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Question Number 54909 Answers: 0 Comments: 5

Do you know a geometrical proof of the irrationality of number (√2) ?

$${Do}\:{you}\:{know}\:{a}\:{geometrical}\:{proof} \\ $$$${of}\:{the}\:{irrationality}\:{of}\:{number}\:\sqrt{\mathrm{2}}\:? \\ $$

Question Number 54903 Answers: 1 Comments: 0

Question Number 54901 Answers: 1 Comments: 1

Question Number 54897 Answers: 2 Comments: 1

Find value of n so 120 ∣ 5n(n^2 −1)

$$\mathrm{Find}\:\mathrm{value}\:\mathrm{of}\:{n}\:\mathrm{so}\:\mathrm{120}\:\mid\:\mathrm{5}{n}\left({n}^{\mathrm{2}} −\mathrm{1}\right) \\ $$

Question Number 54896 Answers: 1 Comments: 1

∫(√)(x2+2x+2)

$$\int\sqrt{}\left({x}\mathrm{2}+\mathrm{2}{x}+\mathrm{2}\right) \\ $$

Question Number 54880 Answers: 2 Comments: 0

If x^2 −y^2 =a^2 find (d^2 y/dx^2 ) if a is constant.

$${If}\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} ={a}^{\mathrm{2}} \:\:{find}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:{if}\:{a}\:{is} \\ $$$${constant}. \\ $$

Question Number 54876 Answers: 1 Comments: 1

find the coefficientof x^2 in the binomial expansion of (x^2 +(2/x))^4

$$\mathrm{find}\:\mathrm{the}\:\mathrm{coefficientof}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{binomial} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left(\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{2}}{\mathrm{x}}\right)^{\mathrm{4}} \\ $$

Question Number 54875 Answers: 2 Comments: 0

Given that((log(3x+1)^(2x−1) )/(log(3x+1)))=5,find the value of x.

$$\mathrm{Given}\:\mathrm{that}\frac{\mathrm{log}\left(\mathrm{3x}+\mathrm{1}\right)^{\mathrm{2x}−\mathrm{1}} }{\mathrm{log}\left(\mathrm{3x}+\mathrm{1}\right)}=\mathrm{5},\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}. \\ $$

Question Number 54869 Answers: 1 Comments: 0

Question Number 54868 Answers: 0 Comments: 1

Question Number 54860 Answers: 1 Comments: 1

Question Number 54858 Answers: 2 Comments: 0

(Q1) The expansion (x−(1/(3x)))^(12) (i) find the term independent of x (ii) find the term x^4 (Q2) There are some nut in a bag. when 2 ounces of peanut are added to the mixture, the percentage of peanut becomes 20% . Richard added 2 ounces of cashew to the mixture and the percentage of cashew nut was 33.33% . find the percentage of cashew nut that were there initially. please sir help

$$\left({Q}\mathrm{1}\right)\:{The}\:{expansion}\:\left({x}−\frac{\mathrm{1}}{\mathrm{3}{x}}\right)^{\mathrm{12}} \\ $$$$\left({i}\right)\:{find}\:{the}\:{term}\:{independent}\:{of}\:{x} \\ $$$$\left({ii}\right)\:{find}\:{the}\:{term}\:{x}^{\mathrm{4}} \\ $$$$\left({Q}\mathrm{2}\right)\:{There}\:{are}\:{some}\:{nut}\:{in}\:{a}\:{bag}.\:{when} \\ $$$$\:\mathrm{2}\:{ounces}\:{of}\:{peanut}\:{are}\:{added}\:{to}\:{the} \\ $$$${mixture},\:{the}\:{percentage}\:{of}\:{peanut}\: \\ $$$${becomes}\:\mathrm{20\%}\:.\:{Richard}\:\:{added}\:\:\mathrm{2}\: \\ $$$${ounces}\:{of}\:{cashew}\:{to}\:{the}\:{mixture}\:{and} \\ $$$${the}\:{percentage}\:{of}\:{cashew}\:{nut}\:{was}\: \\ $$$$\mathrm{33}.\mathrm{33\%}\:.\:{find}\:{the}\:{percentage}\:{of}\: \\ $$$${cashew}\:{nut}\:{that}\:{were}\:{there}\:{initially}. \\ $$$${please}\:{sir}\:{help} \\ $$

Question Number 54857 Answers: 1 Comments: 0

Question Number 54856 Answers: 1 Comments: 2

Question Number 54841 Answers: 1 Comments: 0

Question Number 54830 Answers: 0 Comments: 1

let V_n = ∫_0 ^∞ ((cos(nx))/(n +x^2 ))dx with n integr nstural not 0 . 1) calculate V_n 2)calculate lim_(n→+∞) nV_n 3) calculate the sum Σ_(n=0) ^∞ V_n

$${let}\:{V}_{{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{{n}\:+{x}^{\mathrm{2}} }{dx}\:\:\:{with}\:{n}\:{integr}\:{nstural}\:{not}\:\mathrm{0}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{V}_{{n}} \\ $$$$\left.\mathrm{2}\right){calculate}\:{lim}_{{n}\rightarrow+\infty} {nV}_{{n}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{the}\:{sum}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{V}_{{n}} \\ $$

