Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1201

Question Number 94960    Answers: 2   Comments: 0

Question Number 94956    Answers: 1   Comments: 7

Question Number 94955    Answers: 0   Comments: 0

Prove by set theory or otherwise lcm( gcd(x,y),gcd(y,z),gcd(z,x) ) is equal to gcd( lcm(x,y),lcm(y,z),lcm(z,x) ) Or give a counter example.

$${Prove}\:{by}\:{set}\:{theory}\:{or}\:{otherwise} \\ $$$$\:\:\mathrm{lcm}\left(\:\mathrm{gcd}\left(\mathrm{x},\mathrm{y}\right),\mathrm{gcd}\left(\mathrm{y},\mathrm{z}\right),\mathrm{gcd}\left(\mathrm{z},\mathrm{x}\right)\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\:\mathrm{gcd}\left(\:\mathrm{lcm}\left(\mathrm{x},\mathrm{y}\right),\mathrm{lcm}\left(\mathrm{y},\mathrm{z}\right),\mathrm{lcm}\left(\mathrm{z},\mathrm{x}\right)\:\right) \\ $$$$\:\:{Or}\:{give}\:{a}\:{counter}\:{example}. \\ $$

Question Number 94954    Answers: 1   Comments: 0

For any curve, prove that: ((d^2 x/ds^2 ))^2 +((d^2 y/dx^2 ))^2 = (1/ρ^2 )

$$\:\:\boldsymbol{\mathrm{For}}\:\boldsymbol{\mathrm{any}}\:\boldsymbol{\mathrm{curve}},\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}}: \\ $$$$\:\:\:\left(\frac{\mathrm{d}^{\mathrm{2}} \mathrm{x}}{\mathrm{ds}^{\mathrm{2}} }\right)^{\mathrm{2}} +\left(\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{dx}^{\mathrm{2}} }\right)^{\mathrm{2}} =\:\frac{\mathrm{1}}{\rho^{\mathrm{2}} } \\ $$$$\:\: \\ $$

Question Number 94945    Answers: 0   Comments: 2

How do you make p the subject of equation q = (m/((√p) )) + (p^2 /m)

$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{make}\:\mathrm{p}\:\mathrm{the}\:\mathrm{subject} \\ $$$$\mathrm{of}\:\mathrm{equation}\:{q}\:=\:\frac{{m}}{\sqrt{{p}}\:}\:+\:\frac{{p}^{\mathrm{2}} }{{m}}\: \\ $$

Question Number 94934    Answers: 3   Comments: 1

Question Number 94931    Answers: 1   Comments: 0

f is a 2(×) derivable function and L laplace transfom determine L(f^′ ) a L(f^(′′) )

$$\mathrm{f}\:\mathrm{is}\:\mathrm{a}\:\mathrm{2}\left(×\right)\:\mathrm{derivable}\:\mathrm{function}\:\:\mathrm{and}\:\mathrm{L}\:\mathrm{laplace}\:\mathrm{transfom} \\ $$$$\mathrm{determine}\:\mathrm{L}\left(\mathrm{f}^{'} \right)\:\mathrm{a}\:\mathrm{L}\left(\mathrm{f}^{''} \right) \\ $$

Question Number 94925    Answers: 1   Comments: 2

Question Number 94923    Answers: 1   Comments: 0

Question Number 94922    Answers: 1   Comments: 0

Question Number 94921    Answers: 2   Comments: 0

Question Number 94915    Answers: 2   Comments: 0

We suppose in R^2 the base (i^→ ;j^→ ). we have these vectors: u^→ =(m^2 −m)i^→ +2mj^→ ; v^→ =(m−1)i^→ +(m+1)j^→ m ∈ R^∗ 1)Determinate m for which the system (u^→ ;v^→ ) is linear dependant( det(u^→ ;v^→ )=0)

$$\mathrm{We}\:\mathrm{suppose}\:\mathrm{in}\:\mathbb{R}^{\mathrm{2}} \:\mathrm{the}\:\mathrm{base}\:\left(\overset{\rightarrow} {{i}};\overset{\rightarrow} {{j}}\right). \\ $$$$\mathrm{we}\:\mathrm{have}\:\mathrm{these}\:\mathrm{vectors}: \\ $$$$\overset{\rightarrow} {\mathrm{u}}=\left(\mathrm{m}^{\mathrm{2}} −\mathrm{m}\right)\overset{\rightarrow} {{i}}+\mathrm{2m}\overset{\rightarrow} {{j}}\:;\: \\ $$$$\overset{\rightarrow} {\mathrm{v}}=\left(\mathrm{m}−\mathrm{1}\right)\overset{\rightarrow} {{i}}+\left(\mathrm{m}+\mathrm{1}\right)\overset{\rightarrow} {{j}}\:\mathrm{m}\:\in\:\mathbb{R}^{\ast} \\ $$$$\left.\mathrm{1}\right)\mathrm{Determinate}\:\mathrm{m}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{system} \\ $$$$\left(\overset{\rightarrow} {\mathrm{u}};\overset{\rightarrow} {\mathrm{v}}\right)\:\mathrm{is}\:\mathrm{linear}\:\mathrm{dependant}\left(\:\mathrm{det}\left(\overset{\rightarrow} {\mathrm{u}};\overset{\rightarrow} {\mathrm{v}}\right)=\mathrm{0}\right) \\ $$$$ \\ $$

