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Question Number 166695 Answers: 2 Comments: 0

Question Number 166693 Answers: 0 Comments: 0

((√7)/(8sin (π/7)sin ((2π)/7)sin ((3π)/7))) =?

$$\:\:\:\:\:\:\frac{\sqrt{\mathrm{7}}}{\mathrm{8sin}\:\frac{\pi}{\mathrm{7}}\mathrm{sin}\:\frac{\mathrm{2}\pi}{\mathrm{7}}\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{7}}}\:=? \\ $$

Question Number 166660 Answers: 1 Comments: 0

calculate Ω = Σ_(n=0) ^∞ (1/((3n)!)) = ?

$$ \\ $$$$\:\:\:{calculate} \\ $$$$\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{3}{n}\right)!}\:\:=\:? \\ $$$$\:\:\:\:\: \\ $$

Question Number 166649 Answers: 0 Comments: 1

Question Number 166648 Answers: 1 Comments: 0

u_(n+1) = (√(2+u_n )) show that u_(n+1) −u_n and u_n −u_(n−1) have same sign

$${u}_{{n}+\mathrm{1}} \:=\:\sqrt{\mathrm{2}+{u}_{{n}} } \\ $$$${show}\:{that}\:{u}_{{n}+\mathrm{1}} −{u}_{{n}} \:{and}\:{u}_{{n}} −{u}_{{n}−\mathrm{1}} \\ $$$${have}\:{same}\:{sign} \\ $$$$ \\ $$

Question Number 166641 Answers: 1 Comments: 1

From the standard equation of a circle, using the origin (0,0), we deduced the eqution (x−a)^2 +(y−b)^2 =r^2 to x^2 +y^2 =r^2 . In what terms do we use this formular?

$$\mathrm{From}\:\mathrm{the}\:\mathrm{standard}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}, \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{origin}\:\left(\mathrm{0},\mathrm{0}\right),\:\mathrm{we}\:\mathrm{deduced}\:\mathrm{the}\:\mathrm{eqution} \\ $$$$\left(\mathrm{x}−\mathrm{a}\right)^{\mathrm{2}} +\left(\mathrm{y}−\mathrm{b}\right)^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} \:\mathrm{to}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} . \\ $$$$\mathrm{In}\:\mathrm{what}\:\mathrm{terms}\:\mathrm{do}\:\mathrm{we}\:\mathrm{use}\:\mathrm{this}\:\mathrm{formular}? \\ $$

Question Number 166640 Answers: 1 Comments: 0

Question Number 166633 Answers: 1 Comments: 0

Question Number 166628 Answers: 0 Comments: 0

Question Number 166627 Answers: 2 Comments: 2

If f(x)=x+x^3 +x^5 +...+x^n and lim_(x→1) ((f^2 (x)−f^2 (1))/(x−1)) = 2^(10) then n = ?

$$\:\:\:\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{5}} +...+\mathrm{x}^{\mathrm{n}} \:\mathrm{and}\: \\ $$$$\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{f}^{\mathrm{2}} \left(\mathrm{1}\right)}{\mathrm{x}−\mathrm{1}}\:=\:\mathrm{2}^{\mathrm{10}} \:\mathrm{then}\:\mathrm{n}\:=\:? \\ $$

Question Number 166625 Answers: 0 Comments: 0

((18)/({x}))−((19)/x) ≤ ((20)/(x−1))

$$\:\:\:\frac{\mathrm{18}}{\left\{\mathrm{x}\right\}}−\frac{\mathrm{19}}{\mathrm{x}}\:\leqslant\:\frac{\mathrm{20}}{\mathrm{x}−\mathrm{1}}\: \\ $$

Question Number 166653 Answers: 0 Comments: 0

Question Number 166620 Answers: 2 Comments: 0

Question Number 166619 Answers: 1 Comments: 0

(2/(log_(10) (6)))=(π^x /7) How much the x is?

