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Question Number 77420 Answers: 0 Comments: 10

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Question Number 77394 Answers: 1 Comments: 4

a 6 digit number formed with the first number is 2 and contains 4 equal number. many number can be made are

$$\mathrm{a}\:\mathrm{6}\:\mathrm{digit}\:\mathrm{number}\:\mathrm{formed}\: \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{first}\:\mathrm{number}\:\mathrm{is}\:\mathrm{2}\:\mathrm{and}\: \\ $$$$\mathrm{contains}\:\mathrm{4}\:\mathrm{equal}\:\mathrm{number}.\:\mathrm{many} \\ $$$$\mathrm{number}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made}\:\mathrm{are}\: \\ $$

Question Number 77390 Answers: 2 Comments: 1

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Question Number 77367 Answers: 1 Comments: 1

let the cercle (x+1)^(2 ) +(y−3)^2 =9 and the point A(4,1) vrrify that A is out of circle and determine the equation of two tangentes to circle wich passes by point A.

$${let}\:{the}\:{cercle}\:\:\left({x}+\mathrm{1}\right)^{\mathrm{2}\:} +\left({y}−\mathrm{3}\right)^{\mathrm{2}} =\mathrm{9} \\ $$$${and}\:{the}\:{point}\:\:{A}\left(\mathrm{4},\mathrm{1}\right) \\ $$$${vrrify}\:{that}\:\:{A}\:\:{is}\:{out}\:{of}\:{circle} \\ $$$${and}\:\:{determine}\:{the}\:{equation}\:{of} \\ $$$${two}\:{tangentes}\:{to}\:{circle}\:{wich} \\ $$$${passes}\:{by}\:{point}\:{A}. \\ $$

Question Number 77356 Answers: 1 Comments: 0

The plan is provided with an orthonormal reference ( O.I.J). the following points are given A(1,2) B(−2,3) C(1,9). We assume that the point O is the barycenter of the point A,B,C. →O=bar{(A;3),(B;1),(C;−1)} Question 1 knowing that 3MA^2 +MB^2 −MC^2 =3MO^2 +3OA^2 +OB^2 −OC^2 Determine and construct the set of points M on the plane such as 3MA^2 +MB^2 −MC^2 =−42

$$\mathrm{The}\:\mathrm{plan}\:\mathrm{is}\:\mathrm{provided}\:\mathrm{with}\:\mathrm{an}\: \\ $$$$\mathrm{orthonormal}\:\mathrm{reference}\:\left(\:\mathrm{O}.\mathrm{I}.\mathrm{J}\right). \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{points}\:\mathrm{are}\:\mathrm{given} \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{2}\right)\:\mathrm{B}\left(−\mathrm{2},\mathrm{3}\right)\:\mathrm{C}\left(\mathrm{1},\mathrm{9}\right). \\ $$$$\mathrm{We}\:\mathrm{assume}\:\mathrm{that}\:\mathrm{the}\:\mathrm{point}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{barycenter}\:\mathrm{of}\:\mathrm{the}\:\mathrm{point}\:\mathrm{A},\mathrm{B},\mathrm{C}. \\ $$$$\rightarrow\mathrm{O}=\mathrm{bar}\left\{\left(\mathrm{A};\mathrm{3}\right),\left(\mathrm{B};\mathrm{1}\right),\left(\mathrm{C};−\mathrm{1}\right)\right\} \\ $$$$ \\ $$$$\mathrm{Question}\:\mathrm{1} \\ $$$$\mathrm{knowing}\:\mathrm{that} \\ $$$$\mathrm{3MA}^{\mathrm{2}} +\mathrm{MB}^{\mathrm{2}} −\mathrm{MC}^{\mathrm{2}} =\mathrm{3MO}^{\mathrm{2}} +\mathrm{3OA}^{\mathrm{2}} +\mathrm{OB}^{\mathrm{2}} −\mathrm{OC}^{\mathrm{2}} \\ $$$$\mathrm{Determine}\:\mathrm{and}\:\mathrm{construct}\:\mathrm{the}\:\mathrm{set}\: \\ $$$$\mathrm{of}\:\mathrm{points}\:\mathrm{M}\:\mathrm{on}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{such}\:\mathrm{as} \\ $$$$\mathrm{3MA}^{\mathrm{2}} +\mathrm{MB}^{\mathrm{2}} −\mathrm{MC}^{\mathrm{2}} =−\mathrm{42} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 77347 Answers: 2 Comments: 1

if ∫sin(f(x))dx=g(x) ∫cos(f(x))dx=?

