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AllQuestion and Answers: Page 26

Question Number 213738 Answers: 1 Comments: 0

Question Number 213735 Answers: 2 Comments: 0

Question Number 213726 Answers: 1 Comments: 0

ax = by = cz = 36 (1/x) + (1/y) + (1/z) = (1/9) a + b + c = ?

$$\mathrm{ax}\:=\:\mathrm{by}\:=\:\mathrm{cz}\:=\:\mathrm{36} \\ $$$$\frac{\mathrm{1}}{\mathrm{x}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{y}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{z}}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{9}} \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:=\:? \\ $$

Question Number 213725 Answers: 3 Comments: 0

please prove (1/x) = x^(−1)

$${please}\:{prove}\:\frac{\mathrm{1}}{{x}}\:=\:{x}^{−\mathrm{1}} \\ $$

Question Number 213724 Answers: 0 Comments: 1

Question Number 213721 Answers: 3 Comments: 0

Resoudre le systeme d′ equations: { (((x+y)xy=84)),((x^2 +y^2 =25)) :}

$$\boldsymbol{\mathrm{Resoudre}}\:\boldsymbol{\mathrm{le}}\:\boldsymbol{\mathrm{systeme}}\:\boldsymbol{\mathrm{d}}'\:\boldsymbol{\mathrm{equations}}: \\ $$$$\begin{cases}{\left(\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\right)\boldsymbol{\mathrm{xy}}=\mathrm{84}}\\{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\boldsymbol{\mathrm{y}}^{\mathrm{2}} \:\:\:\:\:\:=\mathrm{25}}\end{cases} \\ $$

Question Number 213713 Answers: 0 Comments: 0

Does Volume integral V=π∙∫_0 ^( ∞) J_ν ^( 2) (z)dz is divergence...?? J_ν (z) is ν(nu)′th Bessel function

$$\mathrm{Does}\:\mathrm{Volume}\:\mathrm{integral}\: \\ $$$${V}=\pi\centerdot\int_{\mathrm{0}} ^{\:\infty} {J}_{\nu} ^{\:\mathrm{2}} \left({z}\right)\mathrm{d}{z}\:\mathrm{is}\:\mathrm{divergence}...?? \\ $$$${J}_{\nu} \left({z}\right)\:\mathrm{is}\:\nu\left(\mathrm{nu}\right)'\mathrm{th}\:\mathrm{Bessel}\:\mathrm{function} \\ $$

Question Number 213705 Answers: 1 Comments: 0

Question Number 213693 Answers: 2 Comments: 3

Find: sin^2 (7° 44′ 22,54′′)∙800

$$\mathrm{Find}: \\ $$$$\mathrm{sin}^{\mathrm{2}} \:\left(\mathrm{7}°\:\mathrm{44}'\:\mathrm{22},\mathrm{54}''\right)\centerdot\mathrm{800} \\ $$

Question Number 213688 Answers: 2 Comments: 0

Question Number 213680 Answers: 0 Comments: 3

Question Number 213679 Answers: 0 Comments: 0

Q213662 ...... Not easy....... _p F_q (z; a,b) is hypergeometric function Li_ν (z) is Dilogarithm function.

$${Q}\mathrm{213662} \\ $$$$...... \\ $$$$\mathrm{Not}\:\mathrm{easy}....... \\ $$$$\:\:_{{p}} \boldsymbol{\mathrm{F}}_{{q}} \left({z};\cancel{\underbrace{ }}\:\boldsymbol{\mathrm{a}},\boldsymbol{\mathrm{b}}\right)\:\mathrm{is}\:\mathrm{hypergeometric}\:\mathrm{function} \\ $$$$\mathrm{Li}_{\nu} \left({z}\right)\:\mathrm{is}\:\mathrm{Dilogarithm}\:\mathrm{function}. \\ $$

Question Number 213668 Answers: 4 Comments: 1

Question Number 213667 Answers: 0 Comments: 0

Question Number 213664 Answers: 2 Comments: 0

Question Number 213663 Answers: 1 Comments: 0

Given a,b,c is natural numbers such that (a−b)(b−c)(c−a)=a+b+c. find min value of a+b+c

$$\:\:\mathrm{Given}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{is}\:\mathrm{natural}\:\mathrm{numbers} \\ $$$$\:\:\mathrm{such}\:\mathrm{that}\:\left(\mathrm{a}−\mathrm{b}\right)\left(\mathrm{b}−\mathrm{c}\right)\left(\mathrm{c}−\mathrm{a}\right)=\mathrm{a}+\mathrm{b}+\mathrm{c}. \\ $$$$\:\:\mathrm{find}\:\mathrm{min}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}+\mathrm{b}+\mathrm{c}\: \\ $$

Question Number 213662 Answers: 1 Comments: 0

Question Number 213661 Answers: 1 Comments: 1

Question Number 213660 Answers: 0 Comments: 0

prove that ... lim_(n→∞) ∫_0 ^( 3) (( x^2 (1−x )x^n )/(1+ x^(2n) )) dx=^? 0 −−−−−−−−−−−

$$ \\ $$$$\:\:\:\:\:{prove}\:{that}\:... \\ $$$$\mathrm{lim}_{{n}\rightarrow\infty} \int_{\mathrm{0}} ^{\:\mathrm{3}} \frac{\:{x}^{\mathrm{2}} \:\left(\mathrm{1}−{x}\:\right){x}^{{n}} \:}{\mathrm{1}+\:{x}^{\mathrm{2}{n}} }\:{dx}\overset{?} {=}\mathrm{0} \\ $$$$\:\:\:\:\:−−−−−−−−−−− \\ $$$$ \\ $$

