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Question Number 181279    Answers: 3   Comments: 0

Question Number 181275    Answers: 1   Comments: 7

what is the sum of all even factors of 1000?

$${what}\:{is}\:{the}\:{sum}\:{of}\:{all} \\ $$$${even}\:{factors}\:{of}\:\mathrm{1000}? \\ $$

Question Number 181260    Answers: 2   Comments: 0

Calcul Σ_(n=3) ^(+∞) ((2n−1)/(n(n+2)(n−2)))=...??

$${Calcul}\: \\ $$$$\underset{{n}=\mathrm{3}} {\overset{+\infty} {\sum}}\:\frac{\mathrm{2}{n}−\mathrm{1}}{{n}\left({n}+\mathrm{2}\right)\left({n}−\mathrm{2}\right)}=...?? \\ $$

Question Number 181256    Answers: 0   Comments: 7

(1/f)=(n−1)((1/R_1 )−(1/R_2 )) lense′s maker equation. when is positive or negative R_1 and R_2 ?

$$\frac{\mathrm{1}}{{f}}=\left({n}−\mathrm{1}\right)\left(\frac{\mathrm{1}}{{R}_{\mathrm{1}} }−\frac{\mathrm{1}}{{R}_{\mathrm{2}} }\right)\:\:{lense}'{s}\:{maker}\:{equation}. \\ $$$${when}\:{is}\:{positive}\:{or}\:{negative}\:{R}_{\mathrm{1}} \:{and}\:\:{R}_{\mathrm{2}} ? \\ $$

Question Number 181253    Answers: 0   Comments: 5

define microscopic and macroscopic with one one example.

$${define}\:{microscopic}\:{and}\:{macroscopic} \\ $$$${with}\:{one}\:{one}\:{example}. \\ $$

Question Number 181243    Answers: 1   Comments: 0

Solve for x : ((x − a^2 )/(b + c)) + ((x − b^2 )/(c + a)) + ((x − c^2 )/(a + b)) = 4(a + b + c)

$$\mathrm{Solve}\:\mathrm{for}\:{x}\:: \\ $$$$\frac{{x}\:−\:{a}^{\mathrm{2}} }{{b}\:+\:{c}}\:+\:\frac{{x}\:−\:{b}^{\mathrm{2}} }{{c}\:+\:{a}}\:+\:\frac{{x}\:−\:{c}^{\mathrm{2}} }{{a}\:+\:{b}}\:=\:\mathrm{4}\left({a}\:+\:{b}\:+\:{c}\right) \\ $$

Question Number 181238    Answers: 1   Comments: 0

calculer Σ_(n=1) ^(+oo) artan((2/n^2 ))

$${calculer} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}{artan}\left(\frac{\mathrm{2}}{{n}^{\mathrm{2}} }\right) \\ $$

Question Number 181232    Answers: 3   Comments: 1

Question Number 181221    Answers: 1   Comments: 0

Question Number 181219    Answers: 1   Comments: 0

Solve the D.E x(dy/dx)−y=(√(x^2 +y^2 )) .

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{D}.\mathrm{E} \\ $$$$\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}=\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} } \\ $$$$ \\ $$$$. \\ $$

Question Number 181218    Answers: 1   Comments: 0

Solve the Differential equation: x(dy/dx)−y=2y(lnx−lny) .

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{Differential}\:\mathrm{equation}: \\ $$$$\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}−\mathrm{y}=\mathrm{2y}\left(\mathrm{lnx}−\mathrm{lny}\right) \\ $$$$ \\ $$$$. \\ $$

Question Number 181217    Answers: 1   Comments: 0

Question Number 181207    Answers: 1   Comments: 0

cacul ∀x∈]0,1[ Σ_(n=0) ^(+∞) nx^n

$${cacul} \\ $$$$\left.\forall{x}\in\right]\mathrm{0},\mathrm{1}\left[\right. \\ $$$$\underset{{n}=\mathrm{0}} {\overset{+\infty} {\sum}}{nx}^{{n}} \\ $$

Question Number 181201    Answers: 3   Comments: 0

Question Number 181183    Answers: 1   Comments: 0

Ω_n = determinant ((1,1,1,(...),1),(1,2^2 ,2^3 ,(...),2^n ),(1,3^2 ,3^3 ,(...),3^n ),((...),(...),(...),(...),(...)),(1,n^2 ,n^3 ,(...),n^n )) , n ∈ N^∗ Find: Ω =lim_(n→∞) ((Ω_(n+1) /Ω_n ))^(1/n)

$$\Omega_{\boldsymbol{\mathrm{n}}} \:=\:\begin{vmatrix}{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{...}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{2}^{\mathrm{2}} }&{\mathrm{2}^{\mathrm{3}} }&{...}&{\mathrm{2}^{\boldsymbol{\mathrm{n}}} }\\{\mathrm{1}}&{\mathrm{3}^{\mathrm{2}} }&{\mathrm{3}^{\mathrm{3}} }&{...}&{\mathrm{3}^{\boldsymbol{\mathrm{n}}} }\\{...}&{...}&{...}&{...}&{...}\\{\mathrm{1}}&{\mathrm{n}^{\mathrm{2}} }&{\mathrm{n}^{\mathrm{3}} }&{...}&{\mathrm{n}^{\boldsymbol{\mathrm{n}}} }\end{vmatrix}\:\:,\:\:\:\mathrm{n}\:\in\:\mathbb{N}^{\ast} \\ $$$$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\boldsymbol{\mathrm{n}}}]{\frac{\Omega_{\boldsymbol{\mathrm{n}}+\mathrm{1}} }{\Omega_{\boldsymbol{\mathrm{n}}} }}\: \\ $$

