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Question Number 148532 Answers: 1 Comments: 0

Question Number 148513 Answers: 1 Comments: 0

6 + log_2 sin15° - log_(1/2) sin75° = ?

$$\mathrm{6}\:+\:{log}_{\mathrm{2}} \:{sin}\mathrm{15}°\:-\:{log}_{\frac{\mathrm{1}}{\mathrm{2}}} {sin}\mathrm{75}°\:=\:? \\ $$

Question Number 148505 Answers: 1 Comments: 0

Question Number 148502 Answers: 3 Comments: 0

let α and β roots of x^2 +x+2 simplify Σ_(k=0) ^(n−1) (α^k +β^k ) and Σ_(k=0) ^(n−1) ( (1/α^k )+(1/β^k ))

$$\mathrm{let}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{2} \\ $$$$\mathrm{simplify}\:\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}−\mathrm{1}} \:\:\left(\alpha^{\mathrm{k}} \:+\beta^{\mathrm{k}} \right)\:\:\mathrm{and}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}−\mathrm{1}} \left(\:\frac{\mathrm{1}}{\alpha^{\mathrm{k}} }+\frac{\mathrm{1}}{\beta^{\mathrm{k}} }\right) \\ $$

Question Number 148501 Answers: 2 Comments: 0

let U_n ={z∈C /z^n =1} simplify Σ_(p=0) ^(2n−1) w^p with w∈U_n and Σ_(p=0) ^(2n−1) (2w +1)^p

$$\mathrm{let}\:\mathrm{U}_{\mathrm{n}} =\left\{\mathrm{z}\in\mathrm{C}\:/\mathrm{z}^{\mathrm{n}} \:=\mathrm{1}\right\}\:\:\mathrm{simplify} \\ $$$$\sum_{\mathrm{p}=\mathrm{0}} ^{\mathrm{2n}−\mathrm{1}} \:\mathrm{w}^{\mathrm{p}} \:\:\:\:\:\:\:\:\mathrm{with}\:\mathrm{w}\in\mathrm{U}_{\mathrm{n}} \:\:\: \\ $$$$\mathrm{and}\:\:\sum_{\mathrm{p}=\mathrm{0}} ^{\mathrm{2n}−\mathrm{1}} \left(\mathrm{2w}\:+\mathrm{1}\right)^{\mathrm{p}} \\ $$

Question Number 148494 Answers: 1 Comments: 0

(((3+2(√2))^(2008) )/((7+5(√2))^(1338) )) + (3−2(√2)) = log _2 (x) x=?

$$\:\:\:\frac{\left(\mathrm{3}+\mathrm{2}\sqrt{\mathrm{2}}\right)^{\mathrm{2008}} }{\left(\mathrm{7}+\mathrm{5}\sqrt{\mathrm{2}}\right)^{\mathrm{1338}} }\:+\:\left(\mathrm{3}−\mathrm{2}\sqrt{\mathrm{2}}\right)\:=\:\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{x}\right) \\ $$$$\:\mathrm{x}=?\: \\ $$

Question Number 148489 Answers: 1 Comments: 0

Question Number 148482 Answers: 0 Comments: 2

Question Number 148498 Answers: 1 Comments: 0

find ∫_0 ^∞ ((arctan(2x))/(1+x^2 ))dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{arctan}\left(\mathrm{2x}\right)}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$

Question Number 148467 Answers: 2 Comments: 0

Question Number 148466 Answers: 2 Comments: 0

xdx+ydy=xdy−ydx

$$\mathrm{xdx}+\mathrm{ydy}=\mathrm{xdy}−\mathrm{ydx} \\ $$

Question Number 148454 Answers: 2 Comments: 0

sin^6 𝛂 + co^6 𝛂 = (3/4) ⇒ 6cos4𝛂=?

$${sin}^{\mathrm{6}} \boldsymbol{\alpha}\:+\:{co}^{\mathrm{6}} \boldsymbol{\alpha}\:=\:\frac{\mathrm{3}}{\mathrm{4}}\:\:\Rightarrow\:\:\mathrm{6}{cos}\mathrm{4}\boldsymbol{\alpha}=? \\ $$$$ \\ $$

Question Number 148453 Answers: 3 Comments: 0

(((n + 1)!)/(n!)) = 38 ⇒ n=?

$$\frac{\left({n}\:+\:\mathrm{1}\right)!}{{n}!}\:=\:\mathrm{38}\:\:\Rightarrow\:\:{n}=? \\ $$

Question Number 148452 Answers: 2 Comments: 0

∫_( 1) ^( 4) 2sin^2 x dx + ∫_( 1) ^( 4) (1+cos2x)dx = ?

$$\underset{\:\mathrm{1}} {\overset{\:\mathrm{4}} {\int}}\mathrm{2}{sin}^{\mathrm{2}} {x}\:{dx}\:+\:\underset{\:\mathrm{1}} {\overset{\:\mathrm{4}} {\int}}\left(\mathrm{1}+{cos}\mathrm{2}{x}\right){dx}\:=\:? \\ $$

