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Question Number 182360    Answers: 1   Comments: 5

In equation ax^2 +bx+c=0, a,b,c are randomly selected from integers; what is the probability that roots will be real?

$$\mathrm{In}\:\mathrm{equation}\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}=\mathrm{0},\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are} \\ $$$$\mathrm{randomly}\:\mathrm{selected}\:\mathrm{from}\:\mathrm{integers}; \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{roots} \\ $$$$\mathrm{will}\:\mathrm{be}\:\mathrm{real}? \\ $$

Question Number 182348    Answers: 1   Comments: 0

∫_0 ^2 ∫_0 ^3 ∫_0 ^4 e^(x+y+z) dx dy dz=?

$$\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\mathrm{3}} \int_{\mathrm{0}} ^{\mathrm{4}} {e}^{{x}+{y}+{z}} {dx}\:{dy}\:{dz}=? \\ $$

Question Number 182347    Answers: 1   Comments: 0

s(x)=Σ_(nεN) ^(+oo ) ((n^2 (n+1)^2 )/(n!))x^n =?

$${s}\left({x}\right)=\underset{{n}\epsilon{N}} {\overset{+{oo}\:\:} {\sum}}\:\frac{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} }{{n}!}{x}^{{n}} =? \\ $$

Question Number 182346    Answers: 1   Comments: 1

Question Number 182336    Answers: 1   Comments: 0

Question Number 182332    Answers: 2   Comments: 0

If , f (x) = 2cos^( 2) ((x/2)) −⌊ (1/3) +cos(x) ⌋ then find the range of : R_( f)

$$ \\ $$$$\mathrm{If}\:\:,\:\:\:{f}\:\left({x}\right)\:=\:\mathrm{2}{cos}^{\:\mathrm{2}} \left(\frac{{x}}{\mathrm{2}}\right)\:−\lfloor\:\frac{\mathrm{1}}{\mathrm{3}}\:+{cos}\left({x}\right)\:\rfloor \\ $$$$\:\:{then}\:{find}\:{the}\:{range}\:{of}\::\:\:\:{R}_{\:{f}} \\ $$

Question Number 182331    Answers: 1   Comments: 0

a box contains 5 white balls and some black balls. if the probability of drawing a black ball from the bag is twice the prbability of drawimg a white ball then find number of black balls.

$${a}\:{box}\:{contains}\:\mathrm{5}\:{white}\:{balls}\:{and}\:{some}\:{black} \\ $$$${balls}.\:{if}\:{the}\:{probability}\:{of}\:{drawing}\:{a}\:{black} \\ $$$${ball}\:{from}\:{the}\:{bag}\:{is}\:{twice}\:{the}\:{prbability} \\ $$$${of}\:{drawimg}\:{a}\:{white}\:{ball}\:{then}\:{find}\:{number} \\ $$$${of}\:{black}\:{balls}. \\ $$

Question Number 182315    Answers: 0   Comments: 1

Question Number 182311    Answers: 2   Comments: 5

Question Number 182310    Answers: 1   Comments: 0

Question Number 182298    Answers: 1   Comments: 0

Question Number 182295    Answers: 1   Comments: 0

Question Number 182292    Answers: 3   Comments: 0

Question Number 182291    Answers: 0   Comments: 0

I_2 =∫_0 ^∞ (((tan^(−1) x)/x))^2 dx=?? I_3 =∫_0 ^∞ (((tan^(−1) x)/x))^3 dx=??? I_4 =∫_0 ^∞ (((tan^(−1) x)/x))^4 dx=????

$${I}_{\mathrm{2}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}\right)^{\mathrm{2}} {dx}=?? \\ $$$${I}_{\mathrm{3}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}\right)^{\mathrm{3}} {dx}=??? \\ $$$${I}_{\mathrm{4}} =\underset{\mathrm{0}} {\overset{\infty} {\int}}\left(\frac{\mathrm{tan}^{−\mathrm{1}} \:{x}}{{x}}\right)^{\mathrm{4}} {dx}=???? \\ $$

Question Number 182279    Answers: 1   Comments: 0

∫_0 ^∞ ((x^(10) (1+x^5 ))/((1+x)^(27) ))dx = ?

$$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{10}} \left(\mathrm{1}+{x}^{\mathrm{5}} \right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{27}} }{dx}\:=\:? \\ $$

