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Question Number 212716 Answers: 1 Comments: 0

cos(π/7)+cos((3π)/7)+cos((5π)/7)=?

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{cos}\frac{\pi}{\mathrm{7}}+\mathrm{cos}\frac{\mathrm{3}\pi}{\mathrm{7}}+\mathrm{cos}\frac{\mathrm{5}\pi}{\mathrm{7}}=? \\ $$

Question Number 212714 Answers: 2 Comments: 0

Question Number 212711 Answers: 1 Comments: 0

f(x)=(1/(1−x)) y=f(x), z=f(y), f(z)=?

$$\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}−{x}} \\ $$$$\:{y}={f}\left({x}\right),\:{z}={f}\left({y}\right),\:{f}\left({z}\right)=? \\ $$

Question Number 212690 Answers: 1 Comments: 0

Question Number 212686 Answers: 4 Comments: 4

in how many ways can a teacher divide his 10 studens into 4 groups such that each group has at least 2 students?

$${in}\:{how}\:{many}\:{ways}\:{can}\:{a}\:{teacher} \\ $$$${divide}\:{his}\:\mathrm{10}\:{studens}\:{into}\:\mathrm{4}\:{groups} \\ $$$${such}\:{that}\:{each}\:{group}\:{has}\:{at}\:{least}\:\mathrm{2}\: \\ $$$${students}? \\ $$

Question Number 212673 Answers: 3 Comments: 0

(√(2x+3)) + x = x^2 −3

$$\:\:\: \\ $$$$ \sqrt{\mathrm{2x}+\mathrm{3}}\:+\:\mathrm{x}\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{3} \\ $$

Question Number 212669 Answers: 1 Comments: 1

Question Number 212668 Answers: 4 Comments: 0

Question Number 212654 Answers: 1 Comments: 0

Question Number 212651 Answers: 1 Comments: 0

Question Number 212646 Answers: 1 Comments: 1

lim_(n→∞) Σ_(i=1) ^n Σ_(j=i) ^i ((i(i+j))/((n^2 +i^2 )(n^2 +j^2 )))

$$ \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\underset{{j}={i}} {\overset{{i}} {\sum}}\frac{{i}\left({i}+{j}\right)}{\left({n}^{\mathrm{2}} +{i}^{\mathrm{2}} \right)\left({n}^{\mathrm{2}} +{j}^{\mathrm{2}} \right)} \\ $$

Question Number 212645 Answers: 0 Comments: 0

{ ((x=2+ log _2 log _2 y)),((y=2 log _2 z )),((z=2+ log _2 log _2 x )) :}

$$\:\:\begin{cases}{\mathrm{x}=\mathrm{2}+\:\mathrm{log}\:_{\mathrm{2}} \mathrm{log}\:_{\mathrm{2}} \mathrm{y}}\\{\mathrm{y}=\mathrm{2}\:\mathrm{log}\:_{\mathrm{2}} \mathrm{z}\:}\\{\mathrm{z}=\mathrm{2}+\:\mathrm{log}\:_{\mathrm{2}} \:\mathrm{log}\:_{\mathrm{2}} \mathrm{x}\:}\end{cases} \\ $$

Question Number 212643 Answers: 0 Comments: 6

Guess we can make youtube educational videos using this forum′s editor in offline mode. Tinkutara team, let me know. I alresdy made one..here

$${Guess}\:{we}\:{can}\:{make}\:{youtube}\: \\ $$$${educational}\:{videos}\:{using}\:{this}\: \\ $$$${forum}'{s}\:{editor}\:{in}\:{offline}\:{mode}. \\ $$$${Tinkutara}\:{team},\:{let}\:{me}\:{know}. \\ $$$${I}\:{alresdy}\:{made}\:{one}..{here} \\ $$

Question Number 212635 Answers: 1 Comments: 1

m≤∫_1 ^3 ((1 )/(√(2x^2 +7 ))) .dx≤k find the value of the constant m and k

$$\:\:\boldsymbol{{m}}\leqslant\underset{\mathrm{1}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{1}\:}{\sqrt{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{7}\:}}\:.\boldsymbol{{dx}}\leqslant\boldsymbol{{k}}\:\boldsymbol{{find}} \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{value}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{constant}} \\ $$$$\:\:\boldsymbol{{m}}\:\boldsymbol{{and}}\:\boldsymbol{{k}} \\ $$

