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Question Number 119797 Answers: 0 Comments: 0

Q1 Let M_2 be the set of square matrices of order 2 over the real number system and R={(A,B)∈M_2 ×M_2 ∣A=P^( T) BP for some non-singular P ∈M} Then R is (A) symmetric (B) transitive (C) reflexive on M_2 (D) not an equivalence relation on M_2 Q2 For any integer n, let I_n be the interval (n, n+1). Define R={(x, y)∈R∣both x, y ∈ I_n for some n∈Z} Then R is (A) reflexive on R (B) symmetric (C) transitive (D) an equivalence relation

Question Number 119795 Answers: 4 Comments: 0

Solve in real numbers the system of equations { (((3x+y)(x+3y)(√(xy)) =14)),(((x+y)(x^2 +14xy+y^2 )= 36)) :}

$${Solve}\:{in}\:{real}\:{numbers}\:{the}\:{system}\:{of} \\ $$$${equations}\:\begin{cases}{\left(\mathrm{3}{x}+{y}\right)\left({x}+\mathrm{3}{y}\right)\sqrt{{xy}}\:=\mathrm{14}}\\{\left({x}+{y}\right)\left({x}^{\mathrm{2}} +\mathrm{14}{xy}+{y}^{\mathrm{2}} \right)=\:\mathrm{36}}\end{cases}\: \\ $$

Question Number 119790 Answers: 2 Comments: 0

Let x,y,z be nonnegative real numbers, which satisfy x+y+z=1 Find minimum value of Q=(√(2−x)) + (√(2−y)) + (√(2−z)) .

$${Let}\:{x},{y},{z}\:{be}\:{nonnegative}\:{real} \\ $$$${numbers},\:{which}\:{satisfy}\:{x}+{y}+{z}=\mathrm{1} \\ $$$${Find}\:{minimum}\:{value}\:{of}\: \\ $$$${Q}=\sqrt{\mathrm{2}−{x}}\:+\:\sqrt{\mathrm{2}−{y}}\:+\:\sqrt{\mathrm{2}−{z}}\:. \\ $$

Question Number 119784 Answers: 2 Comments: 0

∫ (dx/( (√((4x−x^2 )^3 ))))

$$\:\:\int\:\frac{{dx}}{\:\sqrt{\left(\mathrm{4}{x}−{x}^{\mathrm{2}} \right)^{\mathrm{3}} }} \\ $$$$ \\ $$

Question Number 119774 Answers: 1 Comments: 0

Question Number 119773 Answers: 3 Comments: 0

∫_(−4) ^4 x^3 (√(16−x^2 )) sec x dx

$$\underset{−\mathrm{4}} {\overset{\mathrm{4}} {\int}}\:{x}^{\mathrm{3}} \sqrt{\mathrm{16}−{x}^{\mathrm{2}} \:}\:\mathrm{sec}\:{x}\:{dx}\: \\ $$

Question Number 119821 Answers: 3 Comments: 0

∫_(−3) ^0 ((6x−6)/( (√(x^2 −2x+1)))) dx =?

$$\:\underset{−\mathrm{3}} {\overset{\mathrm{0}} {\int}}\:\frac{\mathrm{6}{x}−\mathrm{6}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{1}}}\:{dx}\:=? \\ $$

Question Number 119762 Answers: 3 Comments: 0

calculate ∫_0 ^∞ ((x^4 dx)/((2x+1)^5 (3x+1)^8 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{x}^{\mathrm{4}} \mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{5}} \left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{8}} } \\ $$

