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Question Number 26159 Answers: 1 Comments: 0

If x^2 + y^2 + 2xy + 2x + 2y + k = 0 represents pair of straight lines then find the value of k.

$If x^{2} + y^{2} + 2 x y + 2 x + 2 y + k = 0$ $represents pair of straight lines then$ $find the value of k .$

Question Number 26156 Answers: 1 Comments: 0

a two digit number is 3 more than 4 times the sum of its digits. if 18 is added to this number .the sum is equal to number obtained by interchanging the digits.find the number

$a t w o d i g i t n u m b e r i s 3 m o r e t h a n$ $4 t i m e s t h e s u m o f i t s d i g i t s . i f$ $18 i s a d d e d t o t h i s n u m b e r . t h e$ $s u m i s e q u a l t o n u m b e r o b t a i n e d$ $b y i n t e r c h a n g i n g t h e d i g i t s . f i n d t h e n u m b e r$

Question Number 26153 Answers: 1 Comments: 0

ratio of income of two persons is 9 is to 7.ratio of their expenses is 4 is to 3 .every person saves rupees 200. find income of each.

$r a t i o o f i n c o m e o f t w o p e r s o n s i s$ $9 i s t o 7 . r a t i o o f t h e i r e x p e n s e s$ $i s 4 i s t o 3 . e v e r y p e r s o n s a v e s$ $r u p e e s 200 . f i n d i n c o m e o f e a c h .$

Question Number 26148 Answers: 2 Comments: 2

Question Number 26147 Answers: 1 Comments: 0

There are 5 more girls than boys in a class. If 2 boys join the class, the ratio of girls to boys will be 5:4. Find the number of of girls in the class.

$There are 5 more girls than boys in a class . If 2 boys join$ $the class, the ratio of girls to boys will be 5 : 4 . Find the$ $number of of girls in the class .$

Question Number 26142 Answers: 0 Comments: 0

Prove that If f(x) is Riemann integrable on [a,b] and ∃M>0 s.t. ∀x∈[a,b] (f(x)≠0 and ∣f(x)∣<M and ∣(1/(f(x)))∣<M), then (1/(f(x))) is Riemann integrable on [a,b].

$Prove that$ $If f (x) is Riemann integrable on [a, b] and$ $\exists M > 0 s . t . \forall x \in [a, b] (f (x) \neq 0 a n d ∣ f (x) ∣< M a n d ∣ \frac{1}{f (x)} ∣< M),$ $then \frac{1}{f (x)} is Riemann integrable on [a, b] .$

Question Number 26143 Answers: 2 Comments: 1

2000^(3000) vs 3000^(2000) who is stronger ?

$2000^{3000} v s 3000^{2000}$ $w h o i s s t r o n g e r ?$

Question Number 26135 Answers: 1 Comments: 1

Prove that b=2asin^2 θ ; when acosθ−bsinθ=c and θ=45°

$Prove that b = {2 asin}^{2} θ;$ $when acos θ - bsin θ = c and θ = 45 °$

Question Number 26133 Answers: 1 Comments: 1

find the value of (C_n ^(0 ) )^2 +(C_n ^1 )^2 +(C_n ^2 )^2 +...(C_n ^n )^2 .

$f i n d t h e v a l u e o f {(C_{n}^{0})}^{2} + {(C_{n}^{1})}^{2} + {(C_{n}^{2})}^{2} + . . . {(C_{n}^{n})}^{2} .$

Question Number 26132 Answers: 0 Comments: 1

let put S_n =Σ_(k=1) ^(k=n) (((−1)^k )/k) find S_(n ) in terms of H_n then lim_(n−>∝) S_n H_n = Σ_(k=1) ^(k=n) (1/k) ( harmonic serie)

$l e t p u t S_{n} = \sum_{k = 1}^{k = n} \frac{{(- 1)}^{k}}{k}$ $f i n d S_{n} i n t e r m s o f H_{n} t h e n {l i m}_{n - >\propto} S_{n}$ $H_{n} = \sum_{k = 1}^{k = n} \frac{1}{k} (h a r m o n i c s e r i e)$

