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Question Number 69459 Answers: 0 Comments: 0

Question Number 69314 Answers: 1 Comments: 1

if 5 x y 40 are in GP .find x and y

$i f 5 x y 40 a r e i n G P . f i n d x a n d y$

Question Number 69247 Answers: 0 Comments: 1

show that c∣a ⇔ −c∣a.

$s h o w t h a t$ $c ∣ a \Leftrightarrow - c ∣ a .$

Question Number 69236 Answers: 0 Comments: 0

Use Residus theorem to prove that ∀ a>0 Σ_(n=0) ^∞ (1/( n^2 +a^2 )) = (1/2)((π/(ash(πa))) −(1/a^2 )) and Σ_(n=0) ^∞ (((−1)^n )/(n^2 +a^2 )) = (1/2)((( π)/(a.th(πa))) −(1/a^2 )) Assume that we can developp in integer serie the functions f(x)=(x/(shx)) and g(x)=(x/(thx)) Give the DL_2 of f and g around zero Why can′t we use that theorem to explicit f(a)=Σ_(n=0) ^∞ (((−1)^n )/( (2n+1)^2 +a^2 )) ???

$U s e R e s i d u s t h e o r e m t o p r o v e t h a t \forall a > 0 \underset{n = 0}{\sum^{\infty}} \frac{1}{n^{2} + a^{2}} = \frac{1}{2} (\frac{π}{a s h (π a)} - \frac{1}{a^{2}})$ $a n d \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{n^{2} + a^{2}} = \frac{1}{2} (\frac{π}{a . t h (π a)} - \frac{1}{a^{2}})$ $A s s u m e t h a t w e c a n d e v e l o p p i n i n t e g e r s e r i e t h e f u n c t i o n s$ $f (x) = \frac{x}{s h x} a n d g (x) = \frac{x}{t h x}$ $G i v e t h e {D L}_{2} o f f a n d g a r o u n d z e r o$ $W h y {c a n}^{'} t w e u s e t h a t t h e o r e m t o e x p l i c i t$ $f (a) = \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n}}{{(2 n + 1)}^{2} + a^{2}} ? ? ?$

Question Number 69207 Answers: 1 Comments: 3

help please. A river is 5m wide and flows at 3.0ms^(−1) . A man can swim at 2.0ms^(−1) in still water. if he sets off at an angle of 90° to the bank calculate a) the mans time and velocity b) his distance downstream from the starting point till when he reaches the other side of the river bank c) the actual distance he swims through the water.

$h e l p p l e a s e .$ $A r i v e r i s 5 m w i d e a n d f l o w s a t 3.0 {m s}^{- 1} . A m a n c a n s w i m a t 2.0 {m s}^{- 1}$ $i n s t i l l w a t e r . i f h e s e t s o f f a t a n a n g l e o f 90 ° t o t h e b a n k$ $c a l c u l a t e$ $a) t h e m a n s t i m e a n d v e l o c i t y$ $b) h i s d i s t a n c e d o w n s t r e a m f r o m t h e s t a r t i n g p o i n t t i l l$ $w h e n h e r e a c h e s t h e o t h e r s i d e o f t h e r i v e r b a n k$ $c) t h e a c t u a l d i s t a n c e h e s w i m s t h r o u g h t h e w a t e r .$

Question Number 69198 Answers: 0 Comments: 0

please someone check Q69159

$p l e a s e s o m e o n e c h e c k Q 69159$

Question Number 69188 Answers: 2 Comments: 2

Question Number 69092 Answers: 1 Comments: 0

Question Number 69106 Answers: 0 Comments: 0

Question Number 69105 Answers: 0 Comments: 0

Question Number 69104 Answers: 0 Comments: 3

Question Number 69098 Answers: 1 Comments: 3

Question Number 69014 Answers: 1 Comments: 0

a) ∫∣ x^2 +2x + 1∣dx b) ∫_0 ^4 ∣x^2 +3x−2∣dx

$a) \int ∣ x^{2} + 2 x + 1 ∣ d x$ $b) \int_{0}^{4} ∣ x^{2} + 3 x - 2 ∣ d x$

Question Number 69010 Answers: 0 Comments: 8

To Tinku Tara, The Developer Sir, You′re going to update this, useful in real sense, precious app. Taking advantage of this opportunity I suggest some revolutionary changes if they′re possible for you. •HIDE/UNHIDE DETALS. It′s very useful to hide some details of an answer for authers in order to offer overall view.If the reader wants these details they can unhide these by clicking some symbol(small triangles etc).Can we expect this feature? •HYPERLINK FACILITY. Some posts contain reference to some other questions.Is it possible to make these question numbers hyperlinks in order to reach these questions directly and come back? •REPLACING A SYMBOL BY AN EXPRESSION. At sometimes the auther needs to replace some symbol/expression by an other symbol/expression in whole document or some portion of it. Pl consider this if it′s not very difficult for you. Forum-friends can request some other features.

