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Question Number 4848    Answers: 1   Comments: 0

please help .... thanks in advance ... Find the value of x ... (√x^x^x ) = 729

$${please}\:{help}\:....\:{thanks}\:{in}\:{advance}\:... \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x}\:... \\ $$$$ \\ $$$$\sqrt{{x}^{{x}^{{x}} } }\:\:=\:\:\mathrm{729} \\ $$

Question Number 4847    Answers: 0   Comments: 0

(√(6+(√(6+(√(6+(√(6+(√6))))))))) SOLUTION let x = (√(6+(√(6+(√(6+(√(6+(√6))))))))) therefore.. x^(2 ) = 6+(√(6+(√(6+(√(6+(√(6 )))))))) the equation is a continuos funtion Thus x^2 = 6+(√(6+(√(6+(√(6+(√(6+(√6) ))))))))...... since x = (√(6+(√(6+(√(6+(√(6+(√6))))))))) Therdfore x^2 = 6 + x x^2 − x − 6 = 0 x^2 − 3x + 2x − 6 = 0 (x^2 − 3x) + (2x − 6) = 0 x(x − 3) + 2(x − 3) = 0 (x − 3)(x + 2) = 0 x − 3 = 0 or x − 2 = 0 x = 3 or x = −2 since negative is not allowed Thus x = 6 Meaning that (√(6+(√(6+(√(6+(√(6+(√(6 )))))))))) = 3 DONE THANK YOU SO MUCH. I UNDERSTAND THE SOLUTION.

$$\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}}}}}} \\ $$$$ \\ $$$${SOLUTION} \\ $$$$ \\ $$$${let}\:{x}\:=\:\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}}}}}} \\ $$$$ \\ $$$${therefore}.. \\ $$$$ \\ $$$${x}^{\mathrm{2}\:} =\:\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}\:\:}}}} \\ $$$$ \\ $$$${the}\:{equation}\:{is}\:{a}\:{continuos}\:{funtion} \\ $$$${Thus} \\ $$$$ \\ $$$${x}^{\mathrm{2}} \:=\:\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}}\:}}}}...... \\ $$$$ \\ $$$${since}\:\:\:{x}\:=\:\:\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}}}}}}\: \\ $$$$ \\ $$$${Therdfore} \\ $$$$ \\ $$$${x}^{\mathrm{2}} \:=\:\mathrm{6}\:+\:{x} \\ $$$$ \\ $$$${x}^{\mathrm{2}} \:−\:{x}\:−\:\mathrm{6}\:=\:\mathrm{0} \\ $$$$ \\ $$$${x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\:+\:\mathrm{2}{x}\:−\:\mathrm{6}\:=\:\mathrm{0} \\ $$$$ \\ $$$$\left({x}^{\mathrm{2}} \:−\:\mathrm{3}{x}\right)\:+\:\left(\mathrm{2}{x}\:−\:\mathrm{6}\right)\:=\:\mathrm{0} \\ $$$$ \\ $$$${x}\left({x}\:−\:\mathrm{3}\right)\:+\:\mathrm{2}\left({x}\:−\:\mathrm{3}\right)\:=\:\mathrm{0} \\ $$$$ \\ $$$$\left({x}\:−\:\mathrm{3}\right)\left({x}\:+\:\mathrm{2}\right)\:=\:\mathrm{0} \\ $$$$ \\ $$$${x}\:−\:\mathrm{3}\:=\:\mathrm{0}\:{or}\:{x}\:−\:\mathrm{2}\:=\:\mathrm{0} \\ $$$$ \\ $$$${x}\:=\:\mathrm{3}\:{or}\:{x}\:=\:−\mathrm{2} \\ $$$$ \\ $$$${since}\:{negative}\:{is}\:{not}\:{allowed} \\ $$$${Thus} \\ $$$$ \\ $$$${x}\:=\:\mathrm{6} \\ $$$$ \\ $$$${Meaning}\:{that} \\ $$$$ \\ $$$$\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}\:}}}}}\:\:\:=\:\:\mathrm{3} \\ $$$$ \\ $$$${DONE} \\ $$$$ \\ $$$${THANK}\:{YOU}\:{SO}\:{MUCH}.\:{I}\:{UNDERSTAND}\:{THE}\:{SOLUTION}. \\ $$

