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Question Number 147500    Answers: 1   Comments: 1

x^2 - y^2 + 2x = 22 what is the number of complete solutions that satisf the equation (x;y).?

$${x}^{\mathrm{2}} \:-\:{y}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:=\:\mathrm{22} \\ $$$${what}\:{is}\:{the}\:{number}\:{of}\:{complete} \\ $$$${solutions}\:{that}\:{satisf}\:{the}\:{equation} \\ $$$$\left({x};{y}\right).? \\ $$

Question Number 147493    Answers: 0   Comments: 0

hi, dears masters ! A = {au+bv, (a, b, u, v) ∈ Z^4 } with a β‰  b. 1. prove that A is ideal of Z. 2. let π›ŒZ = {π›Œn , n ∈ Z}. prove that A has a smaller element π›Œ strictly positive such that A = π›ŒZ. 3. prove that π›Œ = gcd(a,b).

$$\boldsymbol{\mathrm{hi}},\:\boldsymbol{\mathrm{dears}}\:\boldsymbol{\mathrm{masters}}\:! \\ $$$$\boldsymbol{\mathrm{A}}\:=\:\left\{\boldsymbol{{au}}+\boldsymbol{{bv}},\:\left(\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{u}},\:\boldsymbol{{v}}\right)\:\in\:\mathbb{Z}^{\mathrm{4}} \right\}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{{a}}\:\neq\:\boldsymbol{{b}}. \\ $$$$\mathrm{1}.\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{ideal}}\:\boldsymbol{\mathrm{of}}\:\:\mathbb{Z}. \\ $$$$\mathrm{2}.\:\boldsymbol{\mathrm{let}}\:\boldsymbol{\lambda}\mathbb{Z}\:=\:\left\{\boldsymbol{\lambda{n}}\:,\:\boldsymbol{{n}}\:\in\:\mathbb{Z}\right\}.\: \\ $$$$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{smaller}}\:\boldsymbol{\mathrm{element}}\:\boldsymbol{\lambda}\:\boldsymbol{\mathrm{strictly}}\: \\ $$$$\boldsymbol{\mathrm{positive}}\:\boldsymbol{\mathrm{such}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{A}}\:=\:\boldsymbol{\lambda}\mathbb{Z}. \\ $$$$\mathrm{3}.\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\lambda}\:=\:\boldsymbol{\mathrm{gcd}}\left(\boldsymbol{{a}},\boldsymbol{{b}}\right). \\ $$

Question Number 147492    Answers: 2   Comments: 3

2(√(19)) cos [(1/3)tan^(βˆ’1) (((45(√3))/(28)))] it is equal to 8. How?

$$\mathrm{2}\sqrt{\mathrm{19}}\:\mathrm{cos}\:\left[\frac{\mathrm{1}}{\mathrm{3}}\mathrm{tan}^{βˆ’\mathrm{1}} \left(\frac{\mathrm{45}\sqrt{\mathrm{3}}}{\mathrm{28}}\right)\right] \\ $$$${it}\:{is}\:{equal}\:{to}\:\mathrm{8}.\:{How}? \\ $$

Question Number 147488    Answers: 1   Comments: 0

if x;y;zβ‰₯1 then: (1/(3xyβˆ’1)) + (1/(3yzβˆ’1)) + (1/(3zxβˆ’1)) β‰₯ (3/(2xyz))

$${if}\:\:{x};{y};{z}\geqslant\mathrm{1}\:\:{then}: \\ $$$$\frac{\mathrm{1}}{\mathrm{3}{xy}βˆ’\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{3}{yz}βˆ’\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{3}{zx}βˆ’\mathrm{1}}\:\geqslant\:\frac{\mathrm{3}}{\mathrm{2}{xyz}} \\ $$

Question Number 147487    Answers: 1   Comments: 0

(a , 2a +1 ]∩[ a^( 2) βˆ’a , a^( 2) + 4a +1 )β‰  βˆ… a ∈ ?

$$ \\ $$$$ \\ $$$$\left({a}\:,\:\mathrm{2}{a}\:+\mathrm{1}\:\right]\cap\left[\:{a}^{\:\mathrm{2}} \:βˆ’{a}\:,\:{a}^{\:\mathrm{2}} +\:\mathrm{4}{a}\:+\mathrm{1}\:\right)\neq\:\varnothing \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}\:\in\:? \\ $$$$ \\ $$

Question Number 147477    Answers: 1   Comments: 1

Question Number 147475    Answers: 0   Comments: 0

Question Number 147474    Answers: 1   Comments: 0

Question Number 147473    Answers: 0   Comments: 1

p(t)=4t^4 +5t^3 βˆ’t^2 +6 at t=a

$${p}\left({t}\right)=\mathrm{4}{t}^{\mathrm{4}} +\mathrm{5}{t}^{\mathrm{3}} βˆ’{t}^{\mathrm{2}} +\mathrm{6}\:\:{at}\:\:{t}={a} \\ $$

Question Number 147469    Answers: 0   Comments: 1

Question Number 147467    Answers: 3   Comments: 0

f(x)=x^n e^(βˆ’x) 1) calculate f^((n)) (0) and f^((n)) (1) 2)developp f at integr serie 3) calculate ∫_0 ^1 f(x)dx

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{n}} \:\mathrm{e}^{βˆ’\mathrm{x}} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 147466    Answers: 2   Comments: 0

f(x)=x^2 βˆ’2x+5 find ∫ ((f(x))/(f^(βˆ’1) (x)))dx and ∫ ((f^(βˆ’1) (x))/(f(x)))dx

