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AlgebraQuestion and Answers: Page 91

Question Number 184095 Answers: 2 Comments: 0

Question Number 184085 Answers: 1 Comments: 0

(y^2 + xy^2 )y^′ + x^2 − yx^2 = 0

$$\left(\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{xy}^{\mathrm{2}} \right)\mathrm{y}^{'} \:+\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{yx}^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$ \\ $$

Question Number 184084 Answers: 1 Comments: 0

Question Number 184083 Answers: 1 Comments: 0

f(x)= x^( 3) +3x^( 2) −ax is decreasing on [ −1 , 2] then which is correct... 1: [ −3 ,24] 2: [ 24 , +∞) 3: (−∞ ,−3] 4 :(−∞, −3]∪[24, +∞)

$$ \\ $$$$\:\:\:\:{f}\left({x}\right)=\:{x}^{\:\mathrm{3}} \:+\mathrm{3}{x}^{\:\mathrm{2}} −{ax}\:\:\:{is}\:\: \\ $$$$\:\:\:\:\:{decreasing}\:{on}\:\:\left[\:−\mathrm{1}\:,\:\mathrm{2}\right] \\ $$$$\:\:\:\:\:\:{then}\:\:{which}\:\:{is}\:{correct}... \\ $$$$\:\:\:\:\:\mathrm{1}:\:\:\:\left[\:−\mathrm{3}\:,\mathrm{24}\right] \\ $$$$\:\:\:\:\:\mathrm{2}:\:\:\left[\:\mathrm{24}\:,\:+\infty\right) \\ $$$$\:\:\:\:\:\:\mathrm{3}:\:\left(−\infty\:,−\mathrm{3}\right] \\ $$$$\:\:\:\:\:\:\:\:\mathrm{4}\::\left(−\infty,\:−\mathrm{3}\right]\cup\left[\mathrm{24},\:+\infty\right) \\ $$$$ \\ $$

Question Number 184019 Answers: 1 Comments: 2

{ ((y^x = 64)),((y^((x + 1)/(x − 1)) = 16)) :} find “x”

$$\begin{cases}{{y}^{{x}} =\:\mathrm{64}}\\{{y}^{\frac{{x}\:+\:\mathrm{1}}{{x}\:−\:\mathrm{1}}} \:=\:\mathrm{16}}\end{cases} \\ $$$$\:{find}\:``{x}'' \\ $$

Question Number 183864 Answers: 4 Comments: 2

Question Number 183848 Answers: 2 Comments: 1

Question Number 183847 Answers: 5 Comments: 0

Question Number 183846 Answers: 4 Comments: 0

Question Number 183843 Answers: 1 Comments: 0

Question Number 183835 Answers: 2 Comments: 0

Resoudre le systeme abc =30 a+b+c =10 ab+bc+ac=31

$${Resoudre}\:{le}\:{systeme} \\ $$$$\:\:\mathrm{abc}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{30} \\ $$$$\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}\:\:\:\:\:\:\:=\mathrm{10} \\ $$$$\:\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ac}=\mathrm{31} \\ $$$$ \\ $$

Question Number 183825 Answers: 1 Comments: 0

solve for x by using lambert function 2^x +3x=8

$${solve}\:{for}\:{x}\:{by}\:{using}\:{lambert}\:{function} \\ $$$$\mathrm{2}^{{x}} +\mathrm{3}{x}=\mathrm{8} \\ $$

Question Number 183777 Answers: 2 Comments: 1

Question Number 183769 Answers: 0 Comments: 4

solve for x: x^x^x =2^(2048) by using lambert function

$${solve}\:{for}\:{x}: \\ $$$${x}^{{x}^{{x}} } =\mathrm{2}^{\mathrm{2048}} \\ $$$${by}\:{using}\:{lambert}\:{function} \\ $$

Question Number 183756 Answers: 2 Comments: 0

solve for x by using lambert function x^2 =16^x

$${solve}\:{for}\:{x}\:{by}\:{using}\:{lambert}\:{function} \\ $$$${x}^{\mathrm{2}} =\mathrm{16}^{{x}} \\ $$

Question Number 183669 Answers: 4 Comments: 0

f(x)= (x/(1 + x + x^( 2) )) min_( f) = ?

