Question and Answers Forum

A particle moving in a straight line OX has a displacement x from O at time t where x satisfies the equation (d^2 x/(dt^2 )) + 2(dx/dt) + 3x = 0 the damping factor for the motion is [A] e^(−1) [B] e^(−2t) [C] e^(−3t) [D] e^(−5t)

$A particle moving in a straight line O X has a$ $displacement x from O at time t where x satisfies$ $the equation \frac{d^{2} x}{{d t}^{2}} + 2 \frac{d x}{d t} + 3 x = 0$ $the damping factor for the motion is$ $[A] e^{- 1}$ $[B] e^{- 2 t}$ $[C] e^{- 3 t}$ $[D] e^{- 5 t}$

Question Number 84316 Answers: 1 Comments: 1

Which one of the following sets of vectors is a basis for R^2 [A] { ((1),((−2)) ) , (((−3)),(6) )} [B] { ((1),(1) ) , ((2),(2) )} [C] { ((2),(1) ) , ((0),(1) )} [D] { ((1),(2) ) , ((4),(8) ) }

$Which one of the following sets of$ $vectors is a basis for R^{2}$ $[A] {(\begin{matrix} 1 \\ - 2 \end{matrix}), (\begin{matrix} - 3 \\ 6 \end{matrix})}$ $[B] {(\begin{matrix} 1 \\ 1 \end{matrix}), (\begin{matrix} 2 \\ 2 \end{matrix})}$ $[C] {(\begin{matrix} 2 \\ 1 \end{matrix}), (\begin{matrix} 0 \\ 1 \end{matrix})}$ $[D] {(\begin{matrix} 1 \\ 2 \end{matrix}), (\begin{matrix} 4 \\ 8 \end{matrix})}$

Question Number 84242 Answers: 1 Comments: 1

∫_0 ^(ln2) (1/(cosh(x + ln4)))dx

$\underset{0}{\int^{\ln 2}} \frac{1}{\cosh (x + \ln 4)} d x$

Question Number 84263 Answers: 1 Comments: 0

Using the approximation h((dy/dx))_n ≈ y_(n+1) −y_n and that (dy/dx) = 1, y =2 when x = 0 . then , y_1 = [A] h−2 [B] h + 2 [C] h−1 [D] h + 1

$Using the approximation$ $h {(\frac{d y}{d x})}_{n} \approx y_{n + 1} - y_{n} and that \frac{d y}{d x} = 1, y = 2$ $when x = 0 . then, y_{1} =$ $[A] h - 2$ $[B] h + 2$ $[C] h - 1$ $[D] h + 1$

Question Number 84231 Answers: 1 Comments: 0

A compound pendulum oscillates though a small angle θ about its equilibrium position such that 10a((dθ/dt))^2 = 4g cos θ , a >0 . its period is [A] 2π(√(((5a)/(4g)) )) [B] ((2π)/5)(√(a/g)) [C] 2π(√(((2g)/(5a)) )) [D] 2π(√((5a)/g))

$A compound pendulum oscillates though a$ $small angle θ about its equilibrium position$ $such that$ $10 a {(\frac{d θ}{d t})}^{2} = 4 g \cos θ, a > 0 . its period is$ $[A] 2 π \sqrt{\frac{5 a}{4 g}} [B] \frac{2 π}{5} \sqrt{\frac{a}{g}} [C] 2 π \sqrt{\frac{2 g}{5 a}} [D] 2 π \sqrt{\frac{5 a}{g}}$

Question Number 84220 Answers: 1 Comments: 1

find the maximum value of (2/(3cosh2x +2))

$find the maximum value of \frac{2}{3 \cosh 2 x + 2}$

Question Number 84219 Answers: 1 Comments: 0

∫_(−1) ^1 e^(∣x∣) dx =?

$\int_{- 1}^{1} e^{∣ x ∣} d x = ?$

Question Number 84218 Answers: 4 Comments: 1

find the distance between the planes 2x−y−z = 24 and 2x−y−z = 36

$find the distance between the planes$ $2 x - y - z = 24 and 2 x - y - z = 36$

Question Number 84215 Answers: 1 Comments: 0

hi show that the following sequence is limited: U_n =((3n+2)/(2n+1)) precise the upper and lower.

$h i$ $s h o w t h a t t h e f o l l o w i n g s e q u e n c e$ $i s l i m i t e d :$ $U_{n} = \frac{3 n + 2}{2 n + 1}$ $p r e c i s e t h e u p p e r a n d l o w e r .$

Question Number 84134 Answers: 1 Comments: 0

find the general solution of the equation 2sin 3θ = sin 2θ

$find the general solution of the equation$ $2 \sin 3 θ = \sin 2 θ$

Question Number 84121 Answers: 0 Comments: 4

given that g(x) = { ((x + 2 , if 0 ≤ x < 2)),((x^2 , if 2 ≤ x < 4)) :} is periodic of period 4. sketch the curve for g(x) in the interval 0≤ x < 8 evaluate g(−6).

$given that$ $g (x) = {\begin{cases} x + 2, if 0 ⩽ x < 2 \\ x^{2}, if 2 ⩽ x < 4 \end{cases}$ $is periodic of period 4 .$ $sketch the curve for g (x) in the interval$ $0 ⩽ x < 8$ $evaluate g (- 6) .$

Question Number 84021 Answers: 3 Comments: 1

Question Number 83991 Answers: 0 Comments: 1

Find the locus of the points represented by the complex number ,z, such that 2∣z−3∣ = ∣z−6i∣

$Find the locus of the points represented by$ $the complex number, z, such that$ $2 ∣ z - 3 ∣ = ∣ z - 6 i ∣$

Question Number 83989 Answers: 0 Comments: 3

find a. ∫cos 3x cos 5x dx b. ∫xln 2x dx

$find$ $a . \int \cos 3 x \cos 5 x d x$ $b . \int x \ln 2 x d x$

Question Number 83966 Answers: 2 Comments: 0

prove that for any complex number z, if ∣z∣ < 1, then Re(z + 1) > 0

$prove that for any complex number z, if$ $∣ z ∣ < 1, then Re (z + 1) > 0$

Question Number 83965 Answers: 0 Comments: 3

prove or disprove(with counter−example) that a) For all two dimensional vectors a,b,c, a.b = a. c ⇒ b=c. b) For all positive real numbers a,b. ((a +b)/2) ≥ (√(ab))

$prove or disprove (with counter - example) that$ $a) For all two dimensional vectors a, b, c,$ $a . b = a . c \Rightarrow b = c .$ $b) For all positive real numbers a, b .$ $\frac{a + b}{2} ⩾ \sqrt{a b}$

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