$$\mathrm{if}\:\int\mathrm{sin}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}=\mathrm{g}\left(\mathrm{x}\right) \\ $$$$\int\mathrm{cos}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\mathrm{dx}=? \\ $$

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Question Number 77336 Answers: 0 Comments: 2

make x subject of formula x^y^x + 8x = y

$${make}\:\boldsymbol{{x}}\:{subject}\:{of}\:{formula} \\ $$$$ \\ $$$$\boldsymbol{{x}}^{\boldsymbol{{y}}^{\boldsymbol{{x}}} } \:+\:\mathrm{8}\boldsymbol{{x}}\:\:=\:\:\boldsymbol{{y}} \\ $$

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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 77309 Answers: 1 Comments: 4

Question Number 77297 Answers: 1 Comments: 0

If y(x) is a solution of the differential equation (((2+sinx)/(1+y)))(dy/dx)=−cosx and y(0)=1, then find the value of y(π/2) ?

$$\mathrm{If}\:\mathrm{y}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the}\:\mathrm{differential} \\ $$$$\mathrm{equation}\:\left(\frac{\mathrm{2}+\mathrm{sinx}}{\mathrm{1}+\mathrm{y}}\right)\frac{\mathrm{dy}}{\mathrm{dx}}=−\mathrm{cosx}\:\mathrm{and} \\ $$$$\mathrm{y}\left(\mathrm{0}\right)=\mathrm{1},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{y}\left(\pi/\mathrm{2}\right)\:\:? \\ $$

Question Number 77296 Answers: 0 Comments: 4

Determiner et construire l.ensemble des points M tel que: 3MA^2 +MB^2 −MC^2 =−42 Le plan est muni d.un repere orthonorme (O,I,J) A(1,2) B(−2,3) C(1,9). on considere que O=barycentre{(A,3);(B;1);(C;−1)}

$$\mathrm{Determiner}\:\mathrm{et}\:\mathrm{construire}\:\mathrm{l}.\mathrm{ensemble} \\ $$$$\mathrm{des}\:\mathrm{points}\:\mathrm{M}\:\mathrm{tel}\:\mathrm{que}: \\ $$$$\mathrm{3MA}^{\mathrm{2}} +\mathrm{MB}^{\mathrm{2}} −\mathrm{MC}^{\mathrm{2}} =−\mathrm{42} \\ $$$$\mathrm{Le}\:\mathrm{plan}\:\mathrm{est}\:\mathrm{muni}\:\mathrm{d}.\mathrm{un}\:\mathrm{repere}\: \\ $$$$\mathrm{orthonorme}\:\left(\mathrm{O},\mathrm{I},\mathrm{J}\right) \\ $$$$\mathrm{A}\left(\mathrm{1},\mathrm{2}\right)\:\:\:\mathrm{B}\left(−\mathrm{2},\mathrm{3}\right)\:\:\mathrm{C}\left(\mathrm{1},\mathrm{9}\right). \\ $$$$\mathrm{on}\:\mathrm{considere}\:\mathrm{que}\: \\ $$$$\mathrm{O}=\mathrm{barycentre}\left\{\left(\mathrm{A},\mathrm{3}\right);\left(\mathrm{B};\mathrm{1}\right);\left(\mathrm{C};−\mathrm{1}\right)\right\} \\ $$

Question Number 77294 Answers: 1 Comments: 0

f(x)=x^3 −27x Find intervals where given fuction ii is 1.increasing 2.decreasing 3 concave up and down 4 point of inflection

$${f}\left({x}\right)={x}^{\mathrm{3}} −\mathrm{27}{x} \\ $$$${Find}\:{intervals}\:{where}\:{given}\:{fuction}\:{ii} \\ $$$${is} \\ $$$$\mathrm{1}.{increasing} \\ $$$$\mathrm{2}.{decreasing} \\ $$$$\mathrm{3}\:{concave}\:{up}\:{and}\:{down} \\ $$$$\mathrm{4}\:{point}\:{of}\:{inflection} \\ $$

Question Number 77290 Answers: 2 Comments: 3

∫ (√(x^3 + x^4 )) dx

$$\int\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} }\:\:\mathrm{dx} \\ $$

Question Number 77285 Answers: 1 Comments: 0

how to find the Fourier series of f(x) = x , 0 < x<(1/8)

$$\mathrm{how}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{Fourier}\:\mathrm{series}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}\:,\:\mathrm{0}\:<\:\mathrm{x}<\frac{\mathrm{1}}{\mathrm{8}} \\ $$

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