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Question Number 41879 Answers: 1 Comments: 0

If a fraction is added to its denominator , it reduces to (1/2) and when the same fraction added to numerator, it also reduces to (2/3) (a) what is the fraction (b) find the square root such that the result of the fraction is less than 1

$$\mathrm{If}\:\mathrm{a}\:\mathrm{fraction}\:\mathrm{is}\:\mathrm{added}\:\mathrm{to}\:\mathrm{its}\:\mathrm{denominator}\:,\:\:\mathrm{it}\:\mathrm{reduces}\:\mathrm{to}\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\: \\ $$$$\mathrm{when}\:\mathrm{the}\:\mathrm{same}\:\mathrm{fraction}\:\mathrm{added}\:\mathrm{to}\:\mathrm{numerator},\:\mathrm{it}\:\mathrm{also}\:\mathrm{reduces}\:\mathrm{to}\:\frac{\mathrm{2}}{\mathrm{3}} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{fraction} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{find}\:\mathrm{the}\:\mathrm{square}\:\mathrm{root}\:\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{is}\:\mathrm{less} \\ $$$$\mathrm{than}\:\mathrm{1} \\ $$$$ \\ $$

Question Number 41878 Answers: 1 Comments: 0

(√3)sin3x−cos3x+2sin((9x)/4)=2

$$\sqrt{\mathrm{3}}{sin}\mathrm{3}{x}−{cos}\mathrm{3}{x}+\mathrm{2}{sin}\frac{\mathrm{9}{x}}{\mathrm{4}}=\mathrm{2} \\ $$

Question Number 41877 Answers: 1 Comments: 0

The tens digit of a two digit number is 3 greater than the units digit. When the digits are reversed, the number is reduced by 27. what is the number ?

$$\mathrm{The}\:\mathrm{tens}\:\mathrm{digit}\:\mathrm{of}\:\mathrm{a}\:\mathrm{two}\:\mathrm{digit}\:\mathrm{number}\:\mathrm{is}\:\mathrm{3}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{the}\:\mathrm{units}\:\mathrm{digit}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{are}\:\mathrm{reversed},\:\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{reduced}\:\mathrm{by}\:\mathrm{27}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:? \\ $$

Question Number 41870 Answers: 0 Comments: 0

Question Number 41869 Answers: 0 Comments: 0

Question Number 41868 Answers: 0 Comments: 0

Question Number 41867 Answers: 0 Comments: 0

Question Number 41866 Answers: 1 Comments: 0

Question Number 41860 Answers: 0 Comments: 2

(1,2,3,........100)are given number find the value of Σ(1×2)

$$\left(\mathrm{1},\mathrm{2},\mathrm{3},........\mathrm{100}\right){are}\:{given}\:{number} \\ $$$${find}\:{the}\:{value}\:{of}\:\Sigma\left(\mathrm{1}×\mathrm{2}\right) \\ $$

Question Number 41858 Answers: 0 Comments: 3

i have fever...so brain activity got reduced...

$${i}\:{have}\:{fever}...{so}\:{brain}\:{activity}\:{got}\:{reduced}... \\ $$

Question Number 41856 Answers: 1 Comments: 0

Question Number 41855 Answers: 0 Comments: 1

lim_(x→+∞ ) ((n!)/(ln (1+n!))) find the limit

$$\underset{{x}\rightarrow+\infty\:\:} {\mathrm{lim}}\frac{\mathrm{n}!}{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{n}!\right)} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{limit} \\ $$

Question Number 41854 Answers: 0 Comments: 0

1)calculate ∫_0 ^1 ln(1+x+x^2 +x^3 )dx 2)then find the value of ∫_0 ^1 ln( 1−x^5 ) dx 3) find the value of Σ_(n=1) ^∞ (1/(n(5n+1))) .

$$\left.\mathrm{1}\right){calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{3}} \right){dx} \\ $$$$\left.\mathrm{2}\right){then}\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\:\mathrm{1}−{x}^{\mathrm{5}} \right)\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{1}}{{n}\left(\mathrm{5}{n}+\mathrm{1}\right)}\:. \\ $$$$ \\ $$$$ \\ $$

Question Number 41851 Answers: 0 Comments: 2

Question Number 41847 Answers: 1 Comments: 0

let f(x) = ∫_0 ^(π/4) (dt/(x +tan(t))) 1) find anoher expression off (x) 2) calculate ∫_0 ^(π/4) (dt/(2+tan(t))) and A(θ) = ∫_0 ^(π/4) (dt/(sinθ+tant)) 3) calculate ∫_0 ^(π/4) (dt/((1+tant)^2 ))

$${let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\:\frac{{dt}}{{x}\:+{tan}\left({t}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{anoher}\:{expression}\:{off}\:\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dt}}{\mathrm{2}+{tan}\left({t}\right)}\:\:\:{and}\:\:{A}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{dt}}{{sin}\theta+{tant}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\:\:\frac{{dt}}{\left(\mathrm{1}+{tant}\right)^{\mathrm{2}} } \\ $$

Question Number 41846 Answers: 1 Comments: 0

find ∫ (dx/((√(1+x^2 )) +(√(1−x^2 ))))

$${find}\:\:\int\:\:\:\:\:\frac{{dx}}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:\:+\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \\ $$