Question Number 4844    Answers: 1   Comments: 1

y(x)=f(x)+g(x)+h(x) y(x)=x^2 +sin x+x(1−x) f(x) is even g(x) is odd f(0)g(0)−h(0)=?

$${y}\left({x}\right)={f}\left({x}\right)+{g}\left({x}\right)+{h}\left({x}\right) \\ $$$${y}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{sin}\:{x}+{x}\left(\mathrm{1}−{x}\right) \\ $$$${f}\left({x}\right)\:\mathrm{is}\:\mathrm{even} \\ $$$${g}\left({x}\right)\:\mathrm{is}\:\mathrm{odd} \\ $$$${f}\left(\mathrm{0}\right){g}\left(\mathrm{0}\right)−{h}\left(\mathrm{0}\right)=? \\ $$

Question Number 4841    Answers: 0   Comments: 1

what mean for symbol Π?

$$ \\ $$$${what}\:{mean}\:{for}\:{symbol}\:\Pi? \\ $$

Question Number 4862    Answers: 1   Comments: 0

Solve for x x=(√(.1+(√(.1+(√(.1+(√(.1+...))))))))

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}=\sqrt{.\mathrm{1}+\sqrt{.\mathrm{1}+\sqrt{.\mathrm{1}+\sqrt{.\mathrm{1}+...}}}} \\ $$

Question Number 4839    Answers: 3   Comments: 1

(1) S_1 =(√(1−4x)) (2) S_2 =(√(1+4x)) For S_1 ,S_2 ∈Z, x=?

$$\left(\mathrm{1}\right)\:\:\:{S}_{\mathrm{1}} =\sqrt{\mathrm{1}−\mathrm{4}{x}} \\ $$$$\left(\mathrm{2}\right)\:\:\:{S}_{\mathrm{2}} =\sqrt{\mathrm{1}+\mathrm{4}{x}} \\ $$$$\mathrm{For}\:{S}_{\mathrm{1}} ,{S}_{\mathrm{2}} \in\mathbb{Z},\:{x}=? \\ $$

Question Number 4825    Answers: 1   Comments: 2

Find the value of (√(6+(√(6+(√(6+(√(6+(√6)))))))))

$${Find}\:{the}\:{value}\:{of}\: \\ $$$$ \\ $$$$\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}+\sqrt{\mathrm{6}}}}}} \\ $$

Question Number 4822    Answers: 0   Comments: 0

Can you please mathematically explain how some infinities can be bigger than others? Thank you!

$$\mathrm{Can}\:\mathrm{you}\:\mathrm{please}\:\mathrm{mathematically}\:\mathrm{explain} \\ $$$$\mathrm{how}\:\mathrm{some}\:\mathrm{infinities}\:\mathrm{can}\:\mathrm{be}\:\mathrm{bigger}\:\mathrm{than} \\ $$$$\mathrm{others}?\:\mathrm{Thank}\:\mathrm{you}! \\ $$

Question Number 4820    Answers: 1   Comments: 0

y=f(x)+g(x) f(x) − odd function g(x) − even function find f(0), if y= 2x^2 +((sin x)/3)+1

$${y}={f}\left({x}\right)+{g}\left({x}\right) \\ $$$$ \\ $$$${f}\left({x}\right)\:−\:{odd}\:{function} \\ $$$${g}\left({x}\right)\:−\:{even}\:{function} \\ $$$$ \\ $$$${find}\:{f}\left(\mathrm{0}\right),\:{if}\:{y}=\:\mathrm{2}{x}^{\mathrm{2}} +\frac{{sin}\:{x}}{\mathrm{3}}+\mathrm{1} \\ $$

