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Question Number 26313    Answers: 0   Comments: 0

If domain of y = f(x) is [−3, 2] and g(x) = f(∣[x]∣) ([∙] denotes the greatest integer function), then domain of g(x) is

$$\mathrm{If}\:\mathrm{domain}\:\mathrm{of}\:{y}\:=\:{f}\left({x}\right)\:\mathrm{is}\:\left[−\mathrm{3},\:\mathrm{2}\right]\:\mathrm{and} \\ $$$${g}\left({x}\right)\:=\:{f}\left(\mid\left[{x}\right]\mid\right)\:\left(\left[\centerdot\right]\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{greatest}\right. \\ $$$$\left.\mathrm{integer}\:\mathrm{function}\right),\:\mathrm{then}\:\mathrm{domain}\:\mathrm{of}\:{g}\left({x}\right) \\ $$$$\mathrm{is} \\ $$

Question Number 26354    Answers: 1   Comments: 0

Question Number 26281    Answers: 1   Comments: 0

If f(x) is a function satisfying f(x+y)=f(x) f(y) for all x, y ∈ N such that f(1)=3 and Σ_(x=1) ^n f(x)=120. Then the value of n is

$$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{satisfying} \\ $$$$\:{f}\left({x}+{y}\right)={f}\left({x}\right)\:{f}\left({y}\right)\:\mathrm{for}\:\mathrm{all}\:{x},\:{y}\:\in\:{N}\:\:\mathrm{such} \\ $$$$\mathrm{that}\:{f}\left(\mathrm{1}\right)=\mathrm{3}\:\mathrm{and}\:\underset{{x}=\mathrm{1}} {\overset{{n}} {\sum}}\:{f}\left({x}\right)=\mathrm{120}.\:\mathrm{Then} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{n}\:\mathrm{is} \\ $$

Question Number 26274    Answers: 0   Comments: 2

could there be an analytical or numerical meghod for solving this non-linear simultaneous equation x+y=5 x^x +y^y =31 please help if possible

$${could}\:{there}\:{be}\:{an}\:{analytical}\:{or} \\ $$$${numerical}\:{meghod}\:{for}\:{solving} \\ $$$${this}\:{non}-{linear}\:{simultaneous} \\ $$$${equation} \\ $$$${x}+{y}=\mathrm{5} \\ $$$${x}^{{x}} +{y}^{{y}} =\mathrm{31} \\ $$$$ \\ $$$${please}\:{help}\:{if}\:{possible} \\ $$

Question Number 26270    Answers: 0   Comments: 1

∫(√(cosec(x)))dx

$$\int\sqrt{{cosec}\left({x}\right)}{dx} \\ $$

Question Number 26269    Answers: 1   Comments: 0

if x^x =2 what is the value of x?

$${if}\:{x}^{{x}} =\mathrm{2}\:{what}\:{is}\:{the}\:{value}\:{of}\:{x}? \\ $$

Question Number 26264    Answers: 1   Comments: 0

(x/3)+2x=14

$$\frac{\mathrm{x}}{\mathrm{3}}+\mathrm{2x}=\mathrm{14} \\ $$

Question Number 26262    Answers: 1   Comments: 0

(x+5) (x−2)=17−x find the value of x

$$\left(\mathrm{x}+\mathrm{5}\right)\:\left(\mathrm{x}−\mathrm{2}\right)=\mathrm{17}−\mathrm{x}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$

Question Number 26256    Answers: 1   Comments: 1

Question Number 26255    Answers: 0   Comments: 1

if two dice are tossed together what is probability of sim of number on the dice being an even number

$${if}\:{two}\:{dice}\:{are}\:{tossed}\:{together}\:{what}\:{is}\:{probability}\:{of}\:{sim}\:{of}\:{number}\:{on}\:{the}\:{dice}\:{being}\:{an}\:{even}\:{number} \\ $$

Question Number 26250    Answers: 1   Comments: 0

someone should help witb solution please x^3 +y^3 =3x^2 −6x−3y+4 x^2 −y^2 −6x+y−10=(√((y+5)))−(√((4x+y)))

$${someone}\:{should}\:{help}\:{witb}\:{solution}\:{please} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} =\mathrm{3}{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{3}{y}+\mathrm{4} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} −\mathrm{6}{x}+{y}−\mathrm{10}=\sqrt{\left({y}+\mathrm{5}\right)}−\sqrt{\left(\mathrm{4}{x}+{y}\right)} \\ $$

Question Number 26249    Answers: 0   Comments: 1

If x, y, z are in GP and a^x = b^y = c^z , then

$$\mathrm{If}\:\:\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{GP}\:\mathrm{and}\:{a}^{{x}} =\:{b}^{{y}} =\:{c}^{{z}} ,\:\mathrm{then} \\ $$

Question Number 26248    Answers: 0   Comments: 0

lim_(n→∞) ∫_0 ^1 (x^n /(cos x))dx=

$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{n}} }{\mathrm{cos}\:{x}}{dx}= \\ $$

Question Number 26246    Answers: 0   Comments: 0

If normal plasma is 7.4 and normal CO_2 is 1.2mm, what is the normal (H_2 CO_3 ^− )

$$\mathrm{If}\:\:\mathrm{normal}\:\mathrm{plasma}\:\mathrm{is}\:\mathrm{7}.\mathrm{4}\:\mathrm{and}\:\mathrm{normal}\:\:\mathrm{CO}_{\mathrm{2}} \:\mathrm{is}\:\mathrm{1}.\mathrm{2mm},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{normal}\:\left(\mathrm{H}_{\mathrm{2}} \mathrm{CO}_{\mathrm{3}} ^{−} \right) \\ $$

