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Question Number 137252 Answers: 1 Comments: 0

Decompose the function P(x) = ((x^4 +2x^3 +6x^2 +20x+6)/(x^3 +x^2 +x)) in partial fractions.

$Decompose the function P (x) = \frac{x^{4} + {2 x}^{3} + {6 x}^{2} + 20 x + 6}{x^{3} + x^{2} + x}$ $in partial fractions .$

Question Number 137191 Answers: 0 Comments: 0

Some useful approximations of sine function sin((π/7))=((96)/(221)) sin((π/9))=((128)/(373)) sin((π/(11)))=((32)/(113)) ... I am counting more ..thanking you!

$S o m e u s e f u l a p p r o x i m a t i o n s o f s i n e f u n c t i o n$ $s i n (\frac{π}{7}) = \frac{96}{221}$ $s i n (\frac{π}{9}) = \frac{128}{373}$ $s i n (\frac{π}{11}) = \frac{32}{113}$ $. . .$ $I a m c o u n t i n g m o r e . . t h a n k i n g y o u!$

Question Number 136995 Answers: 0 Comments: 0

1−(((1.1.3)/(2.3.4)))(1/(1!))+(((3.3.7)/(2^2 .3^2 .4^2 )))(1/(2!))−(((5.7.10)/(2^3 .3^3 .4^3 )))(1/(3!))−....

$1 - (\frac{1.1.3}{2.3.4}) \frac{1}{1!} + (\frac{3.3.7}{2^{2} . 3^{2} . 4^{2}}) \frac{1}{2!} - (\frac{5.7.10}{2^{3} . 3^{3} . 4^{3}}) \frac{1}{3!} - . . . .$

Question Number 137016 Answers: 1 Comments: 0

Question Number 136950 Answers: 2 Comments: 0

Question Number 136930 Answers: 0 Comments: 6

Question Number 136899 Answers: 2 Comments: 0

Question Number 136892 Answers: 1 Comments: 0

∫(d^2 y/dx^2 )dy

$\int \frac{d^{2} y}{{d x}^{2}} d y$

Question Number 136885 Answers: 1 Comments: 0

Question Number 136850 Answers: 0 Comments: 1

Σ_(n=−∞) ^∞ a^((n(n+1))/2) b^((n(n−1))/2) =1+(√((2a^2 )/π))∫_0 ^∞ e^(−t^2 /2) (((1−a(√(ab)) cosh((√(log(ab))) t))/(a^3 b−2a(√(ab )) cosh((√(log(ab))) t))))dt

$\underset{n = - \infty}{\sum^{\infty}} a^{\frac{n (n + 1)}{2}} b^{\frac{n (n - 1)}{2}} = 1 + \sqrt{\frac{2 a^{2}}{π}} \int_{0}^{\infty} e^{- t^{2} / 2} (\frac{1 - a \sqrt{a b} c o s h (\sqrt{l o g (a b)} t)}{a^{3} b - 2 a \sqrt{a b} c o s h (\sqrt{l o g (a b)} t)}) d t$

Question Number 136826 Answers: 0 Comments: 0

Question Number 136823 Answers: 0 Comments: 0

Question Number 136799 Answers: 0 Comments: 0

∫_0 ^1 Π_(n=1) ^∞ (1−q^n )dq

$\int_{0}^{1} \underset{n = 1}{\prod^{\infty}} (1 - q^{n}) d q$

Question Number 136761 Answers: 1 Comments: 1

Question Number 136760 Answers: 1 Comments: 0

Question Number 136757 Answers: 1 Comments: 0

1+((1/2))^2 (1/(2.1!))+(((1.3)/2^2 ))^2 (1/(2^2 .2!))+(((1.3.5)/2^3 )).(1/(2^3 .3!))+....=(((Γ((1/4)))/((2π^3 )^(1/4) )))^2

$1 + {(\frac{1}{2})}^{2} \frac{1}{2.1!} + {(\frac{1.3}{2^{2}})}^{2} \frac{1}{2^{2} . 2!} + (\frac{1.3.5}{2^{3}}) . \frac{1}{2^{3} . 3!} + . . . . = {(\frac{Γ (\frac{1}{4})}{{(2 π^{3})}^{1 / 4}})}^{2}$

