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Question Number 138299 Answers: 2 Comments: 0

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Given x≠y and x^2 =25x+y, y^2 =x+25y solve for the value of (√(x^2 +y^2 +1)) without using calculators or tools. Show your method.

$${Given}\:{x}\neq{y}\:{and}\:{x}^{\mathrm{2}} =\mathrm{25}{x}+{y},\:{y}^{\mathrm{2}} ={x}+\mathrm{25}{y}\: \\ $$$${solve}\:{for}\:{the}\:{value}\:{of}\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\mathrm{1}}\:{without}\: \\ $$$${using}\:{calculators}\:{or}\:{tools}. \\ $$$${Show}\:{your}\:{method}. \\ $$

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y^2 −x^2 =5(y−x)^2 . Find x:y

$${y}^{\mathrm{2}} −{x}^{\mathrm{2}} =\mathrm{5}\left({y}−{x}\right)^{\mathrm{2}} .\:{Find}\:{x}:{y} \\ $$

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The sum of the squares of two consecutive odd numbers is 130. Find the larger number.

$${The}\:{sum}\:{of}\:{the}\:{squares}\:{of}\:{two}\:{consecutive} \\ $$$${odd}\:{numbers}\:{is}\:\mathrm{130}.\:{Find}\:{the}\:{larger}\:{number}. \\ $$

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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)

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

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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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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!

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

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