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Question Number 56864    Answers: 1   Comments: 3

Find the solution of recurrence relation a_n = 2a_(n−1) + 3a_(n−2) , with a_0 = 1, a_1 = 2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{recurrence}\:\mathrm{relation} \\ $$$${a}_{{n}} \:=\:\mathrm{2}{a}_{{n}−\mathrm{1}} \:+\:\mathrm{3}{a}_{{n}−\mathrm{2}} ,\:\mathrm{with}\:{a}_{\mathrm{0}} \:=\:\mathrm{1},\:{a}_{\mathrm{1}} \:=\:\mathrm{2} \\ $$

Question Number 56861    Answers: 0   Comments: 2

At 20°C, the solubility of Methoxymethane in water is 71.0 g.L^(−1) , however, ethanol and water are miscible. Given that : • Ethanol : H_3 C−C−O • Methoxymethane : H_3 C−O−CH_3 • X(H)=2.2 , X(C)=2.6 , X(O)=3.4 Considering the polarity of these solvents and molecules, how do you explain the difference between the soulubility of ethanol and Methoxymethane in water ? Thank you

$$\mathrm{At}\:\mathrm{20}°\mathrm{C},\:\mathrm{the}\:\mathrm{solubility}\:\mathrm{of}\:\mathrm{Methoxymethane} \\ $$$$\mathrm{in}\:\mathrm{water}\:\mathrm{is}\:\mathrm{71}.\mathrm{0}\:\mathrm{g}.\mathrm{L}^{−\mathrm{1}} ,\:\mathrm{however},\:\mathrm{ethanol}\:\mathrm{and} \\ $$$$\mathrm{water}\:\mathrm{are}\:\mathrm{miscible}. \\ $$$$\: \\ $$$$\:\:\:\mathrm{Given}\:\mathrm{that}\:: \\ $$$$\bullet\:\:\:\:\:\mathrm{Ethanol}\::\:\mathrm{H}_{\mathrm{3}} \mathrm{C}−\mathrm{C}−\mathrm{O} \\ $$$$\bullet\:\:\:\:\:\mathrm{Methoxymethane}\::\:\mathrm{H}_{\mathrm{3}} \mathrm{C}−\mathrm{O}−\mathrm{CH}_{\mathrm{3}} \\ $$$$\bullet\:\:\:\:\:\mathcal{X}\left(\mathrm{H}\right)=\mathrm{2}.\mathrm{2}\:,\:\mathcal{X}\left(\mathrm{C}\right)=\mathrm{2}.\mathrm{6}\:,\:\mathcal{X}\left(\mathrm{O}\right)=\mathrm{3}.\mathrm{4} \\ $$$$\: \\ $$$$\mathrm{Considering}\:\mathrm{the}\:\mathrm{polarity}\:\mathrm{of}\:\mathrm{these}\:\mathrm{solvents} \\ $$$$\mathrm{and}\:\mathrm{molecules},\:\mathrm{how}\:\mathrm{do}\:\mathrm{you}\:\mathrm{explain}\:\mathrm{the} \\ $$$$\mathrm{difference}\:\mathrm{between}\:\mathrm{the}\:\mathrm{soulubility}\:\mathrm{of} \\ $$$$\mathrm{ethanol}\:\mathrm{and}\:\mathrm{Methoxymethane}\:\mathrm{in}\:\mathrm{water}\:? \\ $$$$\: \\ $$$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 56857    Answers: 0   Comments: 0

romi−romo=0 L.x_0 +G.y_n =L.x_n +G.y_0 L(x_0 −x_n )=G(y_0 −y_n ) y_0 =(L/G).(x_0 −x_n )+y_n y_0 =((100)/(200))(0.01−0.001)+0.0005 y_0 =0.005

$${romi}−{romo}=\mathrm{0} \\ $$$$\mathcal{L}.{x}_{\mathrm{0}} +\mathcal{G}.{y}_{{n}} =\mathcal{L}.{x}_{{n}} +\mathcal{G}.{y}_{\mathrm{0}} \\ $$$$\mathcal{L}\left({x}_{\mathrm{0}} −{x}_{{n}} \right)=\mathcal{G}\left({y}_{\mathrm{0}} −{y}_{{n}} \right) \\ $$$${y}_{\mathrm{0}} =\frac{\mathcal{L}}{\mathcal{G}}.\left({x}_{\mathrm{0}} −{x}_{{n}} \right)+{y}_{{n}} \\ $$$${y}_{\mathrm{0}} =\frac{\mathrm{100}}{\mathrm{200}}\left(\mathrm{0}.\mathrm{01}−\mathrm{0}.\mathrm{001}\right)+\mathrm{0}.\mathrm{0005} \\ $$$${y}_{\mathrm{0}} =\mathrm{0}.\mathrm{005} \\ $$$$ \\ $$