Question Number 148447 Answers: 1 Comments: 0

sin(x)=a, a∈

$$\mathrm{sin}\left({x}\right)={a},\:{a}\in \\ $$

Question Number 148446 Answers: 0 Comments: 2

Soit a,b,c et α 4 nombres rationnels telque (α)^(1/3) est irrationnel.. Demontrer que : (a(α)^(1/3) +b(α)^(1/3) =c) ⇒ (a=b=c)..

$$\mathrm{Soit}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{et}\:\alpha\:\mathrm{4}\:\mathrm{nombres}\:\mathrm{rationnels} \\ $$$$\mathrm{telque}\:\sqrt[{\mathrm{3}}]{\alpha}\:\mathrm{est}\:\mathrm{irrationnel}.. \\ $$$$\mathrm{Demontrer}\:\mathrm{que}\:: \\ $$$$\left(\mathrm{a}\sqrt[{\mathrm{3}}]{\alpha}+\mathrm{b}\sqrt[{\mathrm{3}}]{\alpha}=\mathrm{c}\right)\:\Rightarrow\:\left(\mathrm{a}=\mathrm{b}=\mathrm{c}\right).. \\ $$

Question Number 148445 Answers: 1 Comments: 3

if cos𝛂 = (√a) find 5 - 6cos2𝛂 + cos4𝛂 = ?

$${if}\:\:\:{cos}\boldsymbol{\alpha}\:=\:\sqrt{\boldsymbol{{a}}} \\ $$$${find}\:\:\:\mathrm{5}\:-\:\mathrm{6}{cos}\mathrm{2}\boldsymbol{\alpha}\:+\:{cos}\mathrm{4}\boldsymbol{\alpha}\:=\:? \\ $$

Question Number 148443 Answers: 0 Comments: 0

Can i use this app on PC to tinkutara

$${Can}\:{i}\:{use}\:{this}\:{app}\:\:{on}\:{PC} \\ $$$${to}\:{tinkutara} \\ $$

Question Number 148441 Answers: 0 Comments: 0

Σ_(k=1) ^∞ Σ_(m=1) ^n ((n(m−1))/((nk+m−1)(nk+m)))=?

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\underset{\mathrm{m}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}\left(\mathrm{m}−\mathrm{1}\right)}{\left(\mathrm{nk}+\mathrm{m}−\mathrm{1}\right)\left(\mathrm{nk}+\mathrm{m}\right)}=? \\ $$

Question Number 148439 Answers: 3 Comments: 0

lim_(x→2) (((√(x+2)) ((x+6))^(1/3) −x^2 )/(x−2)) =?

$$\:\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{x}+\mathrm{6}}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}−\mathrm{2}}\:=? \\ $$

Question Number 148483 Answers: 1 Comments: 0

Soit f une fonction continu sur R et non identiquement nulle, ∀ x,x′∈R, f(x−x′)+f(x+x′)=2f(x)f(x′) montrer que: f(0)=1 et f(x)=f(−x)..

$$\mathrm{Soit}\:\mathrm{f}\:\mathrm{une}\:\mathrm{fonction}\:\mathrm{continu}\:\mathrm{sur}\:\mathbb{R} \\ $$$$\mathrm{et}\:\mathrm{non}\:\mathrm{identiquement}\:\mathrm{nulle}, \\ $$$$\forall\:\mathrm{x},\mathrm{x}'\in\mathbb{R},\:\mathrm{f}\left(\mathrm{x}−\mathrm{x}'\right)+\mathrm{f}\left(\mathrm{x}+\mathrm{x}'\right)=\mathrm{2f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{x}'\right) \\ $$$$\mathrm{montrer}\:\mathrm{que}: \\ $$$$\mathrm{f}\left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{et}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{f}\left(−\mathrm{x}\right).. \\ $$

Question Number 148428 Answers: 1 Comments: 0

Question Number 148427 Answers: 2 Comments: 0

Question Number 148421 Answers: 0 Comments: 0

lim_(x→∞) ((cos(x) - x!)/(3^x - 4^x )) = ?

$$\underset{\boldsymbol{{x}}\rightarrow\infty} {{lim}}\frac{{cos}\left({x}\right)\:-\:{x}!}{\mathrm{3}^{\boldsymbol{{x}}} \:-\:\mathrm{4}^{\boldsymbol{{x}}} }\:=\:? \\ $$

Question Number 148418 Answers: 1 Comments: 0

Find the natural roots of the equation x^2 - 51y^2 = 1

$${Find}\:{the}\:{natural}\:{roots}\:{of}\:{the}\:{equation} \\ $$$${x}^{\mathrm{2}} \:-\:\mathrm{51}{y}^{\mathrm{2}} \:=\:\mathrm{1} \\ $$

Question Number 148417 Answers: 0 Comments: 0

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