Question Number 119757 Answers: 0 Comments: 0

For any integer n, let I_n be the interval (n, n+1). Define R={(x, y)∈R∣both x, y ∈ I_n for some n∈Z} Then R is (A) reflexive on R (B) symmetric (C) transitive (D) an equivalence relation

$$\mathrm{For}\:\mathrm{any}\:\mathrm{integer}\:{n},\:\mathrm{let}\:{I}_{{n}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{interval}\:\left({n},\:{n}+\mathrm{1}\right). \\ $$$$\mathrm{Define} \\ $$$$\:\:\:\:\:\:\:\mathcal{R}=\left\{\left(\mathrm{x},\:\mathrm{y}\right)\in\mathbb{R}\mid\mathrm{both}\:\mathrm{x},\:\mathrm{y}\:\in\:{I}_{{n}} \:\mathrm{for}\:\mathrm{some}\:{n}\in\mathbb{Z}\right\} \\ $$$$\mathrm{Then}\:\mathcal{R}\:\mathrm{is} \\ $$$$\left(\mathrm{A}\right)\:\mathrm{reflexive}\:\mathrm{on}\:\mathbb{R} \\ $$$$\left(\mathrm{B}\right)\:\mathrm{symmetric} \\ $$$$\left(\mathrm{C}\right)\:\mathrm{transitive} \\ $$$$\left(\mathrm{D}\right)\:\mathrm{an}\:\mathrm{equivalence}\:\mathrm{relation} \\ $$

Question Number 119755 Answers: 0 Comments: 2

Question Number 119754 Answers: 2 Comments: 3

find Σ_(n=1) ^∞ (u_n /(n!)) if u_n =u_(n+1) +u_(n−1)

$${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{u}_{{n}} }{{n}!}\:{if}\:\:{u}_{{n}} \:={u}_{{n}+\mathrm{1}} +{u}_{{n}−\mathrm{1}} \\ $$

Question Number 119752 Answers: 1 Comments: 0

find I_λ =∫_0 ^∞ ((ch(1+λcosx))/((x^2 +1)^2 ))dx (λ real >0)

$${find}\:{I}_{\lambda} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ch}\left(\mathrm{1}+\lambda{cosx}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left(\lambda\:{real}\:>\mathrm{0}\right) \\ $$

Question Number 119750 Answers: 1 Comments: 0

Π_(k=1) ^(1019) [((2k)/(2k−1))]=?

$$\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{1019}} {\prod}}\left[\frac{\mathrm{2k}}{\mathrm{2k}−\mathrm{1}}\right]=? \\ $$

Question Number 119747 Answers: 1 Comments: 0

Suppose that 7 blue balls , 8 red balls and 9 green balls should be put into three boxes labeled 1,2 and 3, so that any box contains at least one balls of each colour. How many ways can this arrangement be done?

$${Suppose}\:{that}\:\mathrm{7}\:{blue}\:{balls}\:,\:\mathrm{8}\:{red}\:{balls}\:{and}\:\mathrm{9}\:{green} \\ $$$${balls}\:{should}\:{be}\:{put}\:{into}\:{three}\:{boxes}\:{labeled} \\ $$$$\mathrm{1},\mathrm{2}\:{and}\:\mathrm{3},\:{so}\:{that}\:{any}\:{box}\:{contains}\:{at}\:{least} \\ $$$${one}\:{balls}\:{of}\:{each}\:{colour}.\:{How}\:{many}\:{ways} \\ $$$${can}\:{this}\:{arrangement}\:{be}\:{done}? \\ $$

Question Number 119814 Answers: 3 Comments: 0

If a,b,c and d is real numbers satisfy (a/b)=(2/3), (c/d)=(4/5), (d/b)=(6/7) then (a/c) =?

$${If}\:{a},{b},{c}\:{and}\:{d}\:{is}\:{real}\:{numbers} \\ $$$${satisfy}\:\frac{{a}}{{b}}=\frac{\mathrm{2}}{\mathrm{3}},\:\frac{{c}}{{d}}=\frac{\mathrm{4}}{\mathrm{5}},\:\frac{{d}}{{b}}=\frac{\mathrm{6}}{\mathrm{7}} \\ $$$${then}\:\frac{{a}}{{c}}\:=? \\ $$

Question Number 119733 Answers: 1 Comments: 5