Question Number 26127 Answers: 1 Comments: 0

y+2y^3 y^((1)) =(x+4yln (y))y^((1))

$y + 2 y^{3} y^{(1)} = (x + 4 y \ln (y)) y^{(1)}$

Question Number 26125 Answers: 0 Comments: 1

Question Number 26121 Answers: 0 Comments: 0

answer to26109 S_n = Σ_(k=1) ^(k=n) (1/(k^2 (k+1)^2 )) we decompose F(X) = (1/(X^2 (X+1)^2 )) = (a/X) +(b/X^2^ ) +(c/(X+1)) +(d/((X+1)^2 )) we find F(X) = ((−2)/X) +(1/X^2 ) + (2/(X+1)) + (1/((X+1)^2 )) so S_n = −2Σ_(k=1) ^(k=n) (1/k) +2Σ_(k=1) ^(k=n) (1/(k+1)) +Σ_(k=1) ^(k=n) (1/k^2^ ) + Σ_(k=1) ^(k=n) (1/((k+1)^2 )) but Σ_(k=1) ^(k=n) (1/k) = H_n Σ_(k=1) ^(k=n) (1/(k+1))= H_(n+1) −1 Σ_(k=1) ^(k=n) (1/((k+1)^2 )) = Σ_(k=1) ^(k=n) (1/k^2 ) + (1/((n+1)^2 )) −1⇒ S_n = 2(H_(n+1) −H_n ) +2 Σ_(k=1) ^(k=n) (1/k^2 ) −3 but lim_(n−>∝) (H_(n+1) − H_n ) =0 and Σ_(k=1) ^∝ (1/k^2 ) = (π^2 /6) ⇒ lim_(n−>∝) S_n = 2 (π^2 /6) −3 = (π^2 /3) −3 .

Question Number 26117 Answers: 1 Comments: 0

(1/6)(√((3log1728)/(1+(1/2)log36+(1/3)log8))) simplify the question above

$\frac{1}{6} \sqrt{\frac{3 l o g 1728}{1 + \frac{1}{2} l o g 36 + \frac{1}{3} l o g 8}}$ $s i m p l i f y t h e q u e s t i o n a b o v e$

Question Number 26115 Answers: 1 Comments: 0

x^2 +(1/x^2 )=3 thrn find the valu of( x−(1/x))^2

$x^{2} + \frac{1}{x^{2}} = 3 thrn find the valu of {(x - \frac{1}{x})}^{2}$

Question Number 26126 Answers: 0 Comments: 1

using 1st principle find the derivative of y=x^x

$u s i n g 1 s t p r i n c i p l e f i n d t h e$ $d e r i v a t i v e o f$ $y = x^{x}$

Question Number 26113 Answers: 1 Comments: 0

Question Number 26107 Answers: 0 Comments: 0

answer to 26024 let put c= ∫_0 ^∞ cos(ax^2 )dx and c = ∫_0 ^∞ sin(ax^2 )dx ew have c−is = ∫_0 ^∞ e^(−iax^2 ) dx =2^(−1) ∫_R e^(−iax^2 ) dx and i put x^(1/2) =r(x)(notation) so 2(c−is) = ∫_R e^(−(r(ia)x)^2 ) dx and by the changement t= r(ia) x we find 2(c+is) = (r(ia))^(−1) ∫_R e^(−t^2 ) dt = r(π)/r(ia) but r(ia) =r(i) r(a) = r(a) e^ −−>2(c+is) = r(π) r(a)^(−1) e^(−iπ/4) ^) −−> c = r(2π)/_(4r(a)) and s = r(2π)/_(4r(a))

