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Question Number 183382 Answers: 2 Comments: 4

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 183594 Answers: 1 Comments: 0

log _(0.5) (√(1+x)) + 3log _(0.25) (1−x)= log _(1/16) (1−x^2 )^2 +2

$$\:\:\:\:\:\mathrm{log}\:_{\mathrm{0}.\mathrm{5}} \:\sqrt{\mathrm{1}+{x}}\:+\:\mathrm{3log}\:_{\mathrm{0}.\mathrm{25}} \left(\mathrm{1}−{x}\right)=\:\mathrm{log}\:_{\mathrm{1}/\mathrm{16}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{2}} +\mathrm{2}\: \\ $$

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 183376 Answers: 2 Comments: 1

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 183426 Answers: 2 Comments: 3

surface de la partie bleu du graphe?

$${surface}\:{de}\:{la}\:{partie}\:{bleu} \\ $$$${du}\:{graphe}? \\ $$

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)

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

Question Number 183353 Answers: 1 Comments: 0

For the function f(x)= { ((x^2 −3 if x<4)),(((x^2 /(x+4)) if x≥4)) :} Find (i) lim_(x→−4) f(x) ii)lim_(x→+4) f(x)

$${For}\:{the}\:{function} \\ $$$${f}\left({x}\right)=\begin{cases}{{x}^{\mathrm{2}} −\mathrm{3}\:{if}\:{x}<\mathrm{4}}\\{\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{4}}\:\:\:\:\:{if}\:{x}\geqslant\mathrm{4}}\end{cases} \\ $$$$\left.{Find}\:\left({i}\right)\:\underset{{x}\rightarrow−\mathrm{4}} {\mathrm{lim}}\:{f}\left({x}\right)\:\:\:\:\:\:{ii}\right)\underset{{x}\rightarrow+\mathrm{4}} {\mathrm{lim}}\:{f}\left({x}\right) \\ $$

Question Number 183352 Answers: 0 Comments: 0

For the function f(x)= { ((1−x^2 if x< 2)),((2x+1 if x≥2)) :} Find (i)lim_(x→^− 2) f(x) (ii) lim_(x→2^+ ) f(x)

$${For}\:{the}\:{function}\: \\ $$$${f}\left({x}\right)=\begin{cases}{\mathrm{1}−{x}^{\mathrm{2}} \:{if}\:{x}<\:\mathrm{2}}\\{\mathrm{2}{x}+\mathrm{1}\:{if}\:{x}\geqslant\mathrm{2}}\end{cases} \\ $$$${Find} \\ $$$$\left({i}\right)\underset{{x}\rightarrow^{−} \mathrm{2}} {\mathrm{lim}}{f}\left({x}\right)\:\:\:\:\:\:\:\left({ii}\right)\:\underset{{x}\rightarrow\mathrm{2}^{+} } {\mathrm{lim}}\:{f}\left({x}\right) \\ $$$$ \\ $$

Question Number 183350 Answers: 3 Comments: 2

Find (a)lim_(x→∞) ((3x+2)/(x^2 −x+1)) (b)lim_(x→∞) ((√(x^2 −1))/(2x+1)) (c)lim_(x→5) (((√(3x+1)) −4)/(x−5))

$${Find}\: \\ $$$$\left({a}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{3}{x}+\mathrm{2}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}} \\ $$$$\left({b}\right)\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}{\mathrm{2}{x}+\mathrm{1}} \\ $$$$\left({c}\right)\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{3}{x}+\mathrm{1}}\:−\mathrm{4}}{{x}−\mathrm{5}} \\ $$

Question Number 183344 Answers: 2 Comments: 1

Question Number 183342 Answers: 3 Comments: 0

Find: 3 − (2/(3 − (2/(3 − (2/(...)))))) = ?

$$\mathrm{Find}:\:\:\:\:\:\mathrm{3}\:−\:\frac{\mathrm{2}}{\mathrm{3}\:−\:\frac{\mathrm{2}}{\mathrm{3}\:−\:\frac{\mathrm{2}}{...}}}\:=\:? \\ $$