Question Number 136661 Answers: 0 Comments: 0

∫_0 ^1 (1−x)^(−(7/8)) (1+x)^(−(1/(16))) dx

$\int_{0}^{1} {(1 - x)}^{- \frac{7}{8}} {(1 + x)}^{- \frac{1}{16}} d x$

Question Number 136593 Answers: 1 Comments: 0

Question Number 136520 Answers: 3 Comments: 1

Question Number 136519 Answers: 1 Comments: 0

1−((1/2))^(2k) +(((1.3)/(2.4)))^(2k) −(((1.3.5)/(2.4.6)))^(2k) +(((1.3.5.7)/(2.4.6.8)))^(2k) −.... Find the general form

$1 - {(\frac{1}{2})}^{2 k} + {(\frac{1.3}{2.4})}^{2 k} - {(\frac{1.3.5}{2.4.6})}^{2 k} + {(\frac{1.3.5.7}{2.4.6.8})}^{2 k} - . . . .$ $F i n d t h e g e n e r a l f o r m$

Question Number 136420 Answers: 2 Comments: 0

Σ_(n=1) ^∞ ((sin(2n+1)θ)/((2n+1)^2 ))=(θ/2)log(2)+sinθ((log(sinθ))/4) _2 F_1 ((1/2),(1/2);(3/2);sin^2 θ)+((sinθ)/(16)) _2 F_1 ((1/2),(1/2),(1/2);(3/2);(3/2);sin^2 θ) Prove or disprove 0<θ<π

$\underset{n = 1}{\sum^{\infty}} \frac{s i n (2 n + 1) θ}{{(2 n + 1)}^{2}} = \frac{θ}{2} l o g (2) + s i n θ \frac{l o g (s i n θ)}{4}_{2} F_{1} (\frac{1}{2}, \frac{1}{2}; \frac{3}{2}; {s i n}^{2} θ) + \frac{s i n θ}{16}_{2} F_{1} (\frac{1}{2}, \frac{1}{2}, \frac{1}{2}; \frac{3}{2}; \frac{3}{2}; {s i n}^{2} θ)$ $P r o v e o r d i s p r o v e 0 < θ < π$

Question Number 136105 Answers: 0 Comments: 4

Question Number 136104 Answers: 0 Comments: 0

((cos(1+(√((43)/3)))π)/1^2 )+((cos(1+(√((43)/3)))2π)/2^2 )+((cos(1+(√((43)/3)))3π)/3^2 )+...=aπ Find a

$\frac{c o s (1 + \sqrt{\frac{43}{3}}) π}{1^{2}} + \frac{c o s (1 + \sqrt{\frac{43}{3}}) 2 π}{2^{2}} + \frac{c o s (1 + \sqrt{\frac{43}{3}}) 3 π}{3^{2}} + . . . = a π$ $F i n d a$

Question Number 136070 Answers: 1 Comments: 0

((sin((√2)))/1^3 )+((sin(2(√2)))/2^3 )+((sin(3(√2)))/3^3 )+...=((π^b +1)/( a(√b)))−(π/b) Find a−b

$\frac{s i n (\sqrt{2})}{1^{3}} + \frac{s i n (2 \sqrt{2})}{2^{3}} + \frac{s i n (3 \sqrt{2})}{3^{3}} + . . . = \frac{π^{b} + 1}{a \sqrt{b}} - \frac{π}{b}$ $F i n d a - b$

Question Number 136110 Answers: 0 Comments: 1

An engine is pumping water from a well 25m deep. It discharges 0.4 m^3 of water each second with a velocity of 12 ms^(−1) . Find the power of the pump given that the density of water is 1000 kg m^(−3) . take g = 10 ms^(−2)

$An engine is pumping water from a well 25 m deep . It discharges$ $0.4 m^{3} of water each second with a velocity of 12 {ms}^{- 1} . Find the$ $power of the pump given that the density of water is 1000 kg m^{- 3} .$ $take g = 10 {ms}^{- 2}$

Question Number 135976 Answers: 1 Comments: 0

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