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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=?

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

Question Number 77346 Answers: 0 Comments: 3

Question Number 77340 Answers: 1 Comments: 0

Question Number 77339 Answers: 1 Comments: 2

Question Number 77335 Answers: 1 Comments: 4

Question Number 77336 Answers: 0 Comments: 2

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

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

Question Number 77330 Answers: 0 Comments: 3

Question Number 77323 Answers: 0 Comments: 2

Question Number 77314 Answers: 0 Comments: 6

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)

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

Question Number 77280 Answers: 0 Comments: 2

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Question Number 77272 Answers: 1 Comments: 3

given T.ABCD is pyramid with AB = BC = 8 and AT = 6 . P is midpoint BC, Q is midpoint AT. If α is the angle between TP and PQ then cos α is ...

$$\mathrm{given}\:\mathrm{T}.\mathrm{ABCD}\:\mathrm{is}\:\mathrm{pyramid}\: \\ $$$$\mathrm{with}\:\mathrm{AB}\:=\:\mathrm{BC}\:=\:\mathrm{8}\:\mathrm{and}\:\mathrm{AT}\:=\:\mathrm{6} \\ $$$$\:.\:\mathrm{P}\:\mathrm{is}\:\mathrm{midpoint}\:\mathrm{BC},\:\mathrm{Q}\:\mathrm{is}\:\mathrm{midpoint}\:\mathrm{AT}. \\ $$$$\mathrm{If}\:\alpha\:\mathrm{is}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{between}\:\mathrm{TP}\:\mathrm{and} \\ $$$$\mathrm{PQ}\:\mathrm{then}\:\mathrm{cos}\:\alpha\:\mathrm{is}\:... \\ $$

Question Number 77271 Answers: 0 Comments: 0

given the function y = (1/(x^2 +1)). The tangent equation of the curve with the smallest gradient is ..

$$\mathrm{given}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{y}\:=\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}.\:\mathrm{The}\:\mathrm{tangent}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{with}\:\mathrm{the}\:\mathrm{smallest}\: \\ $$$$\mathrm{gradient}\:\mathrm{is}\:.. \\ $$

Question Number 77269 Answers: 0 Comments: 1

what is ∫ (1/(tan^3 (x^2 −1))) dx ?

$${what}\:{is}\:\int\:\frac{\mathrm{1}}{\mathrm{tan}\:^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)}\:{dx}\:? \\ $$

Question Number 77252 Answers: 1 Comments: 2

Question Number 77242 Answers: 1 Comments: 3

prove that ∫_0 ^a (√(2+(a/x)−2(√(a/x)) ))dx=a[(1/(√2))ln((√2)+1)+1]

$${prove}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{{a}} \sqrt{\mathrm{2}+\frac{{a}}{{x}}−\mathrm{2}\sqrt{\frac{{a}}{{x}}}\:}{dx}={a}\left[\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}{ln}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)+\mathrm{1}\right] \\ $$

Question Number 77232 Answers: 1 Comments: 0

∫_0 ^1 ln ( (√x) + (√(1−x)) ) dx = ?

$$\underset{\mathrm{0}} {\int}\overset{\mathrm{1}} {\:}\:\mathrm{ln}\:\left(\:\sqrt{{x}}\:+\:\sqrt{\mathrm{1}−{x}}\:\right)\:{dx}\:\:=\:\:? \\ $$

Question Number 77230 Answers: 1 Comments: 0

An astromer finds a new absorption line with λ=164.1nm in the ultraviolet region of the sun′s continuous spectrum. He attributes the line to hydrogen′s Layman series. Is he right? Justify your answer. please help.

$$\mathrm{An}\:\mathrm{astromer}\:\mathrm{finds}\:\mathrm{a}\:\mathrm{new}\:\mathrm{absorption}\: \\ $$$$\mathrm{line}\:\mathrm{with}\:\lambda=\mathrm{164}.\mathrm{1nm}\:\mathrm{in}\:\mathrm{the}\:\mathrm{ultraviolet} \\ $$$$\mathrm{region}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sun}'\mathrm{s}\:\mathrm{continuous}\:\mathrm{spectrum}. \\ $$$$\mathrm{He}\:\mathrm{attributes}\:\mathrm{the}\:\mathrm{line}\:\mathrm{to}\:\mathrm{hydrogen}'\mathrm{s}\: \\ $$$$\mathrm{Layman}\:\mathrm{series}.\:\mathrm{Is}\:\mathrm{he}\:\mathrm{right}?\:\mathrm{Justify} \\ $$$$\mathrm{your}\:\mathrm{answer}. \\ $$$$ \\ $$$$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{help}}. \\ $$

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