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AlgebraQuestion and Answers: Page 349

Question Number 18779 Answers: 0 Comments: 2

If (1/(2x))+(1/2)((1/(2x))+(1/2)((1/(2x))+(1/2)((1/(2x))+......=y what does x equals? a)1/2 b)2/4 c)1 d)1/4

$$\mathrm{If}\:\:\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2x}}+......=\mathrm{y}\right.\right.\right. \\ $$$$\mathrm{what}\:\mathrm{does}\:\mathrm{x}\:\mathrm{equals}? \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\mathrm{1}/\mathrm{2} \\ $$$$\left.\mathrm{b}\right)\mathrm{2}/\mathrm{4} \\ $$$$\left.\mathrm{c}\right)\mathrm{1} \\ $$$$\left.\mathrm{d}\right)\mathrm{1}/\mathrm{4} \\ $$

Question Number 18704 Answers: 1 Comments: 0

Question Number 18640 Answers: 1 Comments: 1

Question Number 18606 Answers: 0 Comments: 0

(1/3)+(3/(3×7))+(5/(3×7×11))+(7/(3×7×11×15))+...n terms

$$\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{3}×\mathrm{7}}+\frac{\mathrm{5}}{\mathrm{3}×\mathrm{7}×\mathrm{11}}+\frac{\mathrm{7}}{\mathrm{3}×\mathrm{7}×\mathrm{11}×\mathrm{15}}+...{n}\: \\ $$$$\:{terms} \\ $$

Question Number 19236 Answers: 1 Comments: 0

Question Number 18432 Answers: 1 Comments: 0

Find interval p so (p − 2)x^2 + 2px + p − 1 = 0 have negative roots

$$\mathrm{Find}\:\mathrm{interval}\:{p}\:\mathrm{so} \\ $$$$\left({p}\:−\:\mathrm{2}\right){x}^{\mathrm{2}} \:+\:\mathrm{2}{px}\:+\:{p}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\mathrm{have}\:\mathrm{negative}\:\mathrm{roots} \\ $$

Question Number 18392 Answers: 1 Comments: 1

Question Number 18388 Answers: 1 Comments: 0

Solve simultaneously. x + y = 5 ....... (i) 5^x + y = 15 ...... (ii)

$$\mathrm{Solve}\:\mathrm{simultaneously}.\: \\ $$$$\mathrm{x}\:+\:\mathrm{y}\:=\:\mathrm{5}\:\:\:\:\:.......\:\left(\mathrm{i}\right) \\ $$$$\mathrm{5}^{\mathrm{x}} \:+\:\mathrm{y}\:=\:\mathrm{15}\:\:\:\:......\:\left(\mathrm{ii}\right) \\ $$

Question Number 18386 Answers: 1 Comments: 1

Prove that ((2 + (√5)))^(1/3) + ((2 − (√5)))^(1/3) is a rational number.

$$\mathrm{Prove}\:\mathrm{that}\:\sqrt[{\mathrm{3}}]{\mathrm{2}\:+\:\sqrt{\mathrm{5}}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{2}\:−\:\sqrt{\mathrm{5}}}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{rational}\:\mathrm{number}. \\ $$

Question Number 18369 Answers: 1 Comments: 0

Prove that a^4 + b^4 + c^4 ≥ abc(a + b + c)

$$\mathrm{Prove}\:\mathrm{that}\:{a}^{\mathrm{4}} \:+\:{b}^{\mathrm{4}} \:+\:{c}^{\mathrm{4}} \:\geqslant\:{abc}\left({a}\:+\:{b}\:+\:{c}\right) \\ $$

Question Number 18299 Answers: 0 Comments: 2

x^x^x = 2, find x

$$\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \:=\:\mathrm{2},\:\:\:\:\:\:\mathrm{find}\:\:\mathrm{x} \\ $$

