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Given that forces F_(1 ) and F_2 position vectors r_(1 ) and r_2 F_1 = (2i + 3j)N r_1 = i + 2j F_2 = (αi−7j) N r_2 = 3i + 4j Given that these system of forces form a couple find the value of α.

$Given that forces F_{1} and F_{2} position vectors r_{1} and r_{2}$ $F_{1} = (2 i + 3 j) N r_{1} = i + 2 j$ $F_{2} = (α i - 7 j) N r_{2} = 3 i + 4 j$ $Given that these system of forces form a couple$ $find the value of α .$

Question Number 87752 Answers: 1 Comments: 0

A particle exhibits simple hamornic motion such that (d^2 x/dt^2 ) + 4x = 0 Calculate the period of the ocsillation

$A particle exhibits simple hamornic motion such that$ $\frac{d^{2} x}{{d t}^{2}} + 4 x = 0$ $Calculate the period of the ocsillation$

Question Number 87751 Answers: 0 Comments: 2

find in the form y= f(x) the general solution of the differentail equation (d^2 y/dx^2 ) −(dy/dx)−6y = e^(3x)

$find in the form y = f (x) the general solution$ $of the differentail equation$ $\frac{d^{2} y}{{d x}^{2}} - \frac{d y}{d x} - 6 y = e^{3 x}$

Question Number 87550 Answers: 0 Comments: 2

(1/(2e^(−x) −1)) > (2/(e^(−x) −2))

$\frac{1}{{2 e}^{- x} - 1} > \frac{2}{e^{- x} - 2}$

Question Number 87536 Answers: 1 Comments: 0

solve ∣2x−1∣=3⌊x⌋+2{x}

$s o l v e$ $∣ 2 x - 1 ∣= 3 ⌊ x ⌋ + 2 {x}$

Question Number 87497 Answers: 0 Comments: 0

A complex number z is defined by z = (1/2)(cos θ + isin θ),such that z^n = (1/2^n ) (cos nθ + isin nθ) Using De Moivre′s theorem,or otherwise, show that (i) Σ_(r=0) ^∞ (1/4^r ) sin 2rθ is a convergent geometic progression. (ii) Σ_(r=0) ^∞ (1/4^r ) sin 2r = ((14 sin 2θ)/(17−16cos 2θ))

$A complex number z is defined by z = \frac{1}{2} (\cos θ + i \sin θ), such that$ $z^{n} = \frac{1}{2^{n}} (\cos n θ + i \sin n θ)$ $Using De {Moivre}^{'} s theorem, or otherwise, show that$ $(i) \underset{r = 0}{\sum^{\infty}} \frac{1}{4^{r}} \sin 2 r θ is a convergent geometic progression .$ $(ii) \underset{r = 0}{\sum^{\infty}} \frac{1}{4^{r}} \sin 2 r = \frac{14 \sin 2 θ}{17 - 16 \cos 2 θ}$

Question Number 87308 Answers: 0 Comments: 0

A sequence (U_n ) is defined reculsively as U_o = (1/2) and U_(n+1) = (2/(1 + U_n )) for n ∈ N a) Show by mathematical induction that all terms in the sequence are positive. b) Given that the sequence (U_n ) is convergent, show that the limit,l, is a solution to the equation x^2 + x−2 = 0. Hence find l c) Given that (V_n ) is a sequence of general term such that V_n = ((U_n −1)/(U_n +2)) , ∀ n ∈ N. show that (V_n ) is convergent and determine its limit. hence deduce the convergence of the sequence (U_n ). Please recommend me textbooks for this topic even youtube vids please

$A sequence (U_{n}) is defined reculsively as$ $U_{o} = \frac{1}{2} and U_{n + 1} = \frac{2}{1 + U_{n}} for n \in N$ $a) Show by mathematical induction that all terms in the sequence$ $are positive .$ $b) Given that the sequence (U_{n}) is convergent, show that the limit, l, is$ $a solution to the equation x^{2} + x - 2 = 0 . Hence find l$ $c) Given that (V_{n}) is a sequence of general term such that$ $V_{n} = \frac{U_{n} - 1}{U_{n} + 2}, \forall n \in N .$ $show that (V_{n}) is convergent and determine its limit .$ $hence deduce the convergence of the sequence (U_{n}) .$ $P l e a s e r e c o m m e n d m e t e x t b o o k s f o r t h i s t o p i c e v e n y o u t u b e v i d s$ $p l e a s e$

