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AllQuestion and Answers: Page 1104

Question Number 108067 Answers: 2 Comments: 0

Question Number 108059 Answers: 1 Comments: 0

((♥JS♥)/(°js°)) Given a matrix A= ((( 3 2)),((−5 −4)) ) and A^2 +♭A−2I=0 where ♭ is a constant , I= (((1 0)),((0 1)) ). If B = (((−3♭ 2)),(( 5♭ −1)) ) , then A^(−1) B =

$$\:\:\:\frac{\heartsuit{JS}\heartsuit}{°{js}°} \\ $$$${Given}\:{a}\:{matrix}\:{A}=\begin{pmatrix}{\:\:\:\mathrm{3}\:\:\:\:\:\:\:\mathrm{2}}\\{−\mathrm{5}\:\:\:−\mathrm{4}}\end{pmatrix} \\ $$$${and}\:{A}^{\mathrm{2}} +\flat{A}−\mathrm{2}{I}=\mathrm{0}\:{where}\:\flat\:{is}\:{a} \\ $$$${constant}\:,\:{I}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix}.\:{If}\:{B}\:= \\ $$$$\begin{pmatrix}{−\mathrm{3}\flat\:\:\:\:\:\:\mathrm{2}}\\{\:\:\:\mathrm{5}\flat\:\:\:\:−\mathrm{1}}\end{pmatrix}\:,\:{then}\:{A}^{−\mathrm{1}} {B}\:=\: \\ $$

Question Number 108053 Answers: 2 Comments: 0

((⋏J S⋏)/^⇉ ) ((y/x)+(√((x^2 +y^2 )/x^2 )))dx=dy

$$\:\:\:\:\:\:\:\:\:\:\:\frac{\curlywedge\mathcal{J}\:\mathbb{S}\curlywedge}{\:^{\rightrightarrows} } \\ $$$$\:\:\:\:\:\left(\frac{{y}}{{x}}+\sqrt{\frac{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} }}\right){dx}={dy} \\ $$

Question Number 108051 Answers: 1 Comments: 0

Question Number 108047 Answers: 1 Comments: 0

((°•BeMath•°)/Σ) y−x (dy/dx) = a (1+x^2 (dy/dx))

$$\:\:\:\:\:\:\frac{°\bullet\mathcal{B}{e}\mathcal{M}{ath}\bullet°}{\Sigma} \\ $$$$\:\:\:{y}−{x}\:\frac{{dy}}{{dx}}\:=\:{a}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \:\frac{{dy}}{{dx}}\right)\: \\ $$

Question Number 108043 Answers: 2 Comments: 0

Given f(x)=x(x+1)(x+2)...(x+n) find the value of f′(0).

$$\mathrm{Given}\:\mathrm{f}\left({x}\right)={x}\left({x}+\mathrm{1}\right)\left({x}+\mathrm{2}\right)...\left({x}+{n}\right) \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f}'\left(\mathrm{0}\right). \\ $$

Question Number 108042 Answers: 0 Comments: 0

A particle in an electric and magnetic field is in motion. The time equations are in polar coordinates. r=r_0 e^(−(t/b)) and θ=(t/b) and b are positive constants. 1\Calculate the vector equation of the velocity of the particle. 2\Show that the angle (v_1 ^′ ,u_0 ′) is constant, and find the value. 3\Find the vector of acceleration of the particle. 4\Show that the angle (v_1 ^→ ,u_n ′) is constant, and find it. 5\Calculate the radius of this trajectory.

Question Number 108094 Answers: 1 Comments: 0

(d^2 Ψ/dt^2 )+(dΨ/dt)+Ψ=0

$$\frac{{d}^{\mathrm{2}} \Psi}{{dt}^{\mathrm{2}} }+\frac{{d}\Psi}{{dt}}+\Psi=\mathrm{0} \\ $$

Question Number 108034 Answers: 1 Comments: 0

Question Number 108022 Answers: 0 Comments: 0

((d^2 /dx^2 )−2x(d/dx)+2n)H_n (x)=0 Determine the first-4 polynomials of Hermite(H_n )

$$\left(\frac{\mathrm{d}^{\mathrm{2}} }{\mathrm{dx}^{\mathrm{2}} }−\mathrm{2x}\frac{\mathrm{d}}{\mathrm{dx}}+\mathrm{2n}\right)\mathrm{H}_{\mathrm{n}} \left(\mathrm{x}\right)=\mathrm{0} \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{first}-\mathrm{4}\:\mathrm{polynomials}\:\mathrm{of}\:\mathrm{Hermite}\left(\mathrm{H}_{\mathrm{n}} \right) \\ $$

Question Number 108016 Answers: 1 Comments: 0

Question Number 108018 Answers: 1 Comments: 0

i. x^3 (dy/dx)+y^2 +x^2 y+2x^4 =0 ii. (dy/dx)=−2−y+y^2 iii. 2cos(x)(dy/dx)=2cos^2 (x)−sin^2 (x)+y^2 ; y(0)=−1

$$\mathrm{i}.\:\:\mathrm{x}^{\mathrm{3}} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y}^{\mathrm{2}} +\mathrm{x}^{\mathrm{2}} \mathrm{y}+\mathrm{2x}^{\mathrm{4}} =\mathrm{0} \\ $$$$\mathrm{ii}.\:\:\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{2}−\mathrm{y}+\mathrm{y}^{\mathrm{2}} \\ $$$$\mathrm{iii}.\:\:\mathrm{2cos}\left(\mathrm{x}\right)\frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{2cos}^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{sin}^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{y}^{\mathrm{2}} \:;\:\mathrm{y}\left(\mathrm{0}\right)=−\mathrm{1} \\ $$

