Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1411

Question Number 63661    Answers: 0   Comments: 1

let 0<a<1 find the valueof ∫_0 ^∞ (t^(a−1) /(1+t^2 ))dt

$${let}\:\mathrm{0}<{a}<\mathrm{1}\:{find}\:{the}\:{valueof}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{a}−\mathrm{1}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 63642    Answers: 2   Comments: 1

Question Number 63641    Answers: 0   Comments: 2

Question Number 63639    Answers: 0   Comments: 0

Question Number 63636    Answers: 0   Comments: 0

Find all solutions of (x, y, a, b) for these equations : x + y^2 = p^a x^2 + y = p^b which x, y, a, b are integers and p prime number .

$${Find}\:\:{all}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y},\:{a},\:{b}\right)\:\:{for}\:\:{these}\:\:{equations}\:: \\ $$$$\:\:\:\:\:\:\:\:{x}\:+\:{y}^{\mathrm{2}} \:\:=\:\:{p}^{{a}} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} \:+\:{y}\:\:=\:\:{p}^{{b}} \\ $$$${which}\:\:\:{x},\:{y},\:{a},\:{b}\:\:{are}\:\:{integers}\:\:{and}\:\:{p}\:\:{prime}\:\:{number}\:. \\ $$

Question Number 63618    Answers: 1   Comments: 5

Question Number 63615    Answers: 0   Comments: 5

Question Number 63643    Answers: 1   Comments: 0

P(α,β) Q(γ,δ) are two points lie on curve tan^2 (x+y)+cos^2 (x+y)+y^2 +2y=0 on XY plane.If d=PQ then cos d= ans:±2nπ,n∈N

$$\mathrm{P}\left(\alpha,\beta\right)\:\mathrm{Q}\left(\gamma,\delta\right)\:\mathrm{are}\:\mathrm{two}\:\mathrm{points}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{curve} \\ $$$$\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{y}\right)+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{y}\right)+\mathrm{y}^{\mathrm{2}} +\mathrm{2y}=\mathrm{0}\:\mathrm{on} \\ $$$$\mathrm{XY}\:\mathrm{plane}.\mathrm{If}\:\mathrm{d}=\mathrm{PQ}\:\mathrm{then}\:\mathrm{cos}\:\mathrm{d}= \\ $$$$\mathrm{ans}:\pm\mathrm{2n}\pi,\mathrm{n}\in\mathrm{N} \\ $$

Question Number 63602    Answers: 2   Comments: 0

32x^3 −48x^2 −22x−3=0

$$\mathrm{32}{x}^{\mathrm{3}} −\mathrm{48}{x}^{\mathrm{2}} −\mathrm{22}{x}−\mathrm{3}=\mathrm{0} \\ $$

Question Number 63597    Answers: 0   Comments: 0

Question Number 63596    Answers: 0   Comments: 1

The surnames of 40 students in a class were arranged in alphabetical order. 16 of the surnames begin with O while 9 of the surnames begin with A. 14 of the letters of the alphabet do not appear as the first letter of any surname. (i) What is the probability that the surname of a child picked at random from the class begins with either A or O (ii) If more than one surname begins with a letter besides A and O. How many surnames begins with that letter ?

$$\mathrm{The}\:\mathrm{surnames}\:\mathrm{of}\:\mathrm{40}\:\mathrm{students}\:\mathrm{in}\:\mathrm{a}\:\mathrm{class}\:\mathrm{were}\:\mathrm{arranged}\:\mathrm{in} \\ $$$$\mathrm{alphabetical}\:\mathrm{order}.\:\mathrm{16}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surnames}\:\mathrm{begin}\:\mathrm{with}\:\mathrm{O}\:\mathrm{while} \\ $$$$\mathrm{9}\:\mathrm{of}\:\mathrm{the}\:\mathrm{surnames}\:\mathrm{begin}\:\mathrm{with}\:\mathrm{A}.\:\:\mathrm{14}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{alphabet}\:\mathrm{do}\:\mathrm{not}\:\mathrm{appear}\:\mathrm{as}\:\mathrm{the}\:\mathrm{first}\:\mathrm{letter}\:\mathrm{of}\:\mathrm{any}\:\mathrm{surname}. \\ $$$$ \\ $$$$\left(\mathrm{i}\right)\:\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{surname}\:\mathrm{of}\:\mathrm{a}\:\mathrm{child}\:\mathrm{picked} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\mathrm{the}\:\mathrm{class}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{either}\:\mathrm{A}\:\mathrm{or}\:\mathrm{O} \\ $$$$\left(\mathrm{ii}\right)\:\:\mathrm{If}\:\mathrm{more}\:\mathrm{than}\:\mathrm{one}\:\mathrm{surname}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{a}\:\mathrm{letter}\:\mathrm{besides}\:\mathrm{A} \\ $$$$\mathrm{and}\:\mathrm{O}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{surnames}\:\mathrm{begins}\:\mathrm{with}\:\mathrm{that}\:\mathrm{letter}\:? \\ $$$$ \\ $$