Question Number 26244    Answers: 0   Comments: 1

(x_i )_(1≤i≤n) n real number positifs wish verfy Σ_(i=1) ^(i=n) x_i =1 prove that Σ_(1≤i≤n) x_i ^2 ≥ (1/n) .

$$\:\left({x}_{{i}} \:\right)_{\mathrm{1}\leqslant{i}\leqslant{n}} \:\:{n}\:{real}\:{number}\:\:{positifs}\:{wish}\:{verfy}\:\:\:\sum_{{i}=\mathrm{1}} ^{{i}={n}} \:{x}_{{i}} =\mathrm{1} \\ $$$${prove}\:{that}\:\:\:\sum_{\mathrm{1}\leqslant{i}\leqslant{n}} {x}_{{i}} ^{\mathrm{2}} \:\:\:\geqslant\:\:\frac{\mathrm{1}}{{n}}\:\:\:. \\ $$

Question Number 26243    Answers: 0   Comments: 1

let put U_n = Σ_(1≤i<j≤n) (1/(ij)) find lim_(n−>∝) U_n

$${let}\:{put}\:{U}_{{n}} \:\:=\:\sum_{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} \:\:\:\frac{\mathrm{1}}{{ij}}\:\:\:\:{find}\:\:{lim}_{{n}−>\propto} \:\:{U}_{{n}} \\ $$

Question Number 26242    Answers: 0   Comments: 1

prove that Σ_(k=0) ^(k=n) cos^2 (kx)= ((n+1)/2) + ((sin((n+1)x)cos(nx))/(2 sinx)) x from R−{ kπ.kεZ}then find the value of integral ∫_0 ^π ((sin((n+1)x)cos(nx))/(sinx))dx

$${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{{k}={n}} \:\:{cos}^{\mathrm{2}} \left({kx}\right)=\:\frac{{n}+\mathrm{1}}{\mathrm{2}}\:\:+\:\frac{{sin}\left(\left({n}+\mathrm{1}\right){x}\right){cos}\left({nx}\right)}{\mathrm{2}\:{sinx}} \\ $$$${x}\:{from}\:{R}−\left\{\:{k}\pi.{k}\varepsilon{Z}\right\}{then}\:{find}\:{the}\:{value}\:{of}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{\pi} \:\:\frac{{sin}\left(\left({n}+\mathrm{1}\right){x}\right){cos}\left({nx}\right)}{{sinx}}{dx} \\ $$$$ \\ $$

Question Number 26241    Answers: 0   Comments: 2

∫(√(sin θ))dθ integration ?? solve quickly

$$\int\sqrt{\mathrm{sin}\:\theta}{d}\theta \\ $$$${integration}\:?? \\ $$$${solve}\:{quickly} \\ $$

Question Number 26240    Answers: 1   Comments: 1

y^((2)) −y=(1−e^(2x) )^((−1)/2)

$${y}^{\left(\mathrm{2}\right)} −{y}=\left(\mathrm{1}−{e}^{\mathrm{2}{x}} \right)^{\frac{−\mathrm{1}}{\mathrm{2}}} \\ $$

Question Number 26237    Answers: 1   Comments: 1

Question Number 26235    Answers: 1   Comments: 0

Find the real root of x^2 +(1/x)=c .

$${Find}\:{the}\:{real}\:{root}\:{of} \\ $$$$\:{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}}={c}\:. \\ $$

Question Number 26229    Answers: 1   Comments: 1

after factorise (x2+2x+1)we get

$$\mathrm{after}\:\mathrm{factorise}\:\left(\mathrm{x2}+\mathrm{2x}+\mathrm{1}\right)\mathrm{we}\:\mathrm{get} \\ $$

Question Number 26228    Answers: 0   Comments: 1

if x^4 +(1/x^4 )=322 find x^3 −(1/x^3 )

$$\mathrm{if}\:\mathrm{x}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }=\mathrm{322}\:\mathrm{find}\:\mathrm{x}^{\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 26227    Answers: 1   Comments: 0

if x^2 +(1/x^2 )=98 find x^3 +(1/x^3 )

$$\mathrm{if}\:\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }=\mathrm{98}\:\mathrm{find}\:\mathrm{x}^{\mathrm{3}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 26222    Answers: 0   Comments: 2

find the value of Σ_(n=1) ^∝ (1/((n+1)(n+2)n^3 )) in terms of ξ(3) we give ξ(x)= Σ_(n=1) ^∝ (1/n^x ) and x>1 (zeta function of Rieman)

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right){n}^{\mathrm{3}} }\:{in}\:{terms}\:{of}\:\xi\left(\mathrm{3}\right) \\ $$$${we}\:{give}\:\xi\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\:{and}\:{x}>\mathrm{1} \\ $$$$\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$

Question Number 26224    Answers: 1   Comments: 1

find the value of x−(1/x).when x^4 +(1/x^4 )=332

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}.\mathrm{when}\:{x}^{\mathrm{4}} +\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{4}} }=\mathrm{332} \\ $$

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