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AlgebraQuestion and Answers: Page 289

Question Number 77377 Answers: 0 Comments: 0

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Question Number 77313 Answers: 0 Comments: 4

x + y + z = 1 x^2 + y^2 + z^2 = 2 x^3 + y^3 + z^3 = 3 find x^8 + y^8 +z^8

$$\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{1} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{2} \\ $$$$\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{y}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \:=\:\mathrm{3} \\ $$$$ \\ $$$$\mathrm{find}\:\mathrm{x}^{\mathrm{8}} \:+\:\mathrm{y}^{\mathrm{8}} \:+\mathrm{z}^{\mathrm{8}} \\ $$

Question Number 77219 Answers: 1 Comments: 0

if log_9 (a)=log_4 (a+b)=log_6 (b) what is (a/b) ?

$${if}\:\mathrm{log}_{\mathrm{9}} \left({a}\right)=\mathrm{log}_{\mathrm{4}} \left({a}+{b}\right)=\mathrm{log}_{\mathrm{6}} \left({b}\right)\: \\ $$$${what}\:{is}\:\frac{{a}}{{b}}\:? \\ $$

Question Number 77204 Answers: 0 Comments: 2

is there a general solution for the equation x[x[x[x...]]]_(n times x) =m with x>0, m>0.

$${is}\:{there}\:{a}\:{general}\:{solution}\:{for} \\ $$$${the}\:{equation} \\ $$$$\underset{{n}\:{times}\:{x}} {\boldsymbol{{x}}\left[\boldsymbol{{x}}\left[\boldsymbol{{x}}\left[\boldsymbol{{x}}...\right]\right]\right]}=\boldsymbol{{m}} \\ $$$${with}\:{x}>\mathrm{0},\:{m}>\mathrm{0}. \\ $$

Question Number 77183 Answers: 1 Comments: 0

what is x satisfy inequality 3^x^2 × 5^(x−1) ≥ 3

$$\mathrm{what}\:\mathrm{is}\:\mathrm{x}\: \\ $$$$\mathrm{satisfy}\:\mathrm{inequality}\: \\ $$$$\mathrm{3}^{\mathrm{x}^{\mathrm{2}} } ×\:\mathrm{5}^{\mathrm{x}−\mathrm{1}} \:\geqslant\:\mathrm{3} \\ $$

Question Number 77154 Answers: 0 Comments: 6

Question Number 77119 Answers: 2 Comments: 0

suppose the equations x^2 +px+4=0 and x^2 +qx+3=0 have a common root, write this root in terms of the other root.

$${suppose}\:{the}\:{equations}\:{x}^{\mathrm{2}} +{px}+\mathrm{4}=\mathrm{0} \\ $$$${and}\:{x}^{\mathrm{2}} +{qx}+\mathrm{3}=\mathrm{0}\:\:{have}\:{a}\:{common}\:{root}, \\ $$$${write}\:{this}\:{root}\:{in}\:{terms}\:{of}\:{the}\:{other}\:{root}. \\ $$

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Question Number 77046 Answers: 1 Comments: 0

x=R^2 (√(1−(t^2 /R^2 )))

$${x}={R}^{\mathrm{2}} \sqrt{\mathrm{1}−\frac{{t}^{\mathrm{2}} }{{R}^{\mathrm{2}} }}\: \\ $$

Question Number 77035 Answers: 1 Comments: 0

Solve for x in: (i) (2(x+3)−3(x−2))(2x−1)≥0 (ii)(x−1)(2x+3)(x+1)(x+3)≤1

$${Solve}\:{for}\:{x}\:{in}: \\ $$$$\left({i}\right)\:\left(\mathrm{2}\left({x}+\mathrm{3}\right)−\mathrm{3}\left({x}−\mathrm{2}\right)\right)\left(\mathrm{2}{x}−\mathrm{1}\right)\geqslant\mathrm{0} \\ $$$$\left({ii}\right)\left({x}−\mathrm{1}\right)\left(\mathrm{2}{x}+\mathrm{3}\right)\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right)\leqslant\mathrm{1} \\ $$

Question Number 77033 Answers: 0 Comments: 1

Suppose the population models of London and Hongkong in tens of thousands are p(t)=((20t)/(t+1)) and q(t)=((240t)/(t+8)) respectively for t years after 2015, Determine the time period in years when the population of London exceeds that of HongKong.

$${Suppose}\:{the}\:{population}\:{models}\:{of}\:{London} \\ $$$${and}\:{Hongkong}\:{in}\:{tens}\:{of}\:{thousands}\:{are} \\ $$$${p}\left({t}\right)=\frac{\mathrm{20}{t}}{{t}+\mathrm{1}}\:{and}\:{q}\left({t}\right)=\frac{\mathrm{240}{t}}{{t}+\mathrm{8}}\:{respectively}\:{for} \\ $$$${t}\:{years}\:{after}\:\mathrm{2015},\:{Determine}\:{the}\:{time}\:{period} \\ $$$${in}\:{years}\:{when}\:{the}\:{population}\:{of}\:{London} \\ $$$${exceeds}\:{that}\:{of}\:{HongKong}. \\ $$