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\frac{{x}}{\mathrm{1}\:+\:{x}\:+\:{x}^{\:\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:{min}_{\:{f}} \:=\:? \\ $$

Question Number 183668 Answers: 1 Comments: 1

x , y , z ∈R: If { (((1/x) +(1/(y+z)) =(1/2))),(((1/y) +(1/(x+z)) = (1/3))),(((1/z_ ) +(1/(x+y)) =(1/4))) :} ⇒ x , y , z =?

$$ \\ $$$$\:\:\:\:\:\:{x}\:,\:{y}\:,\:{z}\:\in\mathbb{R}: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\mathrm{If}\:\:\:\:\begin{cases}{\frac{\mathrm{1}}{{x}}\:+\frac{\mathrm{1}}{{y}+{z}}\:=\frac{\mathrm{1}}{\mathrm{2}}}\\{\frac{\mathrm{1}}{{y}}\:+\frac{\mathrm{1}}{{x}+{z}}\:=\:\frac{\mathrm{1}}{\mathrm{3}}}\\{\frac{\mathrm{1}}{{z}_{\:} }\:+\frac{\mathrm{1}}{{x}+{y}}\:=\frac{\mathrm{1}}{\mathrm{4}}}\end{cases} \\ $$$$\:\:\:\:\:\:\:\Rightarrow\:\:\:\:{x}\:,\:{y}\:,\:{z}\:=? \\ $$$$ \\ $$

Question Number 183660 Answers: 3 Comments: 0

what is larger, 2022^(2022) or 2021^(2023) ?

$${what}\:{is}\:{larger}, \\ $$$$\mathrm{2022}^{\mathrm{2022}} \:{or}\:\mathrm{2021}^{\mathrm{2023}} \:? \\ $$

Question Number 183556 Answers: 1 Comments: 0

Question Number 183424 Answers: 0 Comments: 0

Among the natural numbers not greater than 22 , the probability that the modulus of the difference of any two of the 3 randomly selected numbers is greater than 5 is equal to which of the following? a)15/22 b)1/7 c)1/22 d)1

$$\mathrm{Among}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{numbers}\:\mathrm{not} \\ $$$$\mathrm{greater}\:\mathrm{than}\:\mathrm{22}\:,\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{modulus}\:\mathrm{of}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{any}\: \\ $$$$\mathrm{two}\:\mathrm{of}\:\mathrm{the}\:\mathrm{3}\:\mathrm{randomly}\:\mathrm{selected}\:\mathrm{numbers} \\ $$$$\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{5}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{which}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}? \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{1}\left.\mathrm{5}/\mathrm{22}\:\:\:\mathrm{b}\right)\mathrm{1}/\mathrm{7}\:\:\:\mathrm{c}\right)\mathrm{1}/\mathrm{22}\:\:\:\mathrm{d}\right)\mathrm{1} \\ $$

Question Number 183381 Answers: 1 Comments: 2

((3n^5 + 4n^4 − 7n^3 + 5n^2 − 5)/(n + 1)) There can be no residue: a)0 b)2 c)4 d)5 e)9

$$\frac{\mathrm{3n}^{\mathrm{5}} \:+\:\mathrm{4n}^{\mathrm{4}} \:−\:\mathrm{7n}^{\mathrm{3}} \:+\:\mathrm{5n}^{\mathrm{2}} \:−\:\mathrm{5}}{\mathrm{n}\:+\:\mathrm{1}} \\ $$$$\mathrm{There}\:\mathrm{can}\:\mathrm{be}\:\mathrm{no}\:\mathrm{residue}: \\ $$$$\left.\mathrm{a}\left.\right)\left.\mathrm{0}\left.\:\left.\:\:\mathrm{b}\right)\mathrm{2}\:\:\:\mathrm{c}\right)\mathrm{4}\:\:\:\mathrm{d}\right)\mathrm{5}\:\:\:\mathrm{e}\right)\mathrm{9} \\ $$