Question Number 56854    Answers: 0   Comments: 1

There was a post sime time back about not being able to backup or restore. Can anyone send the requirdd information if you faced the same problem?

$$\mathrm{There}\:\mathrm{was}\:\mathrm{a}\:\mathrm{post}\:\mathrm{sime}\:\mathrm{time}\:\mathrm{back} \\ $$$$\mathrm{about}\:\mathrm{not}\:\mathrm{being}\:\mathrm{able}\:\mathrm{to}\:\mathrm{backup} \\ $$$$\mathrm{or}\:\mathrm{restore}.\:\mathrm{Can}\:\mathrm{anyone}\:\mathrm{send}\:\mathrm{the}\:\mathrm{requirdd} \\ $$$$\mathrm{information}\:\mathrm{if}\:\mathrm{you}\:\mathrm{faced}\:\mathrm{the}\:\mathrm{same} \\ $$$$\mathrm{problem}? \\ $$

Question Number 56852    Answers: 1   Comments: 0

Question Number 56851    Answers: 0   Comments: 0

let: [u_n =(√u_(n−1) )+(√u_(n−2) ),u_0 =1,u_1 =1] ⇒ Σ_0 ^∞ ((1/u_n ))=?

$${let}:\:\left[\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}} =\sqrt{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}−\mathrm{1}} }+\sqrt{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}−\mathrm{2}} },\boldsymbol{\mathrm{u}}_{\mathrm{0}} =\mathrm{1},\boldsymbol{\mathrm{u}}_{\mathrm{1}} =\mathrm{1}\right] \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\underset{\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\boldsymbol{\mathrm{u}}_{\boldsymbol{\mathrm{n}}} }\right)=? \\ $$

Question Number 56847    Answers: 0   Comments: 2

d2y/dx2=x2y=0

$${d}\mathrm{2}{y}/{dx}\mathrm{2}={x}\mathrm{2}{y}=\mathrm{0} \\ $$

Question Number 56845    Answers: 2   Comments: 0

Question Number 56838    Answers: 1   Comments: 0

What would be the diameter of a circle having a heptagon of sides 45m,60m, 60m,50m,40m,45m and 50m inscribed in it?

$${What}\:{would}\:{be}\:{the}\:{diameter}\:{of}\:{a}\:{circle} \\ $$$${having}\:{a}\:{heptagon}\:{of}\:{sides}\:\mathrm{45}{m},\mathrm{60}{m}, \\ $$$$\mathrm{60}{m},\mathrm{50}{m},\mathrm{40}{m},\mathrm{45}{m}\:{and}\:\mathrm{50}{m}\:{inscribed} \\ $$$${in}\:{it}? \\ $$

Question Number 56832    Answers: 0   Comments: 0

let Z_n (x)=sin(narcsinx) with n integr 1) determine roots of Z_n (x) 2) decompose the fraction F =(1/(Z_n (x)))

$${let}\:\:{Z}_{{n}} \left({x}\right)={sin}\left({narcsinx}\right)\:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{roots}\:{of}\:{Z}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{the}\:{fraction}\:{F}\:=\frac{\mathrm{1}}{{Z}_{{n}} \left({x}\right)} \\ $$

Question Number 56831    Answers: 1   Comments: 10

let f(x) =(√(x^2 +3))−2x −1 1) calculate ∫_0 ^1 f(x)dx 2)determine f^(−1) (x) and calculate ∫ f^(−1) (x)dx .

$${let}\:{f}\left({x}\right)\:=\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}−\mathrm{2}{x}\:−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx} \\ $$$$\left.\mathrm{2}\right){determine}\:{f}^{−\mathrm{1}} \left({x}\right)\:{and}\:{calculate}\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx}\:. \\ $$

Question Number 56830    Answers: 0   Comments: 0

let A_n =Π_(k=0) ^(n−1) cos(kx) find a simple form of A_n

$${let}\:{A}_{{n}} =\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{cos}\left({kx}\right) \\ $$$$\:{find}\:{a}\:{simple}\:{form}\:{of}\:{A}_{{n}} \\ $$