Question Number 183330 Answers: 0 Comments: 2

S = sinhx+sinh^2 x + sinh^3 x+...+sinh^n x=?

$$\:\:{S}\:=\:{sinhx}+{sinh}^{\mathrm{2}} {x}\:+\:{sinh}^{\mathrm{3}} {x}+...+{sinh}^{{n}} {x}=? \\ $$

Question Number 183326 Answers: 2 Comments: 1

Question Number 183325 Answers: 1 Comments: 1

Question Number 183324 Answers: 2 Comments: 1

Find the minimum distance between C_f , C_g ; C_f : y^2 = 4ax , C_g : x^2 + y^2 −24ay+ 128a^2 = 0

$${Find}\:{the}\:{minimum}\:{distance}\:{between}\:{C}_{{f}} \:,\:{C}_{{g}} \\ $$$$\:;\:{C}_{{f}} \::\:{y}^{\mathrm{2}} =\:\mathrm{4}{ax}\:,\:{C}_{{g}} :\:{x}^{\mathrm{2}} +\:{y}^{\mathrm{2}} −\mathrm{24}{ay}+\:\mathrm{128}{a}^{\mathrm{2}} =\:\mathrm{0} \\ $$

Question Number 183320 Answers: 1 Comments: 0

∫^(π/2) _0 (dx/(cox(x/2)∙cos(x/2^2 )∙∙∙∙∙cos(x/2^n )))=?

$$\underset{\mathrm{0}} {\int}^{\frac{\pi}{\mathrm{2}}} \frac{{dx}}{{cox}\frac{{x}}{\mathrm{2}}\centerdot{cos}\frac{{x}}{\mathrm{2}^{\mathrm{2}} }\centerdot\centerdot\centerdot\centerdot\centerdot{cos}\frac{{x}}{\mathrm{2}^{{n}} }}=? \\ $$

Question Number 183318 Answers: 0 Comments: 0

Question Number 183307 Answers: 1 Comments: 1

Question Number 183301 Answers: 0 Comments: 3

(((1067)),((249)) )+ (((1067)),((250)) )=?

$$\begin{pmatrix}{\mathrm{1067}}\\{\mathrm{249}}\end{pmatrix}+\begin{pmatrix}{\mathrm{1067}}\\{\mathrm{250}}\end{pmatrix}=? \\ $$

Question Number 183294 Answers: 0 Comments: 0

Question Number 183293 Answers: 1 Comments: 0

Help! A beam being lifted by two forces where F1makes an angle of 23° degrees with the y axis acts in the second quadrant F2 acts in the first quadrant making an angle of 32° degrees with the y axis and the resultant force is 67 N, determine F1 and F2.

$$\: \\ $$$$\:\mathrm{Help}! \\ $$$$\: \\ $$$$\:\mathrm{A}\:\mathrm{beam}\:\mathrm{being}\:\mathrm{lifted}\:\mathrm{by}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{where}\: \\ $$$$\:\mathrm{F1makes}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{23}°\:\mathrm{degrees}\:\mathrm{with}\:\mathrm{the}\:\mathrm{y} \\ $$$$\:\mathrm{axis}\:\mathrm{acts}\:\mathrm{in}\:\mathrm{the}\:\mathrm{second}\:\mathrm{quadrant}\:\mathrm{F2}\:\mathrm{acts}\:\mathrm{in} \\ $$$$\:\mathrm{the}\:\mathrm{first}\:\mathrm{quadrant}\:\mathrm{making}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{32}° \\ $$$$\:\mathrm{degrees}\:\mathrm{with}\:\mathrm{the}\:\mathrm{y}\:\mathrm{axis}\:\mathrm{and}\:\mathrm{the}\:\mathrm{resultant} \\ $$$$\:\mathrm{force}\:\mathrm{is}\:\mathrm{67}\:\mathrm{N},\:\mathrm{determine}\:\mathrm{F1}\:\mathrm{and}\:\mathrm{F2}. \\ $$$$\: \\ $$

Question Number 183285 Answers: 0 Comments: 0

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