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Question Number 137637 Answers: 0 Comments: 0

Prove or disprove ((cos(1+(1/( (√3))))𝛑)/1^2 )+((cos(1+(1/( (√3))))2π)/2^2 )+((cos(1+(1/( (√3))))3π)/3^2 )+...=0

$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{disprove}} \\ $$$$\frac{{cos}\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\right)\boldsymbol{\pi}}{\mathrm{1}^{\mathrm{2}} }+\frac{{cos}\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\right)\mathrm{2}\pi}{\mathrm{2}^{\mathrm{2}} }+\frac{{cos}\left(\mathrm{1}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}\right)\mathrm{3}\pi}{\mathrm{3}^{\mathrm{2}} }+...=\mathrm{0} \\ $$

Question Number 137634 Answers: 1 Comments: 0

x=2^(p ) and y=2^(q ) . Evaluate in terms of x and/ or y (i)2^(p+q) (ii) 2^(2q ) (iii) 2^(p−1)

$${x}=\mathrm{2}^{{p}\:} {and}\:{y}=\mathrm{2}^{{q}\:} .\:{Evaluate}\:{in}\:{terms}\:{of}\:{x}\:{and}/\:{or}\:{y}\: \\ $$$$\left({i}\right)\mathrm{2}^{{p}+{q}} \:\:\left({ii}\right)\:\mathrm{2}^{\mathrm{2}{q}\:} \:\:\:\left({iii}\right)\:\mathrm{2}^{{p}−\mathrm{1}} \\ $$

Question Number 137618 Answers: 1 Comments: 2

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Question Number 137528 Answers: 3 Comments: 1

Question Number 137437 Answers: 2 Comments: 0

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Question Number 137353 Answers: 1 Comments: 0

If 75% of 68 is the same as 85% of n, find n.

$$\mathrm{If}\:\mathrm{75\%}\:\mathrm{of}\:\mathrm{68}\:\mathrm{is}\:\mathrm{the}\:\mathrm{same}\:\mathrm{as}\:\mathrm{85\%}\:\mathrm{of}\:\mathrm{n},\:\mathrm{find}\:\mathrm{n}. \\ $$

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Question Number 137316 Answers: 0 Comments: 0

An alternating current after passing through rectifire has the form i=I_0 sinx for 0≤x≤π =0 for π≤x≤2π where I_0 is the maximum current and period is 2π.express i is a fourire series and evaluate (1/(1.3))+(1/(3.5))+(1/(5.7))+.........∞

$${An}\:{alternating}\:{current}\:{after}\:{passing}\: \\ $$$$\:{through}\:{rectifire}\:{has}\:{the} \\ $$$${form}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{i}={I}_{\mathrm{0}} {sinx}\:\:\:\:\:\:{for}\:\mathrm{0}\leqslant{x}\leqslant\pi \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\:{for}\:\pi\leqslant{x}\leqslant\mathrm{2}\pi \\ $$$${where}\:{I}_{\mathrm{0}} \:{is}\:{the}\:{maximum}\:{current}\: \\ $$$${and}\:{period}\:{is}\:\mathrm{2}\pi.{express}\:{i}\:{is}\:{a}\: \\ $$$${fourire}\:{series}\:{and}\:{evaluate} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}.\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}.\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{5}.\mathrm{7}}+.........\infty \\ $$

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.

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

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!

$${Some}\:{useful}\:{approximations}\:{of}\:{sine}\:{function} \\ $$$${sin}\left(\frac{\pi}{\mathrm{7}}\right)=\frac{\mathrm{96}}{\mathrm{221}} \\ $$$${sin}\left(\frac{\pi}{\mathrm{9}}\right)=\frac{\mathrm{128}}{\mathrm{373}} \\ $$$${sin}\left(\frac{\pi}{\mathrm{11}}\right)=\frac{\mathrm{32}}{\mathrm{113}} \\ $$$$... \\ $$$${I}\:{am}\:{counting}\:{more}\:..{thanking}\:{you}! \\ $$

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!))−....

$$\mathrm{1}−\left(\frac{\mathrm{1}.\mathrm{1}.\mathrm{3}}{\mathrm{2}.\mathrm{3}.\mathrm{4}}\right)\frac{\mathrm{1}}{\mathrm{1}!}+\left(\frac{\mathrm{3}.\mathrm{3}.\mathrm{7}}{\mathrm{2}^{\mathrm{2}} .\mathrm{3}^{\mathrm{2}} .\mathrm{4}^{\mathrm{2}} }\right)\frac{\mathrm{1}}{\mathrm{2}!}−\left(\frac{\mathrm{5}.\mathrm{7}.\mathrm{10}}{\mathrm{2}^{\mathrm{3}} .\mathrm{3}^{\mathrm{3}} .\mathrm{4}^{\mathrm{3}} }\right)\frac{\mathrm{1}}{\mathrm{3}!}−.... \\ $$

Question Number 137016 Answers: 1 Comments: 0

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Question Number 136892 Answers: 1 Comments: 0

∫(d^2 y/dx^2 )dy

$$\int\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }{dy} \\ $$$$ \\ $$

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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

$$\underset{{n}=−\infty} {\overset{\infty} {\sum}}{a}^{\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}} {b}^{\frac{{n}\left({n}−\mathrm{1}\right)}{\mathrm{2}}} =\mathrm{1}+\sqrt{\frac{\mathrm{2}{a}^{\mathrm{2}} }{\pi}}\int_{\mathrm{0}} ^{\infty} {e}^{−{t}^{\mathrm{2}} /\mathrm{2}} \left(\frac{\mathrm{1}−{a}\sqrt{{ab}}\:{cosh}\left(\sqrt{{log}\left({ab}\right)}\:{t}\right)}{{a}^{\mathrm{3}} {b}−\mathrm{2}{a}\sqrt{{ab}\:}\:{cosh}\left(\sqrt{{log}\left({ab}\right)}\:{t}\right)}\right){dt} \\ $$

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∫_0 ^1 Π_(n=1) ^∞ (1−q^n )dq

$$\int_{\mathrm{0}} ^{\mathrm{1}} \underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}−{q}^{{n}} \right){dq} \\ $$

Question Number 136761 Answers: 1 Comments: 1

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