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Question Number 116079 Answers: 1 Comments: 0

prove that Re=((ρ∙v∙d)/μ) renulds number

$${prove}\:{that}\:{Re}=\frac{\rho\centerdot{v}\centerdot{d}}{\mu}\:\:\:\:\:{renulds}\:{number} \\ $$

Question Number 116078 Answers: 1 Comments: 0

prove that Fr=(v^2 /(gh)) froude numer

$${prove}\:{that}\:\:\:{Fr}=\frac{{v}^{\mathrm{2}} }{{gh}}\:\:\:\:{froude}\:{numer} \\ $$

Question Number 116061 Answers: 1 Comments: 0

Kent Mark is running for class president. Assume that there are a total of n ca− ndidates running, where n is a natu− ral number. After the votes are tallied, Kent Mark is told only the fraction of votes that he recieved. Suppose he recieved less than (1/n) of the votes. Show that he cannot have won the election.

$$\mathrm{Kent}\:\mathrm{Mark}\:\mathrm{is}\:\mathrm{running}\:\mathrm{for}\:\mathrm{class}\:\mathrm{president}. \\ $$$$\mathrm{Assume}\:\mathrm{that}\:\mathrm{there}\:\mathrm{are}\:\mathrm{a}\:\mathrm{total}\:\mathrm{of}\:\mathrm{n}\:\mathrm{ca}− \\ $$$$\mathrm{ndidates}\:\mathrm{running},\:\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{a}\:\mathrm{natu}− \\ $$$$\mathrm{ral}\:\mathrm{number}. \\ $$$$\mathrm{After}\:\mathrm{the}\:\mathrm{votes}\:\mathrm{are}\:\mathrm{tallied},\:\mathrm{Kent}\:\mathrm{Mark} \\ $$$$\mathrm{is}\:\mathrm{told}\:\mathrm{only}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{of}\:\mathrm{votes}\:\mathrm{that}\:\mathrm{he} \\ $$$$\mathrm{recieved}. \\ $$$$\mathrm{Suppose}\:\mathrm{he}\:\mathrm{recieved}\:\mathrm{less}\:\mathrm{than}\:\frac{\mathrm{1}}{\mathrm{n}}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{votes}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{he}\:\mathrm{cannot}\:\mathrm{have}\:\mathrm{won} \\ $$$$\mathrm{the}\:\mathrm{election}. \\ $$

Question Number 116059 Answers: 2 Comments: 0

Σ_(n=1) ^∞ ((n!)/3^(n+1) )

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}!}{\mathrm{3}^{{n}+\mathrm{1}} } \\ $$

Question Number 116057 Answers: 2 Comments: 0

Σ_(n=2) ^∞ (3/(3n+1))=?

$$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{3}}{\mathrm{3}{n}+\mathrm{1}}=? \\ $$

Question Number 116056 Answers: 2 Comments: 0

Σ_(n=1) ^∞ (5^n /(n!))=?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{5}^{{n}} }{{n}!}=? \\ $$

Question Number 116055 Answers: 1 Comments: 1

3(d^2 y/dx^2 )+4(dy/dx)+5y=0 y=?

$$\mathrm{3}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{4}\frac{{dy}}{{dx}}+\mathrm{5}{y}=\mathrm{0}\:\:\:\:\:\:{y}=? \\ $$

Question Number 116054 Answers: 1 Comments: 1

(x^2 +2xy+1)dx+(x^2 +y^2 −1)dy=0 y=?

$$\left({x}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{1}\right){dx}+\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{1}\right){dy}=\mathrm{0} \\ $$$${y}=? \\ $$

Question Number 116053 Answers: 2 Comments: 0

y(dy/dx)=1+x^2 y=?

$${y}\frac{{dy}}{{dx}}=\mathrm{1}+{x}^{\mathrm{2}} \:\:\:\:\:\:\:\:{y}=? \\ $$

Question Number 116052 Answers: 2 Comments: 1

(d^2 y/dx^2 )+25y=0 y=?