Question Number 63588    Answers: 1   Comments: 1

Question Number 63574    Answers: 0   Comments: 12

prove that Σ_(k = 1) ^∞ (1/(k(2k + 1))) = 2 − 2ln(2)

$$\mathrm{prove}\:\mathrm{that}\:\:\:\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{1}}{\mathrm{k}\left(\mathrm{2k}\:+\:\mathrm{1}\right)}\:\:=\:\:\mathrm{2}\:−\:\mathrm{2ln}\left(\mathrm{2}\right) \\ $$

Question Number 63573    Answers: 0   Comments: 0

Question Number 63570    Answers: 1   Comments: 3

Question Number 63566    Answers: 0   Comments: 2

prove that ∫sin^n (x) dx , p∈n , p≥2 =− (1/n)cos(x) sin^(n−1) (x) + (p−1)∫sin^(n−2) (x) dx

$${prove}\:{that} \\ $$$$ \\ $$$$\int{sin}^{{n}} \left({x}\right)\:{dx}\:,\:{p}\in{n}\:,\:{p}\geqslant\mathrm{2}\:=−\:\frac{\mathrm{1}}{{n}}{cos}\left({x}\right)\:{sin}^{{n}−\mathrm{1}} \left({x}\right)\:+\:\left({p}−\mathrm{1}\right)\int{sin}^{{n}−\mathrm{2}} \left({x}\right)\:{dx} \\ $$

Question Number 63565    Answers: 0   Comments: 0

Question Number 63564    Answers: 1   Comments: 0

Question Number 63561    Answers: 1   Comments: 0

Question Number 63560    Answers: 0   Comments: 2

developp at laurent series 1) f(z) =(1/(z−2)) 2)g(z) =(3/(z^2 −3z +2)) 3)h(z) =(1/(z^2 +4))

$${developp}\:{at}\:{laurent}\:{series} \\ $$$$\left.\mathrm{1}\right)\:{f}\left({z}\right)\:=\frac{\mathrm{1}}{{z}−\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){g}\left({z}\right)\:=\frac{\mathrm{3}}{{z}^{\mathrm{2}} −\mathrm{3}{z}\:+\mathrm{2}} \\ $$$$\left.\mathrm{3}\right){h}\left({z}\right)\:=\frac{\mathrm{1}}{{z}^{\mathrm{2}} +\mathrm{4}} \\ $$

Question Number 63552    Answers: 1   Comments: 1

Calculate ∫_0 ^(1/2) x(√(x^2 +1)) dx+∫_(1/2) ^1 x^2 (√(x^3 +1)) dx+∫_1 ^2 x^3 (√(x^4 +1)) dx+∫_2 ^3 x^4 (√(x^5 +1 ))dx+...+∫_(78) ^(79) x^(80) (√(x^(81) +1)) dx+∫_(79) ^(80) x^(81) (√(x^(82) +1)) dx usingΣ_(n=2) ^(80) ∫_(n−1) ^n x^(n+1) (√(x^(n+2) +1))dx