Question Number 212630 Answers: 2 Comments: 1

Question Number 212627 Answers: 1 Comments: 0

lim_(n→∞) (((√(1∙2))/(n^2 +1))+((√(2∙3))/(n^2 +2))+…+((√(n(n+1)))/(n^2 +n)))

$$ \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\sqrt{\mathrm{1}\centerdot\mathrm{2}}}{{n}^{\mathrm{2}} +\mathrm{1}}+\frac{\sqrt{\mathrm{2}\centerdot\mathrm{3}}}{{n}^{\mathrm{2}} +\mathrm{2}}+\ldots+\frac{\sqrt{{n}\left({n}+\mathrm{1}\right)}}{{n}^{\mathrm{2}} +{n}}\right) \\ $$

Question Number 212626 Answers: 1 Comments: 0

let f(x)=(1/( (√((x−a)(x−b)(x−c))))) let a, b, c ∈R ∧a<b<c ⇒ D(f(x))=(a, b)∪(c, ∞) prove ∫_a ^b f(x)dx=∫_c ^∞ f(x)dx

$$\mathrm{let}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\left({x}−{a}\right)\left({x}−{b}\right)\left({x}−{c}\right)}} \\ $$$$\mathrm{let}\:{a},\:{b},\:{c}\:\in\mathbb{R}\:\wedge{a}<{b}<{c} \\ $$$$\Rightarrow\:{D}\left({f}\left({x}\right)\right)=\left({a},\:{b}\right)\cup\left({c},\:\infty\right) \\ $$$$\mathrm{prove}\:\underset{{a}} {\overset{{b}} {\int}}{f}\left({x}\right){dx}=\underset{{c}} {\overset{\infty} {\int}}{f}\left({x}\right){dx} \\ $$

Question Number 212621 Answers: 0 Comments: 1

A group of n people are standing in a circle. They are numbered with 1, 2, 3, etc. Starting with the person with the number 1, every second person is removed from the circle and this process continues until only one person remains in the circle. What will be the number of the last person left.

$$\mathrm{A}\:\mathrm{group}\:\mathrm{of}\:\boldsymbol{\mathrm{n}}\:\mathrm{people}\:\mathrm{are}\:\mathrm{standing}\:\mathrm{in} \\ $$$$\mathrm{a}\:\mathrm{circle}.\:\:\mathrm{They}\:\mathrm{are}\:\mathrm{numbered}\:\mathrm{with}\: \\ $$$$\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{etc}.\:\mathrm{Starting}\:\mathrm{with}\:\mathrm{the}\:\mathrm{person} \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{number}\:\mathrm{1},\:\mathrm{every}\:\mathrm{second}\: \\ $$$$\mathrm{person}\:\mathrm{is}\:\mathrm{removed}\:\mathrm{from}\:\mathrm{the}\:\mathrm{circle}\:\mathrm{and}\: \\ $$$$\mathrm{this}\:\mathrm{process}\:\mathrm{continues}\:\mathrm{until}\:\mathrm{only}\:\mathrm{one}\: \\ $$$$\mathrm{person}\:\mathrm{remains}\:\mathrm{in}\:\mathrm{the}\:\mathrm{circle}.\:\:\mathrm{What} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{person} \\ $$$$\mathrm{left}. \\ $$

Question Number 212618 Answers: 0 Comments: 1

lim_(n→0) (Π_(k=1) ^n ((k^2 +3k+2)/(k^2 +2k+1)))^(1/n)

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{{k}^{\mathrm{2}} +\mathrm{3}{k}+\mathrm{2}}{{k}^{\mathrm{2}} +\mathrm{2}{k}+\mathrm{1}}\right)^{\frac{\mathrm{1}}{{n}}} \\ $$

Question Number 212616 Answers: 0 Comments: 1

if f(x)=^a x=x^x^x^⋰^x (there are a x′s;a∈N and a≠0) ∫f(x)dx=?

$$ \\ $$$$ \\ $$$${if}\:\:\mathrm{f}\left(\mathrm{x}\right)=\:^{{a}} {x}={x}^{{x}^{{x}^{\iddots^{{x}} } } } \left({there}\:{are}\:{a}\:{x}'{s};{a}\in\mathbb{N}\:{and}\:{a}\neq\mathrm{0}\right) \\ $$$$\int{f}\left({x}\right){dx}=? \\ $$

Question Number 212612 Answers: 1 Comments: 0

Solve the differential equation: (dy/dx) = cos(x + y)

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}: \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:\:=\:\:\mathrm{cos}\left(\mathrm{x}\:+\:\mathrm{y}\right) \\ $$

Question Number 212609 Answers: 1 Comments: 0

If 0≤x≤2 Prove that: 2^x + 1 − (√(10,5x + 4)) ≤ 0