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AllQuestion and Answers: Page 114

Question Number 212752 Answers: 1 Comments: 1

Question Number 212745 Answers: 2 Comments: 0

Question Number 212741 Answers: 1 Comments: 0

a, b,c ∈ N^∗ Show that ab<c ⇒ a+b≤c

$${a},\:{b},{c}\:\in\:\mathbb{N}^{\ast} \\ $$$$ \\ $$$${Show}\:{that}\:{ab}<{c}\:\Rightarrow\:{a}+{b}\leqslant{c} \\ $$$$ \\ $$

Question Number 212736 Answers: 3 Comments: 0

Question Number 212733 Answers: 1 Comments: 0

Question Number 212723 Answers: 1 Comments: 1

Question Number 212721 Answers: 2 Comments: 0

Question Number 212720 Answers: 1 Comments: 0

Question Number 212719 Answers: 3 Comments: 0

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

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

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