Question Number 4817    Answers: 0   Comments: 1

f(αx)=αf(x−α) f(x)=?

$${f}\left(\alpha{x}\right)=\alpha{f}\left({x}−\alpha\right) \\ $$$${f}\left({x}\right)=? \\ $$

Question Number 4816    Answers: 0   Comments: 1

Question Number 4812    Answers: 0   Comments: 6

Question Number 4809    Answers: 1   Comments: 0

Show that ((x^2 +a^2 )/(x^2 −a^2 )) > ((x+a)/(x−a)).

$${Show}\:{that}\:\frac{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{{x}^{\mathrm{2}} −{a}^{\mathrm{2}} }\:>\:\frac{{x}+{a}}{{x}−{a}}. \\ $$

Question Number 4807    Answers: 1   Comments: 2

Find X if... ∫_0 ^e x≠0 and ((xr)/r^e )=(√(e+n)) or Σ_(n!) e=0 and ((℧x≠y)/(℧y≠x))=−1

$${Find}\:\mathbb{X}\:{if}... \\ $$$$\underset{\mathrm{0}} {\overset{{e}} {\int}}{x}\neq\mathrm{0}\:{and}\:\frac{{xr}}{{r}^{{e}} }=\sqrt{{e}+{n}} \\ $$$${or} \\ $$$$\underset{{n}!} {\sum}{e}=\mathrm{0}\:{and}\:\frac{\mho{x}\neq{y}}{\mho{y}\neq{x}}=−\mathrm{1} \\ $$

Question Number 4800    Answers: 2   Comments: 0

m(d^2 x/dt^(2 ) )=f−k(dx/dt) x(0)=x_0 x′(0)=v_0 x(t)=?

$${m}\frac{{d}^{\mathrm{2}} {x}}{{dt}^{\mathrm{2}\:} }={f}−{k}\frac{{dx}}{{dt}} \\ $$$${x}\left(\mathrm{0}\right)={x}_{\mathrm{0}} \\ $$$${x}'\left(\mathrm{0}\right)={v}_{\mathrm{0}} \\ $$$${x}\left({t}\right)=? \\ $$

Question Number 4793    Answers: 0   Comments: 1

please explain. V(x)=−∫F(x)dx

$${please}\:{explain}. \\ $$$${V}\left({x}\right)=−\int{F}\left({x}\right){dx} \\ $$$$ \\ $$$$ \\ $$

Question Number 4795    Answers: 1   Comments: 0

a,b,c∈C x_0 =a y_0 =b z_0 =c x_(n+1) =x_n −y_n y_(n+1) =y_n −z_n z_(n+1) =z_n −x_n x_n +y_n +z_n =?,n≥1

$${a},{b},{c}\in\mathbb{C} \\ $$$${x}_{\mathrm{0}} ={a} \\ $$$${y}_{\mathrm{0}} ={b} \\ $$$${z}_{\mathrm{0}} ={c} \\ $$$${x}_{{n}+\mathrm{1}} ={x}_{{n}} −{y}_{{n}} \\ $$$${y}_{{n}+\mathrm{1}} ={y}_{{n}} −{z}_{{n}} \\ $$$${z}_{{n}+\mathrm{1}} ={z}_{{n}} −{x}_{{n}} \\ $$$${x}_{{n}} +{y}_{{n}} +{z}_{{n}} =?,{n}\geqslant\mathrm{1} \\ $$