Question Number 41845 Answers: 1 Comments: 0

1)find ∫ (x/((√(1+x)) +(√(1−x)))) dx 2) calculate ∫_1 ^3 (x/((√(1+x)) +(√(1−x)))) dx

$$\left.\mathrm{1}\right){find}\:\:\:\:\int\:\:\:\:\:\:\:\:\:\frac{{x}}{\sqrt{\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{1}} ^{\mathrm{3}} \:\:\:\:\:\frac{{x}}{\sqrt{\mathrm{1}+{x}}\:+\sqrt{\mathrm{1}−{x}}}\:{dx} \\ $$

Question Number 41848 Answers: 0 Comments: 3

let f(a) = ∫_0 ^(π/2) (dx/(1+asinx)) with a∈R 1) find a simple form of f(a) 2) calculate ∫_0 ^(π/2) (dx/(1+sinx)) and ∫_0 ^(π/2) (dx/(1+2sinx)) 3) find the value of ∫_0 ^(π/2) ((cosx)/((1+asinx)^2 ))dx 4) find the value of ∫_0 ^(π/2) ((cosx)/((1+sinx)^2 ))dx and ∫_0 ^(π/2) ((cosx)/((1+2sinx)^2 ))dx

$${let}\:{f}\left({a}\right)\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\:\frac{{dx}}{\mathrm{1}+{asinx}}\:\:\:{with}\:{a}\in{R} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{1}+{sinx}}\:{and}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dx}}{\mathrm{1}+\mathrm{2}{sinx}} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{cosx}}{\left(\mathrm{1}+{asinx}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{4}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{cosx}}{\left(\mathrm{1}+{sinx}\right)^{\mathrm{2}} }{dx}\:{and}\:\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{cosx}}{\left(\mathrm{1}+\mathrm{2}{sinx}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 42310 Answers: 1 Comments: 1

Question Number 41828 Answers: 1 Comments: 0

{ (((y^y /x)+(x^x /y)=129)),((x^y +y^x =32)) :} find x and y? by k.khaled

$$\begin{cases}{\frac{{y}^{{y}} }{{x}}+\frac{{x}^{{x}} }{{y}}=\mathrm{129}}\\{{x}^{{y}} +{y}^{{x}} =\mathrm{32}}\end{cases} \\ $$$${find}\:{x}\:{and}\:{y}? \\ $$$$\:{by}\:{k}.{khaled} \\ $$

Question Number 41824 Answers: 3 Comments: 0

if ^n C_5 = ^n C_(11) find ^(18) C_n

$$\mathrm{if}\:\:\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{5}} \:=\:\overset{\mathrm{n}} {\:}\mathrm{C}_{\mathrm{11}} \:\:\:\mathrm{find}\:\:\:\:\:\:\overset{\mathrm{18}} {\:}\mathrm{C}_{\mathrm{n}} \\ $$

Question Number 41820 Answers: 1 Comments: 0

If α, β are the roots of the equation ax^2 +bx+c=0, then the value of the determinant determinant ((1,(cos (β−α)),(cos α)),((cos (α−β)),1,(cos β)),((cos α),(cos β),1)) is

$$\mathrm{If}\:\alpha,\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0},\:\mathrm{then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{determinant} \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{cos}\:\left(\beta−\alpha\right)}&{\mathrm{cos}\:\alpha}\\{\mathrm{cos}\:\left(\alpha−\beta\right)}&{\mathrm{1}}&{\mathrm{cos}\:\beta}\\{\mathrm{cos}\:\alpha}&{\mathrm{cos}\:\beta}&{\mathrm{1}}\end{vmatrix}\:\mathrm{is} \\ $$

Question Number 41813 Answers: 1 Comments: 0

Any workings for this simultaneous equation ? x^x + y^y = 31 ........ equation (i) x + y = 5 ........ equation (ii)

$$\mathrm{Any}\:\mathrm{workings}\:\mathrm{for}\:\mathrm{this}\:\mathrm{simultaneous}\:\mathrm{equation}\:? \\ $$$$\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{x}} \:+\:\mathrm{y}^{\mathrm{y}} \:=\:\mathrm{31}\:\:........\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{x}\:+\:\mathrm{y}\:=\:\mathrm{5}\:\:\:\:\:\:........\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$

Question Number 41806 Answers: 1 Comments: 1

Question Number 41798 Answers: 0 Comments: 5

Solve: x^3 − 3x + 4 = 0 how can i know when to use: let x = y + (1/y)

$$\mathrm{Solve}:\:\:\:\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{3x}\:+\:\mathrm{4}\:=\:\mathrm{0} \\ $$$$\mathrm{how}\:\mathrm{can}\:\mathrm{i}\:\mathrm{know}\:\mathrm{when}\:\mathrm{to}\:\mathrm{use}:\:\:\:\:\mathrm{let}\:\mathrm{x}\:=\:\mathrm{y}\:+\:\frac{\mathrm{1}}{\mathrm{y}} \\ $$

Question Number 41797 Answers: 1 Comments: 0

Find x: 48log_a 4 + 5log_4 a = (a/8)

$$\mathrm{Find}\:\mathrm{x}:\:\:\:\:\:\:\:\:\mathrm{48log}_{\mathrm{a}} \mathrm{4}\:\:+\:\:\mathrm{5log}_{\mathrm{4}} \mathrm{a}\:\:=\:\:\frac{\mathrm{a}}{\mathrm{8}} \\ $$

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