Question Number 183380 Answers: 0 Comments: 1

a>0 , b>0 { (((x−1)^2 + (y−7)^2 = a^2 )),(((x−2)^2 + (y−3)^2 = b^2 )) :} Find: (a+b)_(min) = ?

$$\mathrm{a}>\mathrm{0}\:,\:\mathrm{b}>\mathrm{0} \\ $$$$\begin{cases}{\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} \:+\:\left(\mathrm{y}−\mathrm{7}\right)^{\mathrm{2}} \:=\:\mathrm{a}^{\mathrm{2}} }\\{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} \:+\:\left(\mathrm{y}−\mathrm{3}\right)^{\mathrm{2}} \:=\:\mathrm{b}^{\mathrm{2}} }\end{cases} \\ $$$$\mathrm{Find}:\:\:\:\left(\mathrm{a}+\mathrm{b}\right)_{\boldsymbol{\mathrm{min}}} \:=\:? \\ $$

Question Number 183592 Answers: 1 Comments: 0

{ (((√(x/y)) +(√(y/z)) +(√(z/x)) = 3)),(((√(y/x)) +(√(z/y)) +(√(x/z)) = 3)),(((√(xyz)) = 1)) :}

$$\:\:\:\:\:\begin{cases}{\sqrt{\frac{{x}}{{y}}}\:+\sqrt{\frac{{y}}{{z}}}\:+\sqrt{\frac{{z}}{{x}}}\:=\:\mathrm{3}}\\{\sqrt{\frac{{y}}{{x}}}\:+\sqrt{\frac{{z}}{{y}}}\:+\sqrt{\frac{{x}}{{z}}}\:=\:\mathrm{3}}\\{\sqrt{{xyz}}\:=\:\mathrm{1}}\end{cases} \\ $$$$\: \\ $$$$ \\ $$

Question Number 183366 Answers: 0 Comments: 2

6 of the 23 given points in the plane lie on a circle. Let n be the number of circles passing through at least 3 of these points. What is the maximum number of n?

$$\mathrm{6}\:\mathrm{of}\:\mathrm{the}\:\mathrm{23}\:\mathrm{given}\:\mathrm{points}\:\mathrm{in}\:\mathrm{the}\:\mathrm{plane} \\ $$$$\mathrm{lie}\:\mathrm{on}\:\mathrm{a}\:\mathrm{circle}.\:\mathrm{Let}\:\boldsymbol{\mathrm{n}}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of} \\ $$$$\mathrm{circles}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:\mathrm{of} \\ $$$$\mathrm{these}\:\mathrm{points}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{number}\:\mathrm{of}\:\boldsymbol{\mathrm{n}}? \\ $$

Question Number 183363 Answers: 1 Comments: 0

Find: 2003∙2005^3 −2004∙2002^3

$$\mathrm{Find}: \\ $$$$\mathrm{2003}\centerdot\mathrm{2005}^{\mathrm{3}} −\mathrm{2004}\centerdot\mathrm{2002}^{\mathrm{3}} \\ $$

Question Number 183354 Answers: 0 Comments: 2

Given three point.Find the for the plane through the point P(0,1,0) Q(3,1,4) R(−1,0,1)

$${Given}\:{three}\:{point}.{Find}\:{the} \\ $$$${for}\:{the}\:{plane}\:\:{through}\:{the}\:{point} \\ $$$${P}\left(\mathrm{0},\mathrm{1},\mathrm{0}\right)\:\:{Q}\left(\mathrm{3},\mathrm{1},\mathrm{4}\right)\:\:{R}\left(−\mathrm{1},\mathrm{0},\mathrm{1}\right) \\ $$

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