Question Number 4790    Answers: 0   Comments: 0

Function Γ is a+b a+b=AB a≠b−4 b−4=4+b b=a−1 a−1=2 b=2 a=3 Function Γ is (a/b)+sin a+b Γ=(a/b)+sin a+b a=b−1 b=5 a=4 9−a=b 9−b=a Funcion Γ is ((sin a+sin b)/(sin^(−1) a+sin^(−1) b))×(a+b) sin a+sin b<c_1 c_1 =a×3 a=b+3 b=2 b+3=2+3 2+3=5 a=5 a×3=15 c_1 =15 c_2 =c_1 ÷5 c_1 ÷5=3 c_2 =3 c_1 +c_2 =c_3 c_3 =18 c_3 ≈sin a+b a×b×2=20 sin 20=sin a+b c_3 ≈20

$${Function}\:\Gamma\:{is}\:{a}+{b} \\ $$$${a}+{b}={AB} \\ $$$${a}\neq{b}−\mathrm{4} \\ $$$${b}−\mathrm{4}=\mathrm{4}+{b} \\ $$$${b}={a}−\mathrm{1} \\ $$$${a}−\mathrm{1}=\mathrm{2} \\ $$$${b}=\mathrm{2} \\ $$$${a}=\mathrm{3} \\ $$$${Function}\:\Gamma\:{is}\:\frac{{a}}{{b}}+\mathrm{sin}\:{a}+{b} \\ $$$$\Gamma=\frac{{a}}{{b}}+\mathrm{sin}\:{a}+{b} \\ $$$${a}={b}−\mathrm{1} \\ $$$${b}=\mathrm{5} \\ $$$${a}=\mathrm{4} \\ $$$$\mathrm{9}−{a}={b} \\ $$$$\mathrm{9}−{b}={a} \\ $$$${Funcion}\:\Gamma\:{is}\:\frac{\mathrm{sin}\:{a}+\mathrm{sin}\:{b}}{\mathrm{sin}^{−\mathrm{1}} {a}+\mathrm{sin}^{−\mathrm{1}} {b}}×\left({a}+{b}\right) \\ $$$$\mathrm{sin}\:{a}+\mathrm{sin}\:{b}<{c}_{\mathrm{1}} \\ $$$${c}_{\mathrm{1}} ={a}×\mathrm{3} \\ $$$${a}={b}+\mathrm{3} \\ $$$${b}=\mathrm{2} \\ $$$${b}+\mathrm{3}=\mathrm{2}+\mathrm{3} \\ $$$$\mathrm{2}+\mathrm{3}=\mathrm{5} \\ $$$${a}=\mathrm{5} \\ $$$${a}×\mathrm{3}=\mathrm{15} \\ $$$${c}_{\mathrm{1}} =\mathrm{15} \\ $$$${c}_{\mathrm{2}} ={c}_{\mathrm{1}} \boldsymbol{\div}\mathrm{5} \\ $$$${c}_{\mathrm{1}} \boldsymbol{\div}\mathrm{5}=\mathrm{3} \\ $$$${c}_{\mathrm{2}} =\mathrm{3} \\ $$$${c}_{\mathrm{1}} +{c}_{\mathrm{2}} ={c}_{\mathrm{3}} \\ $$$${c}_{\mathrm{3}} =\mathrm{18} \\ $$$${c}_{\mathrm{3}} \approx\mathrm{sin}\:{a}+{b} \\ $$$${a}×{b}×\mathrm{2}=\mathrm{20} \\ $$$$\mathrm{sin}\:\mathrm{20}=\mathrm{sin}\:{a}+{b} \\ $$$${c}_{\mathrm{3}} \approx\mathrm{20} \\ $$

Question Number 4785    Answers: 0   Comments: 2

n^i (n/(i×i))≈sin n^i +α

$${n}^{{i}} \frac{{n}}{{i}×{i}}\approx\mathrm{sin}\:{n}^{{i}} +\alpha \\ $$

Question Number 4783    Answers: 0   Comments: 1

cos α+β ≈(((cos α+cos β)/(cos^(−1) α+cos^(−1) β)))^(α+β) sin a+b≈(((sin a+sin b)/(sin^(−1) a+sin^(−1) b)))^(a+b) tan (a+(a/b))^k ≈(((tan (a+b)×k)/(tan^(−1) (a+b)×k)))

