Question and Answers Forum

AllQuestion and Answers: Page 1330

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

Question Number 77279 Answers: 0 Comments: 0

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.

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

Question Number 77229 Answers: 1 Comments: 1

Question Number 77221 Answers: 2 Comments: 0

∫ (((√(2+x)) dx)/(√x^5 )) = ?

$$\int\:\frac{\sqrt{\mathrm{2}+{x}}\:{dx}}{\sqrt{{x}^{\mathrm{5}} }}\:=\:? \\ $$

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 77218 Answers: 1 Comments: 0

what is solution in R ((sin (x)−∣x+2∣)/(x^2 −4x−5))≥0 ?

$${what}\:{is}\:{solution}\:{in}\:\mathbb{R}\: \\ $$$$\frac{\mathrm{sin}\:\left({x}\right)−\mid{x}+\mathrm{2}\mid}{{x}^{\mathrm{2}} −\mathrm{4}{x}−\mathrm{5}}\geqslant\mathrm{0}\:?\: \\ $$

Question Number 77216 Answers: 0 Comments: 0

Question Number 77213 Answers: 0 Comments: 3

Question Number 77208 Answers: 0 Comments: 1

some thoughts on this forum... we cannot solve the unanswered questions much greater mathematicians haven′t been able to solve yet thus it makes absolutely no sense to post them here also it makes no sense to post problems from books or from the www if you don′t have the foggiest idea of their meaning or how to solve them. it might be fun for us to solve some of them but mostly it′s like casting pearls...

$$\mathrm{some}\:\mathrm{thoughts}\:\mathrm{on}\:\mathrm{this}\:\mathrm{forum}... \\ $$$$\mathrm{we}\:\mathrm{cannot}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{unanswered}\:\mathrm{questions} \\ $$$$\mathrm{much}\:\mathrm{greater}\:\mathrm{mathematicians}\:\mathrm{haven}'\mathrm{t}\:\mathrm{been} \\ $$$$\mathrm{able}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{yet} \\ $$$$\mathrm{thus}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{absolutely}\:\mathrm{no}\:\mathrm{sense}\:\mathrm{to}\:\mathrm{post} \\ $$$$\mathrm{them}\:\mathrm{here} \\ $$$$\mathrm{also}\:\mathrm{it}\:\mathrm{makes}\:\mathrm{no}\:\mathrm{sense}\:\mathrm{to}\:\mathrm{post}\:\mathrm{problems}\:\mathrm{from} \\ $$$$\mathrm{books}\:\mathrm{or}\:\mathrm{from}\:\mathrm{the}\:\mathrm{www}\:\mathrm{if}\:\mathrm{you}\:\mathrm{don}'\mathrm{t}\:\mathrm{have}\:\mathrm{the} \\ $$$$\mathrm{foggiest}\:\mathrm{idea}\:\mathrm{of}\:\mathrm{their}\:\mathrm{meaning}\:\mathrm{or}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve} \\ $$$$\mathrm{them}.\:\mathrm{it}\:\mathrm{might}\:\mathrm{be}\:\mathrm{fun}\:\mathrm{for}\:\mathrm{us}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{some}\:\mathrm{of} \\ $$$$\mathrm{them}\:\mathrm{but}\:\mathrm{mostly}\:\mathrm{it}'\mathrm{s}\:\mathrm{like}\:\mathrm{casting}\:\mathrm{pearls}... \\ $$

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.

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

Pg 1325 Pg 1326 Pg 1327 Pg 1328 Pg 1329 Pg 1330 Pg 1331 Pg 1332 Pg 1333 Pg 1334

Contact: info@tinkutara.com