Question Number 87069 Answers: 0 Comments: 1

((cos x−sin x)/(√(1+sin 2x))) = sec 2x−tan 2x prove it

$\frac{\cos x - \sin x}{\sqrt{1 + \sin 2 x}} = \sec 2 x - \tan 2 x$ $prove it$

Question Number 87031 Answers: 1 Comments: 1

Question Number 86886 Answers: 0 Comments: 1

Question Number 86873 Answers: 0 Comments: 0

A company paid a total dividend of K12 600.00 at the end of 2018 on 6000 shares. If Freddy owned 200 shares in the company, how much was paid out in dividents to him?

$A c o m p a n y p a i d a t o t a l d i v i d e n d o f K 12 600.00 a t t h e e n d o f 2018 o n 6000 s h a r e s . I f F r e d d y o w n e d 200 s h a r e s i n t h e c o m p a n y, h o w m u c h w a s p a i d o u t i n d i v i d e n t s t o h i m ?$

Question Number 87017 Answers: 1 Comments: 0

Question Number 86849 Answers: 0 Comments: 0

If z,w ε C and ∣z∣>1, ∣w∣<1 so ∣((z−w)/(1−z^− w))∣>1, demostrate thr veracity of the statment. (V or F)

$I f z, w ϵ C a n d ∣ z ∣> 1, ∣ w ∣< 1$ $s o ∣ \frac{z - w}{1 - \bar{z w}} ∣> 1, d e m o s t r a t e$ $t h r v e r a c i t y o f t h e$ $s t a t m e n t . (V o r F)$

Question Number 86708 Answers: 1 Comments: 0

∫x (√((√2) x−(√(2x^2 −1)))) dx

$\int x \sqrt{\sqrt{2} x - \sqrt{{2 x}^{2} - 1}} dx$

Question Number 86598 Answers: 0 Comments: 1

write out the general summation formula for the maclaurin series expansion for (1/2) (cos x + cosh x)

$write out the general summation formula for$ $the maclaurin series expansion for \frac{1}{2} (\cos x + \cosh x)$

Question Number 86461 Answers: 3 Comments: 0

Use exponential representation of sin θ and cos θ to show that a) sin^2 θ + cos^2 θ = 1 b) cos^2 θ − sin^2 θ = cos2θ c) 2 sinθ cosθ = 2sin2θ.

$Use exponential representation of \sin θ and \cos θ to show that$ $a) \sin^{2} θ + \cos^{2} θ = 1 b) \cos^{2} θ - \sin^{2} θ = \cos 2 θ$ $c) 2 \sin θ \cos θ = 2 \sin 2 θ .$

Question Number 86365 Answers: 0 Comments: 0

I think it will be ∫_0 ^(π/4) (dx/(√(1+tanx))) ≈∫_0 ^(π/4) (dx/(√(1+x))) =(𝛑/4)−(1/2).(1/2).((𝛑/4))^2 +((1.3)/(2.4)).(1/3).((𝛑/4))^3 −((1.3.5)/(2.4.6)).(1/4)((𝛑/4))^4 +....

$I think it will be$ $\int_{0}^{\frac{π}{4}} \frac{dx}{\sqrt{1 + tanx}} \approx \int_{0}^{\frac{π}{4}} \frac{dx}{\sqrt{1 + x}}$ $= \frac{π}{4} - \frac{1}{2} . \frac{1}{2} . {(\frac{π}{4})}^{2} + \frac{1.3}{2.4} . \frac{1}{3} . {(\frac{π}{4})}^{3} - \frac{1.3.5}{2.4.6} . \frac{1}{4} {(\frac{π}{4})}^{4} + . . . .$

Question Number 86356 Answers: 1 Comments: 1

Question Number 86198 Answers: 0 Comments: 7

any methods to sketch these curves r = a(1−cosθ) r= a + b cosθ a>b r= a + bcosθ a<b

$any methods to sketch these curves$ $r = a (1 - \cos θ)$ $r = a + b \cos θ a > b$ $r = a + bcos θ a < b$

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