Question and Answers Forum

AllQuestion and Answers: Page 604

Question Number 158303 Answers: 1 Comments: 0

x;y;z;t>0 solve for real numbers: { ((8x^4 + 64y^4 + 216z^4 + 1728t^4 = 1)),((x + y + z + t = 1)) :}

$$\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}>\mathrm{0} \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\begin{cases}{\mathrm{8x}^{\mathrm{4}} \:+\:\mathrm{64y}^{\mathrm{4}} \:+\:\mathrm{216z}^{\mathrm{4}} \:+\:\mathrm{1728t}^{\mathrm{4}} \:=\:\mathrm{1}}\\{\mathrm{x}\:+\:\mathrm{y}\:+\:\mathrm{z}\:+\:\mathrm{t}\:=\:\mathrm{1}}\end{cases} \\ $$$$ \\ $$

Question Number 158425 Answers: 0 Comments: 0

Question Number 158424 Answers: 1 Comments: 0

Question Number 158301 Answers: 1 Comments: 1

proven that 1^0 =1 et que 0!=1

$${proven}\:{that}\: \\ $$$$\mathrm{1}^{\mathrm{0}} =\mathrm{1}\:{et}\:{que}\:\mathrm{0}!=\mathrm{1} \\ $$

Question Number 158295 Answers: 0 Comments: 0

𝛀 =∫_( 0) ^( 1) ((sin^(-1) x log(1 + x))/x^2 ) dx = ?

$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{sin}^{-\mathrm{1}} \:\mathrm{x}\:\mathrm{log}\left(\mathrm{1}\:+\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=\:? \\ $$$$ \\ $$

Question Number 158285 Answers: 0 Comments: 1

Question Number 158293 Answers: 3 Comments: 0

question# If , Ω =∫_0 ^( 1) ((ln^( 2) (1−x^( 4) ))/x) dx= a ζ b) find the value of , a , b .

$$ \\ $$$$\:\:\:\:\:{question}# \\ $$$$\left.\mathrm{If}\:,\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}^{\:\mathrm{4}} \right)}{{x}}\:{dx}=\:{a}\:\zeta\:{b}\right) \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:,\:\:\:\:\:{a}\:\:,\:{b}\:\:. \\ $$$$ \\ $$$$ \\ $$

Question Number 158317 Answers: 0 Comments: 0

Question Number 158290 Answers: 0 Comments: 0

Question Number 158288 Answers: 1 Comments: 0

Question Number 158287 Answers: 0 Comments: 0

Question Number 158281 Answers: 0 Comments: 2

Question Number 158276 Answers: 0 Comments: 0

if x;y;z≥0 then: 2 Σ_(cyc) x^2 (x^2 + y^2 ) ≥ Σ_(cyc) x(x^3 + z^3 ) + xyz(x+y+z)

$$\mathrm{if}\:\:\mathrm{x};\mathrm{y};\mathrm{z}\geqslant\mathrm{0}\:\:\mathrm{then}: \\ $$$$\mathrm{2}\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \right)\:\geqslant\:\underset{\boldsymbol{\mathrm{cyc}}} {\sum}\:\mathrm{x}\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{z}^{\mathrm{3}} \right)\:+\:\mathrm{xyz}\left(\mathrm{x}+\mathrm{y}+\mathrm{z}\right) \\ $$$$ \\ $$

Question Number 158275 Answers: 2 Comments: 0

Solve for real numbers: x^(32) + x^(16) + y^2 = 2 (√2) x^(12) y

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{32}} \:+\:\mathrm{x}^{\mathrm{16}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{2}\:\sqrt{\mathrm{2}}\:\mathrm{x}^{\mathrm{12}} \:\mathrm{y} \\ $$$$ \\ $$

Question Number 158273 Answers: 0 Comments: 0

Question Number 158272 Answers: 1 Comments: 0

Question Number 158271 Answers: 0 Comments: 0

Question Number 158270 Answers: 0 Comments: 0

82,1336,18670,240004,2933338,34666672,400000006,? is there a valid pattern for these numbers?

$$\mathrm{82},\mathrm{1336},\mathrm{18670},\mathrm{240004},\mathrm{2933338},\mathrm{34666672},\mathrm{400000006},? \\ $$$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{valid}\:\mathrm{pattern}\:\mathrm{for}\:\mathrm{these}\:\mathrm{numbers}? \\ $$

Question Number 158267 Answers: 0 Comments: 0

soit:F={(x,y,z)∈R^3 /x−y−2z} et G=Vect(0,1,1) determiner l′intersection de F et G

$${soit}:{F}=\left\{\left({x},{y},{z}\right)\in{R}^{\mathrm{3}} /{x}−{y}−\mathrm{2}{z}\right\}\:{et} \\ $$$${G}={Vect}\left(\mathrm{0},\mathrm{1},\mathrm{1}\right) \\ $$$${determiner}\:{l}'{intersection}\:{de}\:{F}\:{et}\:{G} \\ $$