Question Number 77028 Answers: 1 Comments: 0

Question Number 77024 Answers: 1 Comments: 0

The possible value of p for which graph of the function f(x)=2p^2 − 3ptan x+tan^2 x+1 does not lie below x-axis for all x∈(((−Π)/2),(Π/2)) is (a)0 (b)4 (c)3 (d)8

$$\mathrm{The}\:\mathrm{possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}\:\mathrm{for}\:\mathrm{which}\: \\ $$$$\mathrm{graph}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2p}^{\mathrm{2}} − \\ $$$$\mathrm{3ptan}\:\mathrm{x}+\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}\:\mathrm{does}\:\mathrm{not}\:\mathrm{lie}\:\mathrm{below}\: \\ $$$$\mathrm{x}-\mathrm{axis}\:\mathrm{for}\:\mathrm{all}\:\mathrm{x}\in\left(\frac{−\Pi}{\mathrm{2}},\frac{\Pi}{\mathrm{2}}\right)\:\mathrm{is} \\ $$$$\left(\mathrm{a}\right)\mathrm{0}\:\:\:\:\:\:\left(\mathrm{b}\right)\mathrm{4}\:\:\:\:\:\:\:\:\left(\mathrm{c}\right)\mathrm{3}\:\:\:\:\:\:\:\:\left(\mathrm{d}\right)\mathrm{8} \\ $$

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Question Number 76904 Answers: 1 Comments: 2

montrer que: ∀x,y,z>0 x^3 +2y^2 +4z≥6xy^(2/3) z^(1/3)

$$\mathrm{montrer}\:\mathrm{que}: \\ $$$$\forall{x},{y},{z}>\mathrm{0}\:\:{x}^{\mathrm{3}} +\mathrm{2}{y}^{\mathrm{2}} +\mathrm{4}{z}\geqslant\mathrm{6}{xy}^{\mathrm{2}/\mathrm{3}} {z}^{\mathrm{1}/\mathrm{3}} \\ $$

Question Number 76883 Answers: 0 Comments: 1

what is the perimeter of the loop? 3ay^2 = x(x−3a)^(2 ) ?

$${what}\:{is}\:{the}\:{perimeter}\:{of}\:{the}\:{loop}? \\ $$$$\mathrm{3}{ay}^{\mathrm{2}} \:=\:{x}\left({x}−\mathrm{3}{a}\right)^{\mathrm{2}\:} ? \\ $$

Question Number 76880 Answers: 0 Comments: 2

(((c/5)−7)/5) −2= 5 Intead of 5 what else could be there?

$$\frac{\frac{{c}}{\mathrm{5}}−\mathrm{7}}{\mathrm{5}}\:−\mathrm{2}=\:\mathrm{5} \\ $$$${Intead}\:{of}\:\mathrm{5}\:{what}\:{else}\:{could}\:{be} \\ $$$${there}? \\ $$

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Question Number 76794 Answers: 1 Comments: 1

Find the sum of x + (x/(1+x)) + (x/((1+x)^2 )) + (x/((1+x)^3 ))+.... for ∣(1/(1+x))∣<1

$${Find}\:{the}\:{sum}\:{of} \\ $$$${x}\:+\:\frac{{x}}{\mathrm{1}+{x}}\:+\:\frac{{x}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }\:+\:\frac{{x}}{\left(\mathrm{1}+{x}\right)^{\mathrm{3}} }+....\:{for} \\ $$$$\mid\frac{\mathrm{1}}{\mathrm{1}+{x}}\mid<\mathrm{1} \\ $$

Question Number 76793 Answers: 2 Comments: 2

The sum of the first n terms of a series is given by: S_n =n^2 +7n+2. (i)Find a formula for the nth term (ii)write down the first 5 terms of the sequence

$${The}\:{sum}\:{of}\:{the}\:{first}\:{n}\:{terms}\:{of}\:{a}\:{series} \\ $$$${is}\:{given}\:{by}:\:{S}_{{n}} ={n}^{\mathrm{2}} +\mathrm{7}{n}+\mathrm{2}. \\ $$$$\left({i}\right){Find}\:{a}\:{formula}\:{for}\:{the}\:{nth}\:{term} \\ $$$$\left({ii}\right){write}\:{down}\:{the}\:{first}\:\mathrm{5}\:{terms}\:{of}\:{the} \\ $$$${sequence} \\ $$$$ \\ $$

Question Number 76777 Answers: 0 Comments: 0

prove that ((cos(40°)))^(1/3) + ((cos(80°)))^(1/3) − ((cos(20°)))^(1/3) =(((3/2)((9)^(1/3) −2)))^(1/3)

$${prove}\:{that} \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{{cos}\left(\mathrm{40}°\right)}\:+\:\sqrt[{\mathrm{3}}]{{cos}\left(\mathrm{80}°\right)}\:−\:\sqrt[{\mathrm{3}}]{{cos}\left(\mathrm{20}°\right)}\:=\sqrt[{\mathrm{3}}]{\frac{\mathrm{3}}{\mathrm{2}}\left(\sqrt[{\mathrm{3}}]{\mathrm{9}}−\mathrm{2}\right)} \\ $$

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