\ $$$$\mathrm{1}.{Determinate}\:{the}\:{set}\:{of}\:{divisors}\:{of} \\ $$$${a}\:{and}\:{the}\:{set}\:{of}\:{divisors}\:{of}\:{b}. \\ $$$$\mathrm{2}.{show}\:{that}\:{S}\left({a}\right)+\mathrm{2}^{{n}+\mathrm{1}}…
Question Number 124106 by mathocean1 last updated on 30/Nov/20 $${U}_{{n}\:} {is}\:{a}\:{sequence}\:{of}\:{real}\:{numbers}\: \\ $$$${defined}\:{by}\:{U}_{\mathrm{0}} =\mathrm{0}\:{and}\:{for}\:{n}\:\in\:\mathbb{N},\: \\ $$$${U}_{{n}+\mathrm{1}} =\sqrt{{U}_{{n}} +\mathrm{6}} \\ $$$$\mathrm{1}.\:\mathrm{show}\:\mathrm{that}\:\mathrm{0}\leqslant{U}_{{n}} \leqslant\mathrm{3}. \\ $$$$\mathrm{2}.\:{show}\:{that}\:{U}_{{n}\:} {is}\:{non}−{decreasing}. \\…
Question Number 58568 by olalekan2 last updated on 25/Apr/19 $${factorize} \\ $$$${px}^{\mathrm{2}} −{py}^{\mathrm{2}} +{qy}^{\mathrm{2}} −{px}^{\mathrm{2}} \\ $$ Commented by malwaan last updated on 26/Apr/19 $${I}\:{think}\:{the}\:{last}\:{term}\:{is}\:{qx}^{\mathrm{2}}…
Question Number 189610 by Spillover last updated on 19/Mar/23 $${solve}\:{for}\:{x}\:{if}\:\:\: \\ $$$$\mathrm{log}\:{x}=\frac{{x}^{\mathrm{2}} }{\mathrm{25}} \\ $$ Answered by mr W last updated on 19/Mar/23 $$\mathrm{ln}\:{x}=\frac{{x}^{\mathrm{2}} }{\mathrm{25}}=\frac{{e}^{\mathrm{2ln}\:{x}}…