$$\frac{\mathrm{2}}{\mathrm{log}_{\mathrm{10}} \left(\mathrm{6}\right)}=\frac{\pi^{{x}} }{\mathrm{7}} \\ $$$${How}\:{much}\:{the}\:{x}\:{is}? \\ $$

Question Number 166617 Answers: 2 Comments: 1

Question Number 166616 Answers: 0 Comments: 0

calculate::lim_(n→∞) ((∣cos 1^2 ∣+cos ∣2^2 ∣+∣cos 3^2 ∣+...+∣cos n^2 ∣)/n)=(2/π)

$$\mathrm{calculate}::\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mid\mathrm{cos}\:\mathrm{1}^{\mathrm{2}} \mid+\mathrm{cos}\:\mid\mathrm{2}^{\mathrm{2}} \mid+\mid\mathrm{cos}\:\mathrm{3}^{\mathrm{2}} \mid+...+\mid\mathrm{cos}\:\mathrm{n}^{\mathrm{2}} \mid}{\mathrm{n}}=\frac{\mathrm{2}}{\pi} \\ $$

Question Number 166614 Answers: 0 Comments: 0

calculate:: ∫_0 ^∞ (({x}^2 (1−{x})^2 )/((1+x)^5 ))=(7/(12))−γ

$$\mathrm{calculate}::\:\:\:\int_{\mathrm{0}} ^{\infty} \frac{\left\{\mathrm{x}\right\}^{\mathrm{2}} \left(\mathrm{1}−\left\{\mathrm{x}\right\}\right)^{\mathrm{2}} }{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{5}} }=\frac{\mathrm{7}}{\mathrm{12}}−\gamma \\ $$

Question Number 166612 Answers: 1 Comments: 2

∫_0 ^( (π/2)) (1/(1+cos(x)+2sin(x)))dx=?

$$ \\ $$$$\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{1}}{\mathrm{1}+{cos}\left({x}\right)+\mathrm{2}{sin}\left({x}\right)}{dx}=? \\ $$

Question Number 166606 Answers: 0 Comments: 0

Question Number 166611 Answers: 0 Comments: 0

Given f(x) is a polynom give the remainder x^2 −x−1 when divided by x^4 +4. Find the remainder when f(x) divided by x^2 −2x+2.

$$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{polynom}\:\mathrm{give}\:\mathrm{the}\: \\ $$$$\:\mathrm{remainder}\:\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\: \\ $$$$\:\mathrm{x}^{\mathrm{4}} +\mathrm{4}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\:\mathrm{divided}\:\mathrm{by}\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}. \\ $$

Question Number 166610 Answers: 1 Comments: 1

∫ ((x^2 +3)/(x^4 +5x^2 +9)) dx ?

$$\:\:\:\:\int\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{3}}{\mathrm{x}^{\mathrm{4}} +\mathrm{5x}^{\mathrm{2}} +\mathrm{9}}\:\mathrm{dx}\:? \\ $$

Question Number 166602 Answers: 0 Comments: 0

Determine condition/s that a number divisible by 11 is a palindrome-number.

$$\mathcal{D}{etermine}\:{condition}/{s}\:{that} \\ $$$${a}\:\boldsymbol{{number}}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{11} \\ $$$${is}\:{a}\:\boldsymbol{{palindrome}}-\boldsymbol{{number}}. \\ $$

Question Number 166601 Answers: 0 Comments: 0

What is the condition that a palindrome-number is divisible by 11?

$${What}\:{is}\:{the}\:{condition}\:{that}\: \\ $$$${a}\:\boldsymbol{{palindrome}}-\boldsymbol{{number}} \\ $$$$\:{is}\:\boldsymbol{{divisible}}\:\boldsymbol{{by}}\:\mathrm{11}? \\ $$

Question Number 166597 Answers: 0 Comments: 0

Question Number 166596 Answers: 0 Comments: 0

Question Number 166592 Answers: 1 Comments: 0

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