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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=?

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

Question Number 182203 Answers: 0 Comments: 0

Let A={1^(p^2 −p) , 2^(p^2 −p) ,..., (p−1)^(p^2 −p) , p^2 −p+1} where p is any prime number Prove that for any value of p, however we split this set into two disjunctive sets, the arithmetic means of all elements of both sets cannot be equal to each other.

$${Let}\:{A}=\left\{\mathrm{1}^{{p}^{\mathrm{2}} −{p}} ,\:\mathrm{2}^{{p}^{\mathrm{2}} −{p}} ,...,\:\left({p}−\mathrm{1}\right)^{{p}^{\mathrm{2}} −{p}} ,\:{p}^{\mathrm{2}} −{p}+\mathrm{1}\right\} \\ $$$${where}\:{p}\:{is}\:{any}\:{prime}\:{number} \\ $$$${Prove}\:{that}\:{for}\:{any}\:{value}\:{of}\:{p}, \\ $$$${however}\:{we}\:{split}\:{this}\:{set}\:{into}\:{two} \\ $$$${disjunctive}\:{sets},\:{the}\:{arithmetic} \\ $$$${means}\:{of}\:{all}\:{elements}\:{of}\:{both}\:{sets} \\ $$$${cannot}\:{be}\:{equal}\:{to}\:{each}\:{other}. \\ $$

Question Number 182200 Answers: 2 Comments: 0

1. lim_(a→−x) ((sin(x^2 − a^2 ))/(x^3 + a^3 )) = ? 2. cot 80° (tan 10° + 2 tg 70°) = ?

$$\mathrm{1}.\:\:\:\underset{\boldsymbol{\mathrm{a}}\rightarrow−\boldsymbol{\mathrm{x}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{a}^{\mathrm{2}} \right)}{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{a}^{\mathrm{3}} }\:=\:? \\ $$$$ \\ $$$$\mathrm{2}.\:\:\:\mathrm{cot}\:\mathrm{80}°\:\left(\mathrm{tan}\:\mathrm{10}°\:+\:\mathrm{2}\:\mathrm{tg}\:\mathrm{70}°\right)\:=\:? \\ $$

Question Number 182199 Answers: 2 Comments: 0

Let S={1, 2, 3, 4, 5, 6, 7} If we multiply atleast 2 numbers from this set with each other, what are the chances of the product to turn out to be divisible by 3?

$${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5},\:\mathrm{6},\:\mathrm{7}\right\} \\ $$$${If}\:{we}\:{multiply}\:{atleast}\:\mathrm{2}\:{numbers} \\ $$$${from}\:{this}\:{set}\:{with}\:{each}\:{other},\:{what} \\ $$$${are}\:{the}\:{chances}\:{of}\:{the}\:{product}\:{to} \\ $$$${turn}\:{out}\:{to}\:{be}\:{divisible}\:{by}\:\mathrm{3}? \\ $$

Question Number 182192 Answers: 1 Comments: 1

Question Number 182188 Answers: 2 Comments: 0

((((√5)+2))^(1/3) +(((√5)−2))^(1/3) )^(2014) =?

$$\left(\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}+\mathrm{2}}+\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{5}}−\mathrm{2}}\right)^{\mathrm{2014}} =? \\ $$

Question Number 182183 Answers: 1 Comments: 0

∫_0 ^( 1) e^a a^n da=? n≥1 n∈N

$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \boldsymbol{{e}}^{\boldsymbol{{a}}} \boldsymbol{{a}}^{\boldsymbol{{n}}} \boldsymbol{{da}}=?\:\:\:\:\:\:\:\:\boldsymbol{{n}}\geqslant\mathrm{1}\:\:\:\:\boldsymbol{{n}}\in\boldsymbol{{N}} \\ $$

Question Number 182178 Answers: 1 Comments: 2

The Circle Has A Radius 5cm And the angle between sector from the chord is 73.7397952916880° and their right triangle is AB=4 cm AC=3 cm Find the area of arc triangle EDB with E^⌢ D^⌢ is arc

$${The}\:{Circle}\:{Has}\:{A}\:{Radius}\:\mathrm{5}{cm} \\ $$$${And}\:{the}\:{angle}\:{between} \\ $$$$\:{sector}\:{from}\:{the}\:{chord}\:{is} \\ $$$$\mathrm{73}.\mathrm{7397952916880}° \\ $$$${and}\:{their}\:{right}\:{triangle}\:{is} \\ $$$${AB}=\mathrm{4}\:{cm} \\ $$$${AC}=\mathrm{3}\:{cm} \\ $$$${Find}\:{the}\:{area}\:{of}\:{arc}\:{triangle} \\ $$$${EDB} \\ $$$${with}\:\overset{\frown} {{E}}\overset{\frown} {{D}}\:{is}\:{arc} \\ $$$$ \\ $$

Question Number 182176 Answers: 1 Comments: 0