Question Number 158259 Answers: 1 Comments: 1

Given x,y∈R^+ and ((x/5)+(y/3))((5/x)+(3/y))=139. If maximum and minimum of ((x+y)/( (√(xy)) )) is M and n respectively, then what the value of 3M−4n.

$${Given}\:{x},{y}\in\mathbb{R}^{+} \:{and}\:\left(\frac{{x}}{\mathrm{5}}+\frac{{y}}{\mathrm{3}}\right)\left(\frac{\mathrm{5}}{{x}}+\frac{\mathrm{3}}{{y}}\right)=\mathrm{139}. \\ $$$$\:{If}\:{maximum}\:{and}\:{minimum} \\ $$$$\:{of}\:\frac{{x}+{y}}{\:\sqrt{{xy}}\:}\:{is}\:{M}\:{and}\:{n}\:{respectively}, \\ $$$${then}\:{what}\:{the}\:{value}\:{of}\:\mathrm{3}{M}−\mathrm{4}{n}. \\ $$

Question Number 158252 Answers: 0 Comments: 0

Question Number 158625 Answers: 0 Comments: 1

EI(∂^4 y/∂x^4 )+ρS(∂^2 y/∂t^2 )=0 (1) y(x,0)=U_0 (x) (∂y/∂t)(x,0)=V_0 (x) ; EI(∂^2 y/∂x^2 )(0,t)=EI(∂^2 y/∂x^2 )(L,t)=0

$${EI}\frac{\partial^{\mathrm{4}} {y}}{\partial{x}^{\mathrm{4}} }+\rho{S}\frac{\partial^{\mathrm{2}} {y}}{\partial{t}^{\mathrm{2}} }=\mathrm{0}\:\:\:\left(\mathrm{1}\right) \\ $$$${y}\left({x},\mathrm{0}\right)={U}_{\mathrm{0}} \left({x}\right) \\ $$$$\frac{\partial{y}}{\partial{t}}\left({x},\mathrm{0}\right)={V}_{\mathrm{0}} \left({x}\right)\:\:\:\:\:\:;\:{EI}\frac{\partial^{\mathrm{2}} {y}}{\partial{x}^{\mathrm{2}} }\left(\mathrm{0},{t}\right)={EI}\frac{\partial^{\mathrm{2}} {y}}{\partial{x}^{\mathrm{2}} }\left({L},{t}\right)=\mathrm{0} \\ $$

Question Number 158245 Answers: 1 Comments: 0

Prove that: (((x-1)^2 )/x) + ((x+1)/( (√(x^2 +1)))) ≥ (√2) ; ∀x>0

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\frac{\left(\mathrm{x}-\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{x}}\:+\:\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\geqslant\:\sqrt{\mathrm{2}}\:\:;\:\:\forall\mathrm{x}>\mathrm{0} \\ $$$$ \\ $$

Question Number 158241 Answers: 0 Comments: 0

Prove that: (((x-1)^2 )/x) + ((x+1)/( (√(x^2 +1)))) ≥ 2 ; ∀x>0

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\frac{\left(\mathrm{x}-\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{x}}\:+\:\frac{\mathrm{x}+\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}}\:\geqslant\:\mathrm{2}\:\:;\:\:\forall\mathrm{x}>\mathrm{0} \\ $$

Question Number 158240 Answers: 1 Comments: 0

Prove that 5 divide n(4n^2 + 1)(6n^2 + 1) for any natural number n

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{5}\:\mathrm{divide} \\ $$$$\mathrm{n}\left(\mathrm{4n}^{\mathrm{2}} \:+\:\mathrm{1}\right)\left(\mathrm{6n}^{\mathrm{2}} \:+\:\mathrm{1}\right) \\ $$$$\mathrm{for}\:\mathrm{any}\:\mathrm{natural}\:\mathrm{number}\:\boldsymbol{\mathrm{n}} \\ $$

Question Number 158274 Answers: 1 Comments: 0

Solve for complex numbers: x^4 + (1 + i)x^3 + 2ix^2 + (i - 1)x - 1 = 0

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{complex}\:\mathrm{numbers}: \\ $$$$\mathrm{x}^{\mathrm{4}} \:+\:\left(\mathrm{1}\:+\:\boldsymbol{\mathrm{i}}\right)\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:+\:\mathrm{2}\boldsymbol{\mathrm{ix}}^{\mathrm{2}} \:+\:\left(\boldsymbol{\mathrm{i}}\:-\:\mathrm{1}\right)\boldsymbol{\mathrm{x}}\:-\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$ \\ $$

Pg 599 Pg 600 Pg 601 Pg 602 Pg 603 Pg 604 Pg 605 Pg 606 Pg 607 Pg 608

Contact: info@tinkutara.com