Question Number 54827 Answers: 0 Comments: 0

logx^2 +log_2 (x−6)=3 solve for x

$$\mathrm{logx}^{\mathrm{2}} +\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}−\mathrm{6}\right)=\mathrm{3} \\ $$$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x} \\ $$

Question Number 54826 Answers: 4 Comments: 5

1) ∫_0 ^( 1) ((1−x^7 )^(1/4) −(1−x^4 )^(1/7) )dx = ? 2) If f(x)=x^3 +3x+4 then the value of ∫_(−1) ^( 1) f(x)dx + ∫_0 ^( 4) f^( −1) (x)dx = ? 3) ∫_(−π) ^( π) (1+cosx+cos2x+....+cos13x)(1+sinx+...+sin13x)dx=? 4) ∫_0 ^( 2) ((√(x^3 +1)) + (x^2 +2x)^(1/3) )dx =? (This time func. are not inverse of each other,right ?)

$$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\left(\mathrm{1}−{x}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} −\left(\mathrm{1}−{x}^{\mathrm{4}} \right)^{\frac{\mathrm{1}}{\mathrm{7}}} \right){dx}\:=\:? \\ $$$$\left.\mathrm{2}\right)\:{If}\:{f}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{3}{x}+\mathrm{4}\:{then}\:{the}\:{value}\:{of} \\ $$$$\:\int_{−\mathrm{1}} ^{\:\mathrm{1}} {f}\left({x}\right){dx}\:+\:\int_{\mathrm{0}} ^{\:\mathrm{4}} {f}^{\:−\mathrm{1}} \left({x}\right){dx}\:=\:? \\ $$$$\left.\mathrm{3}\right)\:\int_{−\pi} ^{\:\pi} \left(\mathrm{1}+{cosx}+{cos}\mathrm{2}{x}+....+{cos}\mathrm{13}{x}\right)\left(\mathrm{1}+{sinx}+...+{sin}\mathrm{13}{x}\right){dx}=? \\ $$$$\left.\mathrm{4}\right)\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\left(\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}\:+\:\left({x}^{\mathrm{2}} +\mathrm{2}{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:\right){dx}\:=? \\ $$$$\left({This}\:{time}\:{func}.\:{are}\:{not}\:{inverse}\:{of}\:{each}\right. \\ $$$$\left.{other},{right}\:?\right) \\ $$

Question Number 54825 Answers: 1 Comments: 0

Question Number 54808 Answers: 1 Comments: 2

let p(x)=(1+x^2 )(1+x^4 )...(1+x^2^n ) with n integr natural 1) find a simple form of p(x) 2) find roots of p(x)and decompose p(x) inside C[x] 3)calculate ∫_0 ^1 p(x)dx 4) decompose the fraction F(x)=(1/(p(x))) .

$${let}\:{p}\left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)...\left(\mathrm{1}+{x}^{\mathrm{2}^{{n}} } \right) \\ $$$${with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{roots}\:{of}\:{p}\left({x}\right){and}\:{decompose} \\ $$$${p}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{p}\left({x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{decompose}\:{the}\:{fraction} \\ $$$${F}\left({x}\right)=\frac{\mathrm{1}}{{p}\left({x}\right)}\:. \\ $$

Question Number 54797 Answers: 1 Comments: 0

∫ (√( x + (√( x + (√(x + (√( .....)))))))) dx = ?

$$ \\ $$$$ \\ $$$$\:\:\:\int\:\:\sqrt{\:\boldsymbol{{x}}\:+\:\sqrt{\:\boldsymbol{{x}}\:+\:\sqrt{\boldsymbol{{x}}\:+\:\sqrt{\:.....}}}}\:\:\boldsymbol{{dx}}\:\:=\:\:\:? \\ $$$$ \\ $$

Question Number 54821 Answers: 0 Comments: 1

find lim_(n→+∞) ∫_0 ^n ((arctan(nx))/(n^2 +x^2 ))dx

$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\int_{\mathrm{0}} ^{{n}} \:\:\:\frac{{arctan}\left({nx}\right)}{{n}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 54790 Answers: 3 Comments: 2

differenciatethefollowing i)x^x +(sinx)^(lnx) = ii)sin^(−1) (tanhx)= iii)(√(1+x^2 /1−x^2 =))

$${differenciatethefollowing} \\ $$$$\left.{i}\right){x}^{{x}} +\left({sinx}\right)^{{lnx}} = \\ $$$$\left.{ii}\right){sin}^{−\mathrm{1}} \left({tanhx}\right)= \\ $$$$\left.{iii}\right)\sqrt{\mathrm{1}+{x}^{\mathrm{2}} /\mathrm{1}−{x}^{\mathrm{2}} =} \\ $$

Question Number 54788 Answers: 2 Comments: 1

How can cut a right angeled triangle to make a square? how can cut a equilateral triangle to make a rectangle?