$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} βˆ’\mathrm{2x}+\mathrm{5} \\ $$$$\mathrm{find}\:\int\:\frac{\mathrm{f}\left(\mathrm{x}\right)}{\mathrm{f}^{βˆ’\mathrm{1}} \left(\mathrm{x}\right)}\mathrm{dx}\:\:\:\mathrm{and}\:\int\:\:\frac{\mathrm{f}^{βˆ’\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{f}\left(\mathrm{x}\right)}\mathrm{dx} \\ $$

Question Number 147465    Answers: 0   Comments: 0

if n>2,n∈N then prove that {(2nβˆ’1)^n +(2n)^n }<(2n+1)^n

$${if}\:{n}>\mathrm{2},{n}\in{N}\:{then}\:{prove}\:{that}\: \\ $$$$\left\{\left(\mathrm{2}{n}βˆ’\mathrm{1}\right)^{{n}} +\left(\mathrm{2}{n}\right)^{{n}} \right\}<\left(\mathrm{2}{n}+\mathrm{1}\right)^{{n}} \\ $$

Question Number 147459    Answers: 2   Comments: 0

lim_(xβ†’0) (((√(1+x^2 )) ((8+x^3 ))^(1/3) βˆ’2)/x^2 ) =?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\sqrt[{\mathrm{3}}]{\mathrm{8}+{x}^{\mathrm{3}} }βˆ’\mathrm{2}}{{x}^{\mathrm{2}} }\:=? \\ $$

Question Number 147453    Answers: 1   Comments: 2

(1βˆ’(1/4))(1βˆ’(1/9))(1βˆ’(1/(16)))(1βˆ’(1/(25)))...=?

$$\:\left(\mathrm{1}βˆ’\frac{\mathrm{1}}{\mathrm{4}}\right)\left(\mathrm{1}βˆ’\frac{\mathrm{1}}{\mathrm{9}}\right)\left(\mathrm{1}βˆ’\frac{\mathrm{1}}{\mathrm{16}}\right)\left(\mathrm{1}βˆ’\frac{\mathrm{1}}{\mathrm{25}}\right)...=? \\ $$

Question Number 147444    Answers: 1   Comments: 0

Question Number 147443    Answers: 0   Comments: 0

Question Number 147438    Answers: 0   Comments: 0

Question Number 147434    Answers: 0   Comments: 0

Question Number 147432    Answers: 1   Comments: 0

if { ((2x + a ; x < βˆ’3)),((x^2 - 4 ; βˆ’3 ≀ x < 2)),((x^2 + ax + b ; x β‰₯ 2)) :} find 3a - b = ?

$${if}\:\:\begin{cases}{\mathrm{2}{x}\:+\:{a}\:\:;\:\:{x}\:<\:βˆ’\mathrm{3}}\\{{x}^{\mathrm{2}} \:-\:\mathrm{4}\:\:;\:\:βˆ’\mathrm{3}\:\leqslant\:{x}\:<\:\mathrm{2}}\\{{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b}\:\:;\:\:{x}\:\geqslant\:\mathrm{2}}\end{cases} \\ $$$${find}\:\:\:\mathrm{3}{a}\:-\:{b}\:=\:? \\ $$

Question Number 147431    Answers: 2   Comments: 0

Question Number 147419    Answers: 1   Comments: 0

How can we apply Cardanoβ€²s method in 2x^3 +5x^2 +x+2 i get u and v are solution of t^2 βˆ’56t+6859=0 but i think itβ€²s wrong pls help

$${How}\:{can}\:{we}\:{apply}\:{Cardano}'{s}\:{method}\:{in} \\ $$$$\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +{x}+\mathrm{2} \\ $$$$ \\ $$$${i}\:{get}\:{u}\:{and}\:{v}\:{are}\:{solution}\:{of}\:{t}^{\mathrm{2}} βˆ’\mathrm{56}{t}+\mathrm{6859}=\mathrm{0} \\ $$$${but}\:{i}\:{think}\:{it}'{s}\:{wrong}\:{pls}\:{help} \\ $$

Question Number 147418    Answers: 1   Comments: 0

In an RLC series circuit, R=1kilo ohms,L=0.2H,C=1 F. If the voltage source is given by: (V=150 sin 377t )V. What is the peak current delivered by the source?

$$\mathrm{In}\:\mathrm{an}\:\mathrm{R}{LC}\:\mathrm{series}\:\mathrm{circuit}, \\ $$$$\mathrm{R}=\mathrm{1kilo}\:\mathrm{ohms},\mathrm{L}=\mathrm{0}.\mathrm{2H},\mathrm{C}=\mathrm{1} \mathrm{F}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{voltage}\:\mathrm{source}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}: \\ $$$$\left(\mathrm{V}=\mathrm{150}\:\mathrm{sin}\:\mathrm{377t}\:\right)\mathrm{V}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{peak}\:\mathrm{current}\:\mathrm{delivered}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{source}? \\ $$

Question Number 147417    Answers: 1   Comments: 0

how can find taylor series of f(z)=cot(z) when z=5Ο€

$${how}\:{can}\:{find}\:{taylor}\:{series}\:{of}\:{f}\left({z}\right)={cot}\left({z}\right)\:{when}\:{z}=\mathrm{5}\pi \\ $$

Question Number 147411    Answers: 2   Comments: 0

Question Number 147406    Answers: 1   Comments: 0

find ∫_C ((z+2)/(sin((z/2))))dz ,∣z∣=3Ο€

$${find}\:\int_{{C}} \frac{{z}+\mathrm{2}}{{sin}\left(\frac{{z}}{\mathrm{2}}\right)}{dz}\:\:\:,\mid{z}\mid=\mathrm{3}\pi \\ $$

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