Question Number 94914    Answers: 1   Comments: 0

Question Number 94910    Answers: 1   Comments: 0

Solve in [0;2π] 2sin(4x−(π/6))≥1 Please sirs...

$$\mathrm{Solve}\:\mathrm{in}\:\left[\mathrm{0};\mathrm{2}\pi\right] \\ $$$$\mathrm{2sin}\left(\mathrm{4}{x}−\frac{\pi}{\mathrm{6}}\right)\geqslant\mathrm{1} \\ $$$$\mathrm{Please}\:\mathrm{sirs}... \\ $$

Question Number 94907    Answers: 2   Comments: 0

1)calculate ∫ (dx/((2+(√(x−1)))^2 )) 2) find the value of ∫_2 ^(+∞) (dx/((2+(√(x−1)))^2 ))

$$\left.\mathrm{1}\right)\mathrm{calculate}\:\int\:\:\frac{\mathrm{dx}}{\left(\mathrm{2}+\sqrt{\mathrm{x}−\mathrm{1}}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\int_{\mathrm{2}} ^{+\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2}+\sqrt{\mathrm{x}−\mathrm{1}}\right)^{\mathrm{2}} } \\ $$

Question Number 94906    Answers: 2   Comments: 0

calculate ∫_1 ^(+∞) (dx/(x^2 (x+1)^3 (x+2)^4 ))

$$\mathrm{calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{4}} } \\ $$

Question Number 94905    Answers: 2   Comments: 0

calculate ∫_3 ^(+∞) ((xdx)/((x+1)^3 (x−2)^2 ))

$$\mathrm{calculate}\:\:\int_{\mathrm{3}} ^{+\infty} \:\:\:\:\:\frac{\mathrm{xdx}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} \left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$

Question Number 94904    Answers: 0   Comments: 0

solve y^(′′) +x^2 y =xsin(2x)

$$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{x}^{\mathrm{2}} \mathrm{y}\:=\mathrm{xsin}\left(\mathrm{2x}\right) \\ $$

Question Number 94903    Answers: 2   Comments: 0

solve y^(′′) +2y^′ +y =xe^(−x)

$$\mathrm{solve}\:\:\mathrm{y}^{''} \:+\mathrm{2y}^{'} \:+\mathrm{y}\:=\mathrm{xe}^{−\mathrm{x}} \\ $$

Question Number 94882    Answers: 1   Comments: 0

solve the equation tan θ+tan 2θ+tan 3θ = tan θ.tan 2θ.tan 3θ

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\mathrm{tan}\:\theta+\mathrm{tan}\:\mathrm{2}\theta+\mathrm{tan}\:\mathrm{3}\theta\:=\: \\ $$$$\mathrm{tan}\:\theta.\mathrm{tan}\:\mathrm{2}\theta.\mathrm{tan}\:\mathrm{3}\theta\: \\ $$

Question Number 94948    Answers: 1   Comments: 3

∫_0 ^((√(2 ln (3))) ) xe^(x^2 /2) dx = . . .

$$\int_{\mathrm{0}} ^{\sqrt{\mathrm{2}\:{ln}\:\left(\mathrm{3}\right)}\:} {xe}^{\frac{{x}^{\mathrm{2}} }{\mathrm{2}}} \:{dx}\:=\:.\:.\:. \\ $$

Question Number 94877    Answers: 1   Comments: 2

Solve for x in [0;2π]: sin(4x−(π/6))=(1/2)

$$\mathrm{Solve}\:\mathrm{for}\:{x}\:\mathrm{in}\:\left[\mathrm{0};\mathrm{2}\pi\right]: \\ $$$$\mathrm{sin}\left(\mathrm{4}{x}−\frac{\pi}{\mathrm{6}}\right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 94874    Answers: 1   Comments: 1

Question Number 94868    Answers: 0   Comments: 5

Question Number 94862    Answers: 0   Comments: 4

Show that cos^6 x+sin^6 x=(1/8)(5+3cos(4x)) By using the formula: a^3 +b^3 =(a+b)(a^2 −ab+b^2 )

$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{cos}^{\mathrm{6}} {x}+{sin}^{\mathrm{6}} {x}=\frac{\mathrm{1}}{\mathrm{8}}\left(\mathrm{5}+\mathrm{3}{cos}\left(\mathrm{4}{x}\right)\right) \\ $$$$\mathrm{By}\:\mathrm{using}\:\mathrm{the}\:\mathrm{formula}: \\ $$$$\mathrm{a}^{\mathrm{3}} +\mathrm{b}^{\mathrm{3}} =\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}^{\mathrm{2}} −\mathrm{ab}+\mathrm{b}^{\mathrm{2}} \right) \\ $$

Question Number 94861    Answers: 0   Comments: 1

Show that (g○f)′(x)=g′(f(x))∙f′(x)

$$\mathrm{Show}\:\mathrm{that} \\ $$$$\left(\mathrm{g}\circ\mathrm{f}\right)'\left(\mathrm{x}\right)=\mathrm{g}'\left(\mathrm{f}\left(\mathrm{x}\right)\right)\centerdot\mathrm{f}'\left(\mathrm{x}\right) \\ $$

  Pg 1196      Pg 1197      Pg 1198      Pg 1199      Pg 1200      Pg 1201      Pg 1202      Pg 1203      Pg 1204      Pg 1205   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com