Question Number 18247 Answers: 0 Comments: 0

(((x+1)(x−1))/(x^2 +2x+3))

$$\frac{\left({x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}} \\ $$

Question Number 18152 Answers: 0 Comments: 0

Question Number 18149 Answers: 1 Comments: 2

Question Number 18053 Answers: 0 Comments: 5

Question Number 17997 Answers: 0 Comments: 0

Solve on Z_(18) { (([6]_(18) x+[7]_(18) y=[1]_(18) )),(([2]_(18) x+[3]_(18) y=[11]_(18) )) :}

$${Solve}\:{on}\:\mathbb{Z}_{\mathrm{18}} \\ $$$$\begin{cases}{\left[\mathrm{6}\right]_{\mathrm{18}} {x}+\left[\mathrm{7}\right]_{\mathrm{18}} {y}=\left[\mathrm{1}\right]_{\mathrm{18}} }\\{\left[\mathrm{2}\right]_{\mathrm{18}} {x}+\left[\mathrm{3}\right]_{\mathrm{18}} {y}=\left[\mathrm{11}\right]_{\mathrm{18}} }\end{cases} \\ $$

Question Number 17985 Answers: 1 Comments: 0

solve simultaneously. x^3 + y^3 = 35 x^4 + y^4 = 97

$$\mathrm{solve}\:\mathrm{simultaneously}. \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{35} \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\mathrm{y}^{\mathrm{4}} \:=\:\mathrm{97} \\ $$

Question Number 17775 Answers: 2 Comments: 0

Σ_(m=1) ^(10) (((sin 2πm)/(11)) − i((cos 2πm)/(11))) =????? Solve..it

$$\underset{{m}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\left(\frac{\mathrm{sin}\:\mathrm{2}\pi{m}}{\mathrm{11}}\:−\:{i}\frac{\mathrm{cos}\:\mathrm{2}\pi{m}}{\mathrm{11}}\right)\:=????? \\ $$$${Solve}..{it} \\ $$$$ \\ $$

Question Number 17759 Answers: 1 Comments: 0

2^(4(y^2 −2)) =y^((y^2 −8)) please help me find y... pls!

$$\mathrm{2}^{\mathrm{4}\left(\mathrm{y}^{\mathrm{2}} −\mathrm{2}\right)} =\mathrm{y}^{\left(\mathrm{y}^{\mathrm{2}} −\mathrm{8}\right)} \\ $$$$ \\ $$$$ \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{find}\:\mathrm{y}...\:\mathrm{pls}! \\ $$

Question Number 17742 Answers: 1 Comments: 1

x^3 = 3^x , find x.

$$\mathrm{x}^{\mathrm{3}} \:=\:\mathrm{3}^{\mathrm{x}} ,\:\:\:\mathrm{find}\:\mathrm{x}. \\ $$

Question Number 17740 Answers: 0 Comments: 1

Question Number 17638 Answers: 0 Comments: 4

please help me with this confusing question x^(2x/y) ×y^(y/x) =4......(1) (xy)^(xy+yx) =16.....(2) solve for x and y

$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{this} \\ $$$$\mathrm{confusing}\:\mathrm{question} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2x}/\mathrm{y}} ×\mathrm{y}^{\mathrm{y}/\mathrm{x}} =\mathrm{4}......\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\left(\mathrm{xy}\right)^{\mathrm{xy}+\mathrm{yx}} =\mathrm{16}.....\left(\mathrm{2}\right) \\ $$$$ \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$

Question Number 17576 Answers: 1 Comments: 0

solve the equation x^y =y^x .......(1) x^2 =y^3 .......(2)

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{y}} =\mathrm{y}^{\mathrm{x}} .......\left(\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{x}^{\mathrm{2}} =\mathrm{y}^{\mathrm{3}} .......\left(\mathrm{2}\right) \\ $$

Question Number 17575 Answers: 0 Comments: 3

Question Number 17454 Answers: 1 Comments: 0

Find all integers n such that (n^2 − n − 1)^(n + 2) = 1

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{integers}\:{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left({n}^{\mathrm{2}} \:−\:{n}\:−\:\mathrm{1}\right)^{{n}\:+\:\mathrm{2}} \:=\:\mathrm{1} \\ $$

Question Number 17279 Answers: 0 Comments: 3

Is cosh^2 (3x) = (1/2)[1 + cos(6x)] ??????

$$\mathrm{Is}\:\:\mathrm{cosh}^{\mathrm{2}} \left(\mathrm{3x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{1}\:+\:\mathrm{cos}\left(\mathrm{6x}\right)\right]\:\:?????? \\ $$

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