$${Calculate}\:\underset{\mathrm{0}} {\overset{\frac{\mathrm{1}}{\mathrm{2}}} {\int}}{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}+\underset{\frac{\mathrm{1}}{\mathrm{2}}} {\overset{\mathrm{1}} {\int}}{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}+\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}{x}^{\mathrm{3}} \sqrt{{x}^{\mathrm{4}} +\mathrm{1}}\:{dx}+\underset{\mathrm{2}} {\overset{\mathrm{3}} {\int}}{x}^{\mathrm{4}} \sqrt{{x}^{\mathrm{5}} +\mathrm{1}\:}{dx}+...+\underset{\mathrm{78}} {\overset{\mathrm{79}} {\int}}{x}^{\mathrm{80}} \sqrt{{x}^{\mathrm{81}} +\mathrm{1}}\:{dx}+\underset{\mathrm{79}} {\overset{\mathrm{80}} {\int}}{x}^{\mathrm{81}} \sqrt{{x}^{\mathrm{82}} +\mathrm{1}}\:{dx} \\ $$$${using}\underset{{n}=\mathrm{2}} {\overset{\mathrm{80}} {\sum}}\underset{{n}−\mathrm{1}} {\overset{{n}} {\int}}{x}^{{n}+\mathrm{1}} \sqrt{{x}^{{n}+\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 63539    Answers: 1   Comments: 2

The minimum value of 2x^2 −3x+2 is ___.

$$\mathrm{The}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\:\mathrm{is}\:\_\_\_. \\ $$

Question Number 63536    Answers: 0   Comments: 1

a) if y= x^m (1−x)^n , where n∈ Z^+ , the set of positive integers, show that when (dy/dx)=0, x=(m/(m+n)) b)if y = 2(x−5)(√(x+4)) ,show that (dy/dx) = ((3(x+1))/((√(x+4)) )) c) solve the equation sinx−sin5x+cos3x = 0 for 0°≤x≤180°

$$\left.{a}\right)\:\:{if}\:{y}=\:{x}^{{m}} \left(\mathrm{1}−{x}\right)^{{n}} ,\:{where}\:{n}\in\:\mathbb{Z}^{+} ,\:{the}\:{set}\:{of}\:{positive}\:{integers}, \\ $$$${show}\:{that}\:{when}\:\frac{{dy}}{{dx}}=\mathrm{0},\:{x}=\frac{{m}}{{m}+{n}} \\ $$$$\left.{b}\right){if}\:{y}\:=\:\mathrm{2}\left({x}−\mathrm{5}\right)\sqrt{{x}+\mathrm{4}}\:,{show}\:{that}\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{3}\left({x}+\mathrm{1}\right)}{\sqrt{{x}+\mathrm{4}}\:} \\ $$$$\left.{c}\right)\:{solve}\:{the}\:{equation}\:\:{sinx}−{sin}\mathrm{5}{x}+{cos}\mathrm{3}{x}\:=\:\mathrm{0}\:{for}\:\:\mathrm{0}°\leqslant{x}\leqslant\mathrm{180}° \\ $$

Question Number 63534    Answers: 1   Comments: 0

find the set of values of x for which y is real if y=(((x−2)(x−1))/(x+2)) , x≠−2, x∈R

$${find}\:{the}\:{set}\:{of}\:{values}\:{of}\:{x}\:{for}\:{which}\:{y}\:{is}\:{real}\:{if}\: \\ $$$$\:{y}=\frac{\left({x}−\mathrm{2}\right)\left({x}−\mathrm{1}\right)}{{x}+\mathrm{2}}\:,\:{x}\neq−\mathrm{2},\:{x}\in\mathbb{R} \\ $$

Question Number 63532    Answers: 1   Comments: 0

prove that there exist unique intergers p and s sucb that a = bp + s with −((∣b∣)/2)< s ≤((∣b∣)/2) hence find p and s given that a=49 and b=26

$${prove}\:{that}\:{there}\:{exist}\:{unique}\:{intergers}\:{p}\:{and}\:{s}\:{sucb}\:{that} \\ $$$${a}\:=\:{bp}\:+\:{s}\:{with}\:−\frac{\mid{b}\mid}{\mathrm{2}}<\:{s}\:\leqslant\frac{\mid{b}\mid}{\mathrm{2}} \\ $$$${hence}\:{find}\:{p}\:{and}\:{s}\:{given}\:{that}\:{a}=\mathrm{49}\:{and}\:{b}=\mathrm{26} \\ $$

Question Number 63522    Answers: 0   Comments: 2

  Pg 1406      Pg 1407      Pg 1408      Pg 1409      Pg 1410      Pg 1411      Pg 1412      Pg 1413      Pg 1414      Pg 1415   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com