$a n s w e r t o 26024 l e t p u t c = \int_{0}^{\infty} c o s ({a x}^{2}) d x a n d c = \int_{0}^{\infty} s i n ({a x}^{2}) d x$ $e w h a v e c - i s = \int_{0}^{\infty} e^{- {i a x}^{2}} d x = 2^{- 1} \int_{R} e^{- {i a x}^{2}} d x a n d i p u t$ $x^{1 / 2} = r (x) (n o t a t i o n) s o 2 (c - i s) = \int_{R} e^{- {(r (i a) x)}^{2}} d x$ $a n d b y t h e c h a n g e m e n t t = r (i a) x w e f i n d$ $2 (c + i s) = {(r (i a))}^{- 1} \int_{R} e^{- t^{2}} d t = r (π) / r (i a) b u t$ $r (i a) = r (i) r (a) = r (a) e^{} - - > 2 (c + i s) = r (π) r {(a)}^{- 1} e^{- i π / 4}^{)}$ $- - > c = r (2 π) /_{4 r (a)} a n d s = r (2 π) /_{4 r (a)}$

Question Number 26111 Answers: 0 Comments: 2

find the radius of convergence for the serie Σ_(n=1) ^∝ H_n x^n H_n = Σ_(k=1) ^(k=n) (1/k) .

$f i n d t h e r a d i u s o f c o n v e r g e n c e f o r t h e s e r i e \sum_{n = 1}^{\propto} H_{n} x^{n}$ $H_{n} = \sum_{k = 1}^{k = n} \frac{1}{k} .$

Question Number 26223 Answers: 1 Comments: 1

let put ξ(x)= Σ_(n=1) ^∝ (1/n^x ) with x>1 and δ(x) =Σ_(n=1) ^∝ (((−1)^n )/n^x ) find a relation between ξ(x) and δ(x).

$l e t p u t ξ (x) = \sum_{n = 1}^{\propto} \frac{1}{n^{x}} w i t h x > 1$ $a n d δ (x) = \sum_{n = 1}^{\propto} \frac{{(- 1)}^{n}}{n^{x}} f i n d a r e l a t i o n$ $b e t w e e n ξ (x) a n d δ (x) .$

Question Number 26098 Answers: 0 Comments: 0

Question Number 26090 Answers: 1 Comments: 0

∫((asin^3 θ+bcos^3 θ)/(sin^2 θ.cos^2 θ))dθ

$\int \frac{a \sin^{3} θ + b \cos^{3} θ}{\sin^{2} θ . \cos^{2} θ} d θ$

Question Number 26087 Answers: 0 Comments: 2

Given f(x) = (1 − x + x^2 − x^3 + ... − x^(2015) + x^(2016) )^2 Find the sum of all odd coeffisiens! Ex. f(x) = (x^2 + x + 1)^2 = 1x^4 + 2x^3 + 3x^2 + 2x + 1 The sum of odd coeffisien is 1 + 3 = 4

$Given$ $f (x) = {(1 - x + x^{2} - x^{3} + . . . - x^{2015} + x^{2016})}^{2}$ $Find the sum of all odd coeffisiens!$ $Ex . f (x) = {(x^{2} + x + 1)}^{2} = 1 x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1$ $The sum of odd coeffisien is 1 + 3 = 4$

Question Number 26078 Answers: 1 Comments: 0

x^2 −x−42 factorise

$x^{2} - x - 42 factorise$

Question Number 26073 Answers: 0 Comments: 2

solve the differential equation(D^2 +2D+1)y=x^2 +2x+1

$s o l v e t h e d i f f e r e n t i a l e q u a t i o n (D^{2} + 2 D + 1) y = x^{2} + 2 x + 1$

Question Number 26067 Answers: 2 Comments: 0

Find the value of ((2 + 3^2 )/(1! + 2! + 3! + 4!)) + ((3 + 4^2 )/(2! + 3! + 4! + 5!)) + ... + ((2013 + 2014^2 )/(2012! + 2013! + 2014! + 2015!))

$Find the value of$ $\frac{2 + 3^{2}}{1! + 2! + 3! + 4!} + \frac{3 + 4^{2}}{2! + 3! + 4! + 5!} + . . . + \frac{2013 + 2014^{2}}{2012! + 2013! + 2014! + 2015!}$

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