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Question Number 166718 Answers: 0 Comments: 1

csc10−(√3)sec10=?

$${csc}\mathrm{10}−\sqrt{\mathrm{3}}{sec}\mathrm{10}=? \\ $$

Question Number 166715 Answers: 1 Comments: 0

The perimeter of an equilateral triangle is 24. Find it′s area.

$$\mathrm{The}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}\:\mathrm{is}\:\mathrm{24}.\:\mathrm{Find}\:\mathrm{it}'\mathrm{s}\:\mathrm{area}. \\ $$

Question Number 166707 Answers: 1 Comments: 0

(8/(1×5×9))+(8/(5×9×13))+(8/(9×13×17))+…+(1/(41×45×49))=? by M.A

$$\frac{\mathrm{8}}{\mathrm{1}×\mathrm{5}×\mathrm{9}}+\frac{\mathrm{8}}{\mathrm{5}×\mathrm{9}×\mathrm{13}}+\frac{\mathrm{8}}{\mathrm{9}×\mathrm{13}×\mathrm{17}}+\ldots+\frac{\mathrm{1}}{\mathrm{41}×\mathrm{45}×\mathrm{49}}=? \\ $$$$ \\ $$$$ \\ $$$$\boldsymbol{{by}}\:\boldsymbol{{M}}.\boldsymbol{{A}} \\ $$

Question Number 166702 Answers: 0 Comments: 1

∫e^x ln(x)dx=..???

$$\int{e}^{{x}} {ln}\left({x}\right){dx}=..??? \\ $$

Question Number 166701 Answers: 2 Comments: 0

Question Number 166699 Answers: 1 Comments: 0

lim_(n→∞) Σ_(k=n) ^(2n) sin (π/k)=?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{n}} {\overset{\mathrm{2n}} {\sum}}\mathrm{sin}\:\frac{\pi}{\mathrm{k}}=? \\ $$

Question Number 166697 Answers: 0 Comments: 1

Σ_(n=0) ^∞ (1/((3n)!)) =^? (1/3) [e + ((2cos((3/( 2(√3)))))/( (√e)))]

$$\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{3n}\right)!}\:\overset{?} {=}\:\frac{\mathrm{1}}{\mathrm{3}}\:\left[\mathrm{e}\:+\:\frac{\mathrm{2cos}\left(\frac{\mathrm{3}}{\:\mathrm{2}\sqrt{\mathrm{3}}}\right)}{\:\sqrt{\mathrm{e}}}\right] \\ $$$$\: \\ $$

Question Number 166690 Answers: 1 Comments: 0

Calculate If , 𝛗= ∫_0 ^( 1) (( tanh^( −1) ( x^( 3) ))/x) dx = α.ζ( 2) then , α = ? ■ M.N −−−−−−−

$$ \\ $$$$\:\:\:\:\:\:\:\:\:{Calculate}\: \\ $$$$\:\:\:\:\:{If}\:\:,\:\boldsymbol{\phi}=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{tanh}^{\:−\mathrm{1}} \left(\:{x}^{\:\mathrm{3}} \:\right)}{{x}}\:{dx}\:=\:\alpha.\zeta\left(\:\mathrm{2}\right)\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{then}\:,\:\:\:\:\:\alpha\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\blacksquare\:\mathscr{M}.\mathscr{N}\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−−−−−−− \\ $$$$ \\ $$

Question Number 166687 Answers: 1 Comments: 1

log _((2x−1)) (x+1) > log _((4−2x)) (x+1) x=?

$$\:\:\:\mathrm{log}\:_{\left(\mathrm{2x}−\mathrm{1}\right)} \left(\mathrm{x}+\mathrm{1}\right)\:>\:\mathrm{log}\:_{\left(\mathrm{4}−\mathrm{2x}\right)} \left(\mathrm{x}+\mathrm{1}\right) \\ $$$$\:\:\mathrm{x}=? \\ $$

Question Number 166686 Answers: 0 Comments: 1

Question Number 166685 Answers: 0 Comments: 0

sec^2 1°+sec^2 2°+sec^2 3°+...+sec^2 89°=?

$$\:\:\:\mathrm{sec}\:^{\mathrm{2}} \mathrm{1}°+\mathrm{sec}\:^{\mathrm{2}} \mathrm{2}°+\mathrm{sec}\:^{\mathrm{2}} \mathrm{3}°+...+\mathrm{sec}\:^{\mathrm{2}} \mathrm{89}°=? \\ $$

Question Number 166684 Answers: 0 Comments: 0

T = ∫ ((sin (x^2 +2))/(2x+4)) dx=?

$$\:\:\:\:\:\:\mathrm{T}\:=\:\int\:\frac{\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)}{\mathrm{2x}+\mathrm{4}}\:\mathrm{dx}=? \\ $$

Question Number 166683 Answers: 0 Comments: 0

Question Number 166678 Answers: 1 Comments: 0

4+x+2x=8+2(3+x)−3 Find x

$$\mathrm{4}+\boldsymbol{{x}}+\mathrm{2}\boldsymbol{{x}}=\mathrm{8}+\mathrm{2}\left(\mathrm{3}+\boldsymbol{{x}}\right)−\mathrm{3} \\ $$$$\boldsymbol{{F}}{ind}\:{x} \\ $$$$ \\ $$

Question Number 166676 Answers: 1 Comments: 0

Question Number 166670 Answers: 0 Comments: 3

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 = ?

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

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