Question Number 213659 Answers: 1 Comments: 0

∫_(−∞) ^∞ ((∣24x−24∣−20)/(22^x +22)) dx =?

$$\:\:\:\:\underset{−\infty} {\overset{\infty} {\int}}\:\frac{\mid\mathrm{24x}−\mathrm{24}\mid−\mathrm{20}}{\mathrm{22}^{\mathrm{x}} +\mathrm{22}}\:\mathrm{dx}\:=? \\ $$

Question Number 213658 Answers: 1 Comments: 0

r=((112452−(((2108)(3820))/(80)))/( (√(67778−(((2108)^2 )/(80))(√(232470−(((3820)^2 )/(80))))))))

$${r}=\frac{\mathrm{112452}−\frac{\left(\mathrm{2108}\right)\left(\mathrm{3820}\right)}{\mathrm{80}}}{\:\sqrt{\mathrm{67778}−\frac{\left(\mathrm{2108}\right)^{\mathrm{2}} }{\mathrm{80}}\sqrt{\mathrm{232470}−\frac{\left(\mathrm{3820}\right)^{\mathrm{2}} }{\mathrm{80}}}}} \\ $$$$ \\ $$$$ \\ $$

Question Number 213656 Answers: 1 Comments: 0

Question Number 213652 Answers: 1 Comments: 0

Show that ∫xdx=(x^2 /x)+C.

$$\mathrm{Show}\:\mathrm{that}\:\int{xdx}=\frac{{x}^{\mathrm{2}} }{{x}}+{C}. \\ $$

Question Number 213650 Answers: 1 Comments: 0

Show that the pythagorean theorem a^2 +b^2 =c^2 exist.

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{pythagorean}\:\mathrm{theorem}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \:\mathrm{exist}. \\ $$

Question Number 213648 Answers: 0 Comments: 0

a_m =Σ_(h=m) ^∞ ((1/h))^2 =(π^2 /6)−Σ_(h=1) ^m ((1/h))^2 a_m ≈𝛙^((1)) (m+1) 𝛙^((n)) (z)=((d^(n+1) )/dz^(n+1) )ln(𝚪(z)) , C\Z_(≤0) aka polygamma function 1. lim_(m→∞) m𝛙^((1)) (m+1)=1. and... 2. lim_(m→∞) m^2 𝛙^((1)) (m+1)=∞ div m^2 𝛙^((1)) (m+1)≈m−𝛜 lim_(m→∞) m^2 𝛙^((1)) (m+1)≈lim_(m→∞) (m−𝛜)=∞

$${a}_{{m}} =\underset{{h}={m}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{{h}}\right)^{\mathrm{2}} =\frac{\pi^{\mathrm{2}} }{\mathrm{6}}−\underset{{h}=\mathrm{1}} {\overset{{m}} {\sum}}\:\left(\frac{\mathrm{1}}{{h}}\right)^{\mathrm{2}} \\ $$$${a}_{{m}} \approx\boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left({m}+\mathrm{1}\right) \\ $$$$\boldsymbol{\psi}^{\left({n}\right)} \left({z}\right)=\frac{\mathrm{d}^{{n}+\mathrm{1}} \:\:}{\mathrm{d}{z}^{{n}+\mathrm{1}} }\mathrm{ln}\left(\boldsymbol{\Gamma}\left({z}\right)\right)\:,\:\mathbb{C}\backslash\mathbb{Z}_{\leq\mathrm{0}} \\ $$$$\mathrm{aka}\:\:\mathrm{polygamma}\:\mathrm{function} \\ $$$$\mathrm{1}.\:\:\underset{{m}\rightarrow\infty} {\mathrm{lim}}\:{m}\boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left({m}+\mathrm{1}\right)=\mathrm{1}. \\ $$$$\mathrm{and}... \\ $$$$\mathrm{2}.\:\:\:\underset{{m}\rightarrow\infty} {\mathrm{lim}}{m}^{\mathrm{2}} \boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left({m}+\mathrm{1}\right)=\infty\:\mathrm{div} \\ $$$${m}^{\mathrm{2}} \boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left({m}+\mathrm{1}\right)\approx{m}−\boldsymbol{\varepsilon} \\ $$$$\underset{{m}\rightarrow\infty} {\mathrm{lim}}\:{m}^{\mathrm{2}} \boldsymbol{\psi}^{\left(\mathrm{1}\right)} \left({m}+\mathrm{1}\right)\approx\underset{{m}\rightarrow\infty} {\mathrm{lim}}\:\left({m}−\boldsymbol{\varepsilon}\right)=\infty \\ $$

Question Number 213643 Answers: 3 Comments: 0

Find the maximum value of 3sin^2 x−8cosx+5=?

$$\:{Find}\:{the}\:{maximum}\:{value}\:{of} \\ $$$$\:\mathrm{3}{sin}^{\mathrm{2}} {x}−\mathrm{8}{cosx}+\mathrm{5}=? \\ $$

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