Question Number 56829    Answers: 1   Comments: 0

let f(t) =∫_0 ^∞ ((cos(t(1+x^2 )))/(1+x^2 )) dx with t≥0 find a explicit form of f(t)

$${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({t}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\right)}{\mathrm{1}+{x}^{\mathrm{2}} }\:{dx}\:\:{with}\:{t}\geqslant\mathrm{0} \\ $$$${find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right)\: \\ $$

Question Number 56828    Answers: 1   Comments: 1

study the convergence of u_(n+1) =2(√(1+u_n ^2 ))−u_n −1 with u_0 =0

$${study}\:{the}\:{convergence}\:{of}\:{u}_{{n}+\mathrm{1}} =\mathrm{2}\sqrt{\mathrm{1}+{u}_{{n}} ^{\mathrm{2}} }−{u}_{{n}} −\mathrm{1}\:\:\:\:{with}\:{u}_{\mathrm{0}} =\mathrm{0} \\ $$

Question Number 56827    Answers: 1   Comments: 1

find the value of ∫_(−∞) ^(+∞) (dx/(x^4 −x^2 +3))

$${find}\:{the}\:{value}\:{of}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{dx}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{3}} \\ $$

Question Number 56824    Answers: 2   Comments: 1

Question Number 56823    Answers: 1   Comments: 1

Question Number 56820    Answers: 0   Comments: 0

the no of traingle formed by the vertices of a decagon such that atleast one side is in common

$$\mathrm{the}\:\mathrm{no}\:\mathrm{of}\:\mathrm{traingle}\:\mathrm{formed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{vertices} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{decagon}\:\mathrm{such}\:\mathrm{that}\:\mathrm{atleast}\:\mathrm{one}\:\mathrm{side} \\ $$$$\mathrm{is}\:\mathrm{in}\:\mathrm{common} \\ $$

Question Number 56818    Answers: 0   Comments: 2

Question Number 56803    Answers: 2   Comments: 2

Evaluate: ∫_( 1) ^( 2) (A∙B × C) dt and ∫_( 1) ^( 2) A × (B × C) dt where, A = ti − 3j + 2tk, B = i − 2j + 2k, C = 3i + tj − k

$$\mathrm{Evaluate}:\:\:\:\int_{\:\mathrm{1}} ^{\:\mathrm{2}} \:\left(\mathrm{A}\centerdot\mathrm{B}\:×\:\mathrm{C}\right)\:\mathrm{dt}\:\:\:\:\mathrm{and}\:\:\:\int_{\:\mathrm{1}} ^{\:\mathrm{2}} \:\mathrm{A}\:×\:\left(\mathrm{B}\:×\:\mathrm{C}\right)\:\:\:\mathrm{dt} \\ $$$$\mathrm{where},\:\:\:\:\:\:\:\:\:\mathrm{A}\:\:=\:\:\mathrm{ti}\:−\:\mathrm{3j}\:+\:\mathrm{2tk},\:\:\:\:\:\:\:\mathrm{B}\:\:=\:\:\mathrm{i}\:−\:\mathrm{2j}\:+\:\mathrm{2k}, \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{C}\:\:=\:\:\mathrm{3i}\:+\:\mathrm{tj}\:−\:\mathrm{k} \\ $$

Question Number 56795    Answers: 1   Comments: 1

dy/dx=x

$${dy}/{dx}={x} \\ $$

Question Number 56801    Answers: 1   Comments: 0

The product of three consecutive terms of 4. The sum of the GP is −(7/3). Find the GP

$${The}\:{product}\:{of}\:{three}\:{consecutive}\:{terms} \\ $$$${of}\:\mathrm{4}.\:{The}\:{sum}\:{of}\:{the}\:{GP}\:{is}\:−\frac{\mathrm{7}}{\mathrm{3}}.\:{Find} \\ $$$${the}\:{GP} \\ $$

Question Number 56800    Answers: 0   Comments: 3

x,y,z are positive integers. find all solutions of x^2 +y^2 +1=xyz.

$${x},{y},{z}\:{are}\:{positive}\:{integers}. \\ $$$${find}\:{all}\:{solutions}\:{of}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}={xyz}. \\ $$

Question Number 56813    Answers: 0   Comments: 0

study the sequence U_(n+1) =(√((1+u_n )/2)) with U_0 =a>0.

$${study}\:{the}\:{sequence}\:\:{U}_{{n}+\mathrm{1}} =\sqrt{\frac{\mathrm{1}+{u}_{{n}} }{\mathrm{2}}} \\ $$$${with}\:{U}_{\mathrm{0}} ={a}>\mathrm{0}. \\ $$

Question Number 56785    Answers: 0   Comments: 1

Question Number 56784    Answers: 0   Comments: 0

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