$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{25}{y}=\mathrm{0}\:\:\:\:\:\:\:{y}=? \\ $$

Question Number 116051 Answers: 1 Comments: 0

What is the modulus and the argument of 1+i(1+(√2)) ?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{modulus}\:\mathrm{and}\:\mathrm{the}\:\mathrm{argument} \\ $$$$\mathrm{of}\:\:\:\mathrm{1}+{i}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)\:\:? \\ $$

Question Number 116043 Answers: 1 Comments: 0

lim_(x→0) ((√(x^2 +x^4 ))/x) ? ∫ sinh^2 (x) cosh (x) dx find x from equation cos (2tan^(−1) (x))= (1/2)

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{4}} }}{\mathrm{x}}\:? \\ $$$$\:\:\:\int\:\mathrm{sinh}\:^{\mathrm{2}} \left(\mathrm{x}\right)\:\mathrm{cosh}\:\left(\mathrm{x}\right)\:\mathrm{dx}\: \\ $$$$\:\:\:\mathrm{find}\:\mathrm{x}\:\mathrm{from}\:\mathrm{equation}\:\mathrm{cos}\:\left(\mathrm{2tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\right)=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 116039 Answers: 1 Comments: 0

lim_(x→(π/2)) (((cos^4 (x)))^(1/(3 )) /((1−sin (x))^(2/3) )) ?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{cos}\:^{\mathrm{4}} \left({x}\right)}}{\left(\mathrm{1}−\mathrm{sin}\:\left({x}\right)\right)^{\frac{\mathrm{2}}{\mathrm{3}}} }\:? \\ $$

Question Number 116037 Answers: 2 Comments: 0

lim_(x→0) ((27^x −1)/(9^x −1)) = ??

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{27}^{{x}} −\mathrm{1}}{\mathrm{9}^{{x}} −\mathrm{1}}\:=\:?? \\ $$

Question Number 116029 Answers: 1 Comments: 0

lim_(x→(π/2)) ((cos x)/((1−sin x)^(2/3) )) =?

$$\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:{x}}{\left(\mathrm{1}−\mathrm{sin}\:{x}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} }\:=?\: \\ $$

Question Number 116024 Answers: 4 Comments: 0

∫ tan^3 2xdx

$$\int\:{tan}^{\mathrm{3}} \mathrm{2}{xdx} \\ $$

Question Number 116023 Answers: 2 Comments: 0

Find the sum to n terms of the series 1 + (x/a) (1 + x)+ (x^2 /a^2 ) (1 + x + x^2 )+ (x^3 /a^3 ) (1 + x + x^2 + x^3 ) + …

$$\:\:\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:+\:\frac{\mathrm{x}}{\mathrm{a}}\:\left(\mathrm{1}\:+\:\mathrm{x}\right)+\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }\:\left(\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \right)+\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{a}^{\mathrm{3}} }\:\left(\mathrm{1}\:+\:\mathrm{x}\:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{x}^{\mathrm{3}} \right)\:+\:\ldots \\ $$$$ \\ $$

Question Number 116338 Answers: 0 Comments: 1

Question Number 116019 Answers: 0 Comments: 3

lim_(x→0) (((d/dx) ∫_0 ^x sin (t^3 ) dt)/(2x^4 )) ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{{d}}{{dx}}\:\underset{\mathrm{0}} {\overset{{x}} {\int}}\:\mathrm{sin}\:\left({t}^{\mathrm{3}} \right)\:{dt}}{\mathrm{2}{x}^{\mathrm{4}} }\:? \\ $$

Question Number 116016 Answers: 1 Comments: 0

∫_(−1) ^1 (dx/( (√(6+x−x^2 )))) ?

$$\underset{−\mathrm{1}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\:\sqrt{\mathrm{6}+{x}−{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 116014 Answers: 1 Comments: 0

...nice calculus ... prove : i:∫_0 ^( ∞) ((ln(x))/((1+x^(√2) )^(√2) )) =0 ✓ ii: ∫_0 ^( ∞) (dx/((1+x^(1+(√2)) )^(1+(√2)) )) =(1/( (√2))) ✓ iii: ∫_0 ^( (π/2)) ln(x^2 +ln^2 (cos(x)))dx=πln(ln(2))✓ ... m.n. july.1970...