Question Number 108017 Answers: 2 Comments: 0

Question Number 108005 Answers: 1 Comments: 0

1. x′′(t)+x(t)=tcos(2t)+(1+t^2 )sin(2t) 2. x′′(t)+x(t)=t^2 cos(2t)

$$\mathrm{1}.\:\:\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{tcos}\left(\mathrm{2t}\right)+\left(\mathrm{1}+\mathrm{t}^{\mathrm{2}} \right)\mathrm{sin}\left(\mathrm{2t}\right) \\ $$$$\mathrm{2}.\:\:\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{t}^{\mathrm{2}} \mathrm{cos}\left(\mathrm{2t}\right) \\ $$

Question Number 107999 Answers: 3 Comments: 5

Question Number 108000 Answers: 1 Comments: 0

If x,y>0 log x+log y=2, What is the minimum value of (1/x)+(1/y)

$$\mathrm{If}\:\mathrm{x},\mathrm{y}>\mathrm{0}\: \\ $$$$\mathrm{log}\:\mathrm{x}+\mathrm{log}\:\mathrm{y}=\mathrm{2}, \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}} \\ $$

Question Number 107995 Answers: 3 Comments: 0

Solve the differential equation; x′′(t)+2x′(t)+x(t)=1+t (using the method of variation of parameters)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}; \\ $$$$\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{2x}'\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{1}+\mathrm{t} \\ $$$$\left(\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{of}\:\mathrm{variation}\:\mathrm{of}\:\mathrm{parameters}\right) \\ $$

Question Number 107993 Answers: 3 Comments: 0

Question Number 107978 Answers: 1 Comments: 0

on the interval of [0,π] solve tan^2 x+3secx= −3

$${on}\:{the}\:{interval}\:{of}\:\left[\mathrm{0},\pi\right]\:{solve} \\ $$$$\mathrm{tan}^{\mathrm{2}} {x}+\mathrm{3}{secx}=\:−\mathrm{3} \\ $$$$ \\ $$

Question Number 107977 Answers: 2 Comments: 0

On the interval of [0,2π] solve sin 6x +sin 2x=0

$${On}\:{the}\:{interval}\:{of}\:\left[\mathrm{0},\mathrm{2}\pi\right]\:{solve} \\ $$$$\mathrm{sin}\:\mathrm{6}{x}\:+\mathrm{sin}\:\mathrm{2}{x}=\mathrm{0} \\ $$$$ \\ $$

Question Number 107976 Answers: 1 Comments: 0

Rewrite cos6xcos 4x as a sum or difference

$${Rewrite}\:\mathrm{cos6}{x}\mathrm{cos}\:\mathrm{4}{x}\:{as}\:{a}\:{sum}\:{or} \\ $$$${difference} \\ $$

Question Number 107975 Answers: 3 Comments: 1

((♣JS♥)/(•≡•)) (1) lim_(x→0) ((sin (tan x)−tan (sin x))/(x−sin x )) (2)lim_(x→∞) x^2 (√((1−cos ((2/x)))(√((1−cos ((2/x)))(√((1−cos ((2/x)))(√(...)))))))) ?

$$\:\:\:\:\:\:\frac{\clubsuit{JS}\heartsuit}{\bullet\equiv\bullet} \\ $$$$\:\left(\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{tan}\:{x}\right)−\mathrm{tan}\:\left(\mathrm{sin}\:{x}\right)}{{x}−\mathrm{sin}\:{x}\:} \\ $$$$\:\left(\mathrm{2}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \sqrt{\left(\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}}{{x}}\right)\right)\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}}{{x}}\right)\right)\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\left(\frac{\mathrm{2}}{{x}}\right)\right)\sqrt{...}}}}\:?\: \\ $$$$ \\ $$

Question Number 107974 Answers: 1 Comments: 0

Σ_(k=1) ^n (√(1+(1/k^2 )+(1/((1+k)^2 ))))

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\sqrt{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }+\frac{\mathrm{1}}{\left(\mathrm{1}+\mathrm{k}\right)^{\mathrm{2}} }} \\ $$

Question Number 107871 Answers: 1 Comments: 1

((✓JS✓)/♥) lim_(x→0) (√((x tan x)/(sin 2x−cos 2x +1))) ?

$$\:\:\:\:\:\:\:\frac{\checkmark\mathcal{JS}\checkmark}{\heartsuit} \\ $$$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt{\frac{{x}\:\mathrm{tan}\:{x}}{\mathrm{sin}\:\mathrm{2}{x}−\mathrm{cos}\:\mathrm{2}{x}\:+\mathrm{1}}}\:?\: \\ $$

Question Number 107965 Answers: 2 Comments: 0

((⊚BeMath⊚)/) ∫ x (√(x/(2a−x))) dx ?

$$\:\:\:\:\frac{\circledcirc\mathcal{B}{e}\mathcal{M}{ath}\circledcirc}{} \\ $$$$\int\:{x}\:\sqrt{\frac{{x}}{\mathrm{2}{a}−{x}}}\:{dx}\:?\: \\ $$

Question Number 107947 Answers: 1 Comments: 0

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