Question Number 181182    Answers: 1   Comments: 0

For what values of a does the system of equations only have one solution: { ((a(x^4 +1)=y+2−∣x∣)),((x^2 +y^2 =4)) :}

$${For}\:{what}\:{values}\:{of}\:{a}\:{does}\:{the}\:{system} \\ $$$${of}\:{equations}\:{only}\:{have}\:{one}\:{solution}: \\ $$$$\begin{cases}{{a}\left({x}^{\mathrm{4}} +\mathrm{1}\right)={y}+\mathrm{2}−\mid{x}\mid}\\{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{4}}\end{cases} \\ $$

Question Number 181173    Answers: 0   Comments: 1

Question Number 181172    Answers: 0   Comments: 2

write snell′s law that light move a concentrative medium to nonconcentrative medium and show with a shape.

$${write}\:{snell}'{s}\:{law}\:{that}\:{light}\:{move}\:{a}\: \\ $$$${concentrative}\:{medium}\:{to}\:{nonconcentrative} \\ $$$${medium}\:{and}\:{show}\:{with}\:{a}\:{shape}. \\ $$

Question Number 181171    Answers: 0   Comments: 1

prove snell′s law

$${prove}\:{snell}'{s}\:{law} \\ $$

Question Number 181152    Answers: 0   Comments: 0

solve the integral ∫_0 ^( 1) ((ln(1+x)ln(1−x))/(1+x))dx=???

$$\boldsymbol{{solve}}\:\boldsymbol{{the}}\:\boldsymbol{{integral}} \\ $$$$\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\boldsymbol{{ln}}\left(\mathrm{1}+\boldsymbol{{x}}\right)\boldsymbol{{ln}}\left(\mathrm{1}−\boldsymbol{{x}}\right)}{\mathrm{1}+\boldsymbol{{x}}}\boldsymbol{{dx}}=??? \\ $$

Question Number 181151    Answers: 4   Comments: 0

Question Number 181196    Answers: 0   Comments: 0

Let a_1 , a_2 , a_3 , ...a_(2022) be numbers ranging from (0, +∞) \ {1}, for which the function f : R→R is defined as f(x)=a_1 ^x +a_2 ^x +a_3 ^x +...a_(2022) ^x . If f(2022)=f(−2022)=2022 prove that this function is constant.

$${Let}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:{a}_{\mathrm{3}} ,\:...{a}_{\mathrm{2022}} \:{be}\:{numbers} \\ $$$${ranging}\:{from}\:\left(\mathrm{0},\:+\infty\right)\:\backslash\:\left\{\mathrm{1}\right\},\:{for}\:{which} \\ $$$${the}\:{function}\:{f}\::\:\mathbb{R}\rightarrow\mathbb{R}\:{is}\:{defined}\:{as} \\ $$$${f}\left({x}\right)={a}_{\mathrm{1}} ^{{x}} +{a}_{\mathrm{2}} ^{{x}} +{a}_{\mathrm{3}} ^{{x}} +...{a}_{\mathrm{2022}} ^{{x}} . \\ $$$${If}\:{f}\left(\mathrm{2022}\right)={f}\left(−\mathrm{2022}\right)=\mathrm{2022}\:{prove} \\ $$$${that}\:{this}\:{function}\:{is}\:{constant}. \\ $$

Question Number 181140    Answers: 0   Comments: 6

I watch a favorite TV program daily for 30 min. If there were ads every 3 hours, what′s the probability that i will see ads once again the next day while watching that program?

$${I}\:{watch}\:{a}\:{favorite}\:{TV}\:{program}\:{daily}\:{for}\:\mathrm{30}\:{min}. \\ $$$$\:{If}\:{there}\:{were}\:{ads}\:{every}\:\mathrm{3}\:{hours},\:{what}'{s}\:{the} \\ $$$$\:{probability}\:{that}\:{i}\:{will}\:{see}\:{ads}\:{once}\:{again}\:{the}\:{next} \\ $$$$\:{day}\:{while}\:{watching}\:{that}\:{program}? \\ $$$$ \\ $$

Question Number 181138    Answers: 1   Comments: 0

If a + b + c = 0 then, (1/(2a^2 + bc)) + (1/(2b^2 + ca)) + (1/(2c^2 + ab)) = ?

$$\mathrm{If}\:{a}\:+\:{b}\:+\:{c}\:=\:\mathrm{0}\:\mathrm{then}, \\ $$$$\frac{\mathrm{1}}{\mathrm{2}{a}^{\mathrm{2}} \:+\:{bc}}\:+\:\frac{\mathrm{1}}{\mathrm{2}{b}^{\mathrm{2}} \:+\:{ca}}\:+\:\frac{\mathrm{1}}{\mathrm{2}{c}^{\mathrm{2}} \:+\:{ab}}\:=\:? \\ $$

Question Number 181153    Answers: 2   Comments: 0

Question Number 181130    Answers: 0   Comments: 0

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