$$\:\:\:\:\:\:\:...{nice}\:\:{calculus}\:...\:\:\: \\ $$$$\:{prove}\:: \\ $$$$\:\:\:{i}:\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({x}\right)}{\left(\mathrm{1}+{x}^{\sqrt{\mathrm{2}}} \right)^{\sqrt{\mathrm{2}}} }\:=\mathrm{0}\:\:\:\:\:\:\checkmark \\ $$$$\:\:\:{ii}:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{1}+\sqrt{\mathrm{2}}} \right)^{\mathrm{1}+\sqrt{\mathrm{2}}} }\:=\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}\:\:\checkmark\:\: \\ $$$$\:\:\:{iii}:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {ln}\left({x}^{\mathrm{2}} +{ln}^{\mathrm{2}} \left({cos}\left({x}\right)\right)\right){dx}=\pi{ln}\left({ln}\left(\mathrm{2}\right)\right)\checkmark \\ $$$$\:\:\:\:\:\:\:...\:{m}.{n}.\:{july}.\mathrm{1970}... \\ $$$$ \\ $$

Question Number 116009 Answers: 2 Comments: 0

{ ((tan(a+b)=y)),((tan (a−b)=x)) :} tan2a=?

$$\begin{cases}{\mathrm{tan}\left(\mathrm{a}+\mathrm{b}\right)=\mathrm{y}}\\{\mathrm{tan}\:\left(\mathrm{a}−\mathrm{b}\right)=\mathrm{x}}\end{cases}\:\:\:\mathrm{tan2a}=? \\ $$

Question Number 116007 Answers: 2 Comments: 0

lim_(x→∝) ((√x)/(√(x+(√(x(√x))))))

$$\underset{{x}\rightarrow\propto} {\mathrm{lim}}\frac{\sqrt{\mathrm{x}}}{\sqrt{\mathrm{x}+\sqrt{\mathrm{x}\sqrt{\mathrm{x}}}}} \\ $$

Question Number 116006 Answers: 1 Comments: 0

3(sin x−cos x)^4 +6(sin x+cos x)^2 +4(sin^6 x+cos^6 x) = _____.

$$\mathrm{3}\left(\mathrm{sin}\:{x}−\mathrm{cos}\:{x}\right)^{\mathrm{4}} +\mathrm{6}\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:+\mathrm{4}\left(\mathrm{sin}^{\mathrm{6}} {x}+\mathrm{cos}^{\mathrm{6}} {x}\right)\:=\:\_\_\_\_\_. \\ $$

Question Number 116005 Answers: 0 Comments: 0

... advanced mathematics... prove that::: lim_(x→1^+ ) ( ζ( x ) −(1/(x − 1))) =^(???) γ γ:: Euler − mascheroni constant. m.n.huly 1970

$$\:\:\:\:\:\:\:\:\:...\:{advanced}\:\:{mathematics}... \\ $$$$ \\ $$$$\:\:\:\:\:{prove}\:\:{that}::: \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{lim}_{{x}\rightarrow\mathrm{1}^{+} } \left(\:\zeta\left(\:{x}\:\right)\:−\frac{\mathrm{1}}{{x}\:−\:\mathrm{1}}\right)\:\overset{???} {=}\gamma\:\:\: \\ $$$$\:\:\gamma::\:\mathscr{E}{uler}\:−\:{mascheroni}\:{constant}. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.{huly}\:\mathrm{1970} \\ $$$$ \\ $$

Question Number 116000 Answers: 0 Comments: 0

U(n)=∫_0 ^∞ ((1−tanh x)/( ((tanh x))^(1/n) ))dx another way?

$${U}\left({n}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}−\mathrm{tanh}\:{x}}{\:\sqrt[{{n}}]{\mathrm{tanh}\:{x}}}{dx} \\ $$$${another}\:{way}? \\ $$$$ \\ $$

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