Question Number 182270    Answers: 0   Comments: 0

Question Number 182256    Answers: 1   Comments: 0

Question Number 182253    Answers: 0   Comments: 3

Question Number 182252    Answers: 0   Comments: 0

Question Number 182272    Answers: 2   Comments: 1

1≤a≤37 1≤b≤37 1+7a+8b +19ab = 0 mod(37) a and b natural nambers (a_1 ;b_1 ) (a_2 ;b_2 )......(a_n ;b_n ) n=?

$$\:\:\:\:\mathrm{1}\leqslant\boldsymbol{\mathrm{a}}\leqslant\mathrm{37} \\ $$$$\:\:\:\:\mathrm{1}\leqslant\boldsymbol{\mathrm{b}}\leqslant\mathrm{37} \\ $$$$\:\:\:\mathrm{1}+\mathrm{7a}+\mathrm{8}\boldsymbol{\mathrm{b}}\:+\mathrm{19}\boldsymbol{\mathrm{ab}}\:\:=\:\mathrm{0}\:\boldsymbol{\mathrm{mod}}\left(\mathrm{37}\right)\: \\ $$$$\:\:\boldsymbol{\mathrm{a}}\:\:\:\boldsymbol{\mathrm{and}}\:\:\boldsymbol{\mathrm{b}}\:\:\boldsymbol{\mathrm{natural}}\:\:\boldsymbol{\mathrm{nambers}} \\ $$$$\:\:\:\:\:\left(\boldsymbol{\mathrm{a}}_{\mathrm{1}} ;\boldsymbol{\mathrm{b}}_{\mathrm{1}} \right)\:\left(\boldsymbol{\mathrm{a}}_{\mathrm{2}} ;\boldsymbol{\mathrm{b}}_{\mathrm{2}} \right)......\left(\boldsymbol{\mathrm{a}}_{\boldsymbol{\mathrm{n}}} ;\boldsymbol{\mathrm{b}}_{\boldsymbol{\mathrm{n}}} \right) \\ $$$$\:\:\:\boldsymbol{\mathrm{n}}=? \\ $$$$\:\:\:\: \\ $$

Question Number 182271    Answers: 2   Comments: 0

Question Number 182247    Answers: 2   Comments: 0

Find: (√(9 + 4 (√5))) − (√(9 − 4 (√5))) = ?

$$\mathrm{Find}: \\ $$$$\sqrt{\mathrm{9}\:+\:\mathrm{4}\:\sqrt{\mathrm{5}}}\:−\:\sqrt{\mathrm{9}\:−\:\mathrm{4}\:\sqrt{\mathrm{5}}}\:=\:? \\ $$

Question Number 182242    Answers: 1   Comments: 0

∫^2 _0 ∫^3 _0 ∫^4 _0 e^(x+y+z) dx dy dz=?

$$\underset{\mathrm{0}} {\int}^{\mathrm{2}} \underset{\mathrm{0}} {\int}^{\mathrm{3}} \underset{\mathrm{0}} {\int}^{\mathrm{4}} {e}^{{x}+{y}+{z}} \:{dx}\:{dy}\:{dz}=? \\ $$

Question Number 182241    Answers: 0   Comments: 0

It is given a family of open interval set (U_r )_(r∈Q) of R that satifies condition ∀r∈Q, r∈U_(r ) . Prove that there exists a family set (U_r )_(r∈Q) which not cover R or ∀ε>0, λ(∪_(r∈Q) U_r )≤ ε .

$$\:\mathrm{It}\:\mathrm{is}\:\mathrm{given}\:\mathrm{a}\:\mathrm{family}\:\mathrm{of}\:\mathrm{open}\:\mathrm{interval}\:\mathrm{set}\:\left({U}_{{r}} \right)_{{r}\in\mathbb{Q}} \:\mathrm{of}\:\mathbb{R} \\ $$$$\mathrm{that}\:\mathrm{satifies}\:\mathrm{condition}\:\forall{r}\in\mathbb{Q},\:{r}\in{U}_{{r}\:} . \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exists}\:\mathrm{a}\:\mathrm{family}\:\mathrm{set}\:\left({U}_{{r}} \right)_{{r}\in\mathbb{Q}} \mathrm{which}\:\mathrm{not}\:\mathrm{cover}\:\mathbb{R}\: \\ $$$$\mathrm{or}\:\forall\varepsilon>\mathrm{0},\:\:\lambda\left(\underset{{r}\in\mathbb{Q}} {\cup}\:{U}_{{r}} \:\right)\leqslant\:\varepsilon\:. \\ $$

Question Number 182238    Answers: 1   Comments: 0

Question Number 182280    Answers: 1   Comments: 2

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