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Question Number 150486 Answers: 0 Comments: 2

x ∈ R ∣x - 1∣ + ∣x + 3∣ + ∣x - 5∣ find the smallest value of a given expression

$$\boldsymbol{\mathrm{x}}\:\in\:\mathbb{R} \\ $$$$\mid\mathrm{x}\:-\:\mathrm{1}\mid\:+\:\mid\mathrm{x}\:+\:\mathrm{3}\mid\:+\:\mid\mathrm{x}\:-\:\mathrm{5}\mid \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{given} \\ $$$$\mathrm{expression} \\ $$

Question Number 150453 Answers: 0 Comments: 0

In △ABC , △A^′ B^′ C^′ the following relationship holds: R^2 R^′ F^′ ≥ 8F(r^′ )^3

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC}\:,\:\bigtriangleup\mathrm{A}^{'} \mathrm{B}^{'} \mathrm{C}^{'} \:\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{relationship}\:\mathrm{holds}: \\ $$$$\mathrm{R}^{\mathrm{2}} \mathrm{R}^{'} \mathrm{F}^{'} \:\geqslant\:\mathrm{8F}\left(\mathrm{r}^{'} \right)^{\mathrm{3}} \\ $$

Question Number 150451 Answers: 2 Comments: 2

Question Number 150446 Answers: 0 Comments: 0

Question Number 150435 Answers: 1 Comments: 0

Solve the equation: ∣x - 3∣^((x^2 - 8x + 15)/(x - 2)) = 1

$$\boldsymbol{\mathrm{S}}\mathrm{olve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\mid\mathrm{x}\:-\:\mathrm{3}\mid^{\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:-\:\mathrm{8x}\:+\:\mathrm{15}}{\boldsymbol{\mathrm{x}}\:-\:\mathrm{2}}} \:=\:\mathrm{1} \\ $$

Question Number 150432 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (((2n+1)!)/(8^n ∙(n!)^2 ))=? Help please

$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(\mathrm{2n}+\mathrm{1}\right)!}{\mathrm{8}^{\mathrm{n}} \centerdot\left(\mathrm{n}!\right)^{\mathrm{2}} }=?\:\:\:\:\:\mathrm{Help}\:\mathrm{please} \\ $$

Question Number 150429 Answers: 1 Comments: 0

Find the equations of the common tangents to the parabola y^2 =4x and the parabola x^2 =2y−3.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equations}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{tangents}\:\mathrm{to}\:\mathrm{the}\:\mathrm{parabola}\:{y}^{\mathrm{2}} =\mathrm{4}{x}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{parabola}\:{x}^{\mathrm{2}} =\mathrm{2}{y}−\mathrm{3}. \\ $$

Question Number 150425 Answers: 0 Comments: 6

Question Number 150421 Answers: 0 Comments: 0

Question Number 150418 Answers: 2 Comments: 3

Question Number 150413 Answers: 0 Comments: 3

Question Number 150410 Answers: 1 Comments: 1

Question Number 150392 Answers: 0 Comments: 0

Question Number 150376 Answers: 1 Comments: 2

Question Number 150374 Answers: 1 Comments: 0

Σ_(k=0) ^∞ ((2^k + 3^k )/5^k ) = ?

$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{2}^{\boldsymbol{\mathrm{k}}} \:+\:\mathrm{3}^{\boldsymbol{\mathrm{k}}} }{\mathrm{5}^{\boldsymbol{\mathrm{k}}} }\:\:=\:? \\ $$

Question Number 150372 Answers: 0 Comments: 1

Question Number 150450 Answers: 0 Comments: 0

show the?connection between the beta distribution(n,p) and hypergeometric distribution(N,k,n)in a limiting case

$$\mathrm{show}\:\mathrm{the}?\mathrm{connection}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{beta}\:\mathrm{distribution}\left(\mathrm{n},\mathrm{p}\right)\:\mathrm{and}\:\mathrm{hypergeometric} \\ $$$$\mathrm{distribution}\left(\mathrm{N},\mathrm{k},\mathrm{n}\right)\mathrm{in}\:\mathrm{a}\:\mathrm{limiting}\:\mathrm{case} \\ $$

Question Number 150366 Answers: 0 Comments: 1

Question Number 150405 Answers: 2 Comments: 0

Question Number 150404 Answers: 4 Comments: 0

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

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

Question Number 150402 Answers: 1 Comments: 1

For m≥1 𝛀 =∫_( 0) ^( ∞) ((x ln^m (x))/(e^x − 1)) = 2 ln^m 𝛇(3)

$$\mathrm{For}\:\:\mathrm{m}\geqslant\mathrm{1} \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\infty} {\int}}\:\frac{\mathrm{x}\:\mathrm{ln}^{\boldsymbol{\mathrm{m}}} \:\left(\mathrm{x}\right)}{\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:−\:\mathrm{1}}\:=\:\mathrm{2}\:\mathrm{ln}^{\boldsymbol{\mathrm{m}}} \:\boldsymbol{\zeta}\left(\mathrm{3}\right) \\ $$

Question Number 150400 Answers: 0 Comments: 0

Question Number 150363 Answers: 2 Comments: 5

Question Number 150469 Answers: 1 Comments: 0

If f(x) = (4^x /(4^x + 2)) find f((1/(17))) + f(((16)/(17))) =^(?)

$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4}^{\boldsymbol{\mathrm{x}}} }{\mathrm{4}^{\boldsymbol{\mathrm{x}}} \:+\:\mathrm{2}}\:\:\:\mathrm{find}\:\:\:\mathrm{f}\left(\frac{\mathrm{1}}{\mathrm{17}}\right)\:+\:\mathrm{f}\left(\frac{\mathrm{16}}{\mathrm{17}}\right)\:\overset{?} {=} \\ $$

Question Number 150351 Answers: 1 Comments: 2

Question Number 150350 Answers: 0 Comments: 0

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