$$\mathrm{cos}\:\alpha+\beta\:\approx\left(\frac{\mathrm{cos}\:\alpha+\mathrm{cos}\:\beta}{\mathrm{cos}^{−\mathrm{1}} \alpha+\mathrm{cos}^{−\mathrm{1}} \beta}\right)^{\alpha+\beta} \\ $$$$\mathrm{sin}\:{a}+{b}\approx\left(\frac{\mathrm{sin}\:{a}+\mathrm{sin}\:{b}}{\mathrm{sin}^{−\mathrm{1}} {a}+\mathrm{sin}^{−\mathrm{1}} {b}}\right)^{{a}+{b}} \\ $$$$\mathrm{tan}\:\left({a}+\frac{{a}}{{b}}\right)^{{k}} \approx\left(\frac{\mathrm{tan}\:\left({a}+{b}\right)×{k}}{\mathrm{tan}^{−\mathrm{1}} \left({a}+{b}\right)×{k}}\right) \\ $$

Question Number 4781    Answers: 0   Comments: 0

((√(δy))/(√(δx)))×f_1 = determinant (((δy)),((δx)))^(x/z)

$$\frac{\sqrt{\delta{y}}}{\sqrt{\delta{x}}}×{f}_{\mathrm{1}} =\begin{vmatrix}{\delta{y}}\\{\delta{x}}\end{vmatrix}^{{x}/{z}} \\ $$

Question Number 4780    Answers: 0   Comments: 0

D_1 ρ=∣(√(f(α+β)))×c^2 ∣

$${D}_{\mathrm{1}} \rho=\mid\sqrt{{f}\left(\alpha+\beta\right)}×{c}^{\mathrm{2}} \mid \\ $$

Question Number 4775    Answers: 0   Comments: 2

Let ∗ be a binary operation on Z defined by x∗y=(1/2)(x+y+1+(1/2)(1+(−1)^(x+y) )). Is ∗ associative?

$${Let}\:\ast\:{be}\:{a}\:{binary}\:{operation}\:{on}\:\mathbb{Z} \\ $$$${defined}\:{by}\: \\ $$$${x}\ast{y}=\frac{\mathrm{1}}{\mathrm{2}}\left({x}+{y}+\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+\left(−\mathrm{1}\right)^{{x}+{y}} \right)\right). \\ $$$${Is}\:\ast\:{associative}? \\ $$

Question Number 4772    Answers: 0   Comments: 4

Let z=Ax^2 +Bxy+Cy^2 . Find conditions on the constants A,B,C that ensure that the point (0,0,0) is a (i) local minimum, (ii) local maximum, (ii) saddle point.

$${Let}\:{z}={Ax}^{\mathrm{2}} +{Bxy}+{Cy}^{\mathrm{2}} .\:{Find}\:{conditions} \\ $$$${on}\:{the}\:{constants}\:{A},{B},{C}\:{that}\:{ensure} \\ $$$${that}\:{the}\:{point}\:\left(\mathrm{0},\mathrm{0},\mathrm{0}\right)\:{is}\:{a}\: \\ $$$$\left({i}\right)\:{local}\:{minimum}, \\ $$$$\left({ii}\right)\:{local}\:{maximum}, \\ $$$$\left({ii}\right)\:{saddle}\:{point}. \\ $$$$ \\ $$$$ \\ $$

Question Number 4773    Answers: 1   Comments: 1

lim_(x→0 ) ((sin(x))/x)= 1 how is this so?

$${lim}_{{x}\rightarrow\mathrm{0}\:} \:\frac{{sin}\left({x}\right)}{{x}}=\:\mathrm{1} \\ $$$${how}\:{is}\:{this}\:{so}? \\ $$$$ \\ $$

Question Number 4760    Answers: 0   Comments: 2

the number 27000001 has 4 prime factors. find thier sum

$${the}\:{number}\:\mathrm{27000001} \\ $$$${has}\:\mathrm{4}\:{prime}\:{factors}. \\ $$$${find}\:{thier}\:{sum} \\ $$

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