$T o T i n k u T a r a, T h e D e v e l o p e r$ $S i r,$ ${Y o u}^{'} r e g o i n g t o u p d a t e t h i s,$ $u s e f u l i n r e a l s e n s e, p r e c i o u s a p p .$ $T a k i n g a d v a n t a g e o f t h i s o p p o r t u n i t y$ $I s u g g e s t s o m e r e v o l u t i o n a r y$ $c h a n g e s i f {t h e y}^{'} r e p o s s i b l e f o r y o u .$ $∙ H I D E / U N H I D E D E T A L S .$ ${I t}^{'} s v e r y u s e f u l t o h i d e s o m e d e t a i l s$ $o f a n a n s w e r f o r a u t h e r s i n o r d e r t o$ $o f f e r o v e r a l l v i e w . I f t h e r e a d e r$ $w a n t s t h e s e d e t a i l s t h e y c a n u n h i d e$ $t h e s e b y c l i c k i n g s o m e s y m b o l (s m a l l$ $t r i a n g l e s e t c) . C a n w e e x p e c t t h i s$ $f e a t u r e ?$ $∙ H Y P E R L I N K F A C I L I T Y .$ $S o m e p o s t s c o n t a i n r e f e r e n c e t o$ $s o m e o t h e r q u e s t i o n s . I s i t p o s s i b l e$ $t o m a k e t h e s e q u e s t i o n n u m b e r s$ $h y p e r l i n k s i n o r d e r t o r e a c h$ $t h e s e q u e s t i o n s d i r e c t l y a n d c o m e$ $b a c k ?$ $∙ R E P L A C I N G A S Y M B O L$ $B Y A N E X P R E S S I O N .$ $A t s o m e t i m e s t h e a u t h e r n e e d s$ $t o r e p l a c e s o m e s y m b o l / e x p r e s s i o n$ $b y a n o t h e r s y m b o l / e x p r e s s i o n i n$ $w h o l e d o c u m e n t o r s o m e p o r t i o n o f$ $i t . P l c o n s i d e r t h i s i f {i t}^{'} s n o t v e r y$ $d i f f i c u l t f o r y o u .$ $F o r u m - f r i e n d s c a n r e q u e s t s o m e$ $o t h e r f e a t u r e s .$

Question Number 68830 Answers: 0 Comments: 0

please can someone check question 68728

$p l e a s e c a n s o m e o n e c h e c k q u e s t i o n 68728$

Question Number 68676 Answers: 0 Comments: 2

Solve the equation tanh^(−1) (((x−2)/(x+1))) = ln 2 show that the set {1,2,4,8} under ×_(15) ,multiplication mod 15 forms a group.

$S o l v e t h e e q u a t i o n$ ${t a n h}^{- 1} (\frac{x - 2}{x + 1}) = l n 2$ $s h o w t h a t t h e s e t {1, 2, 4, 8} u n d e r \times_{15}, m u l t i p l i c a t i o n m o d 15 f o r m s a g r o u p .$

Question Number 68675 Answers: 0 Comments: 3

Express in partial fraction f(x) ≡ ((2x^3 + x + 2)/((x^2 +1)(x+1)(x−2))) x ≠ −1,2 Hence or otherwise show that ∫_0 ^1 f(x) dx = −(1/(12))[ 13ln 2 + π]

$E x p r e s s i n p a r t i a l f r a c t i o n$ $f (x) \equiv \frac{2 x^{3} + x + 2}{(x^{2} + 1) (x + 1) (x - 2)} x \neq - 1, 2$ $H e n c e o r o t h e r w i s e s h o w t h a t$ $\int_{0}^{1} f (x) d x = - \frac{1}{12} [13 l n 2 + π]$