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Question Number 157805    Answers: 1   Comments: 0

Find x∈R: x^3 −2x+3=(√(2x+5))+4(√(x−1))

$$\mathrm{Find}\:\mathrm{x}\in\mathbb{R}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{3}} −\mathrm{2x}+\mathrm{3}=\sqrt{\mathrm{2x}+\mathrm{5}}+\mathrm{4}\sqrt{\mathrm{x}−\mathrm{1}} \\ $$

Question Number 157826    Answers: 1   Comments: 0

Question Number 157824    Answers: 0   Comments: 0

Question Number 157823    Answers: 1   Comments: 0

calculate : Ω := Σ_(n=0) ^∞ (( 1)/((4n+1)^( 3) )) = ?

$$ \\ $$$$\:\:\:\:\:\:\:{calculate}\:: \\ $$$$\:\:\:\:\Omega\::=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\:\mathrm{1}}{\left(\mathrm{4}{n}+\mathrm{1}\right)^{\:\mathrm{3}} }\:\:\:=\:? \\ $$$$\: \\ $$

Question Number 157822    Answers: 0   Comments: 1

Question Number 157803    Answers: 0   Comments: 0

lim_(x→0) ((x tan (tan x)−(tan x)^2 )/x^6 ) =?

$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{tan}\:\left(\mathrm{tan}\:{x}\right)−\left(\mathrm{tan}\:{x}\right)^{\mathrm{2}} }{{x}^{\mathrm{6}} }\:=? \\ $$

Question Number 157797    Answers: 1   Comments: 0

Question Number 157791    Answers: 0   Comments: 0

Question Number 157790    Answers: 1   Comments: 0

Question Number 157788    Answers: 0   Comments: 0

look for a simpler boolean function in POS form of: a.f(r,s,t,u)=Π(4,5,6,9,10,12,14) b.g(w,x,y,z)=Σ(4,8,13,14)

$$\mathrm{look}\:\mathrm{for}\:\mathrm{a}\:\mathrm{simpler}\:\mathrm{boolean}\:\mathrm{function}\:\mathrm{in} \\ $$$$\mathrm{POS}\:\mathrm{form}\:\mathrm{of}: \\ $$$$\mathrm{a}.\mathrm{f}\left(\mathrm{r},\mathrm{s},\mathrm{t},\mathrm{u}\right)=\Pi\left(\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{9},\mathrm{10},\mathrm{12},\mathrm{14}\right) \\ $$$$\mathrm{b}.\mathrm{g}\left(\mathrm{w},\mathrm{x},\mathrm{y},\mathrm{z}\right)=\Sigma\left(\mathrm{4},\mathrm{8},\mathrm{13},\mathrm{14}\right) \\ $$

Question Number 157784    Answers: 0   Comments: 2

from the partical differential equation by eliminating constants indicated in brackets from the following equation z=(x+a) (y+b);(a,b)

$${from}\:{the}\:{partical}\:{differential}\:{equation}\:{by}\:{eliminating}\:{constants}\:{indicated}\:{in}\:{brackets}\:{from}\:{the}\:{following}\:{equation}\:{z}=\left({x}+{a}\right)\:\left({y}+{b}\right);\left({a},{b}\right) \\ $$

Question Number 157781    Answers: 1   Comments: 0

Question Number 157778    Answers: 0   Comments: 0

find fourier′s serie of f(x)=x−[x]

$${find}\:{fourier}'{s}\:{serie}\:{of}\:{f}\left({x}\right)={x}−\left[{x}\right] \\ $$

Question Number 157775    Answers: 0   Comments: 5

Question Number 157774    Answers: 0   Comments: 0

$$ \\ $$$$ \\ $$

Question Number 157770    Answers: 0   Comments: 0

Can you proof this intresting identity? ln x = (x−1)Π_(n=1) ^∞ ((2/(1+(x)^(1/2^n ) )))

$$\mathrm{Can}\:\mathrm{you}\:\mathrm{proof}\:\mathrm{this}\:\mathrm{intresting}\:\mathrm{identity}? \\ $$$$\mathrm{ln}\:\mathrm{x}\:=\:\left(\mathrm{x}−\mathrm{1}\right)\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\left(\frac{\mathrm{2}}{\mathrm{1}+\sqrt[{\mathrm{2}^{\mathrm{n}} }]{\mathrm{x}}}\right) \\ $$

Question Number 157769    Answers: 0   Comments: 5

Question Number 157758    Answers: 0   Comments: 1

Evaluate 3(√((41.02×(√(0.7124)))/(42.87×0.207×0.0404)))

$${Evaluate}\:\:\mathrm{3}\sqrt{\frac{\mathrm{41}.\mathrm{02}×\sqrt{\mathrm{0}.\mathrm{7124}}}{\mathrm{42}.\mathrm{87}×\mathrm{0}.\mathrm{207}×\mathrm{0}.\mathrm{0404}}} \\ $$

Question Number 157753    Answers: 3   Comments: 0

A farmer has numbers of animals in his farm made up of hens and goats. One morning he counted 20 heads and 66 legs of the animals. How many hens and goat were counted by the farmer.

$${A}\:{farmer}\:{has}\:{numbers}\:{of}\:{animals} \\ $$$${in}\:{his}\:{farm}\:{made}\:{up}\:{of}\:{hens}\:{and}\:{goats}. \\ $$$${One}\:{morning}\:{he}\:{counted}\:\mathrm{20}\:{heads}\:{and}\:\mathrm{66}\:{legs} \\ $$$${of}\:{the}\:{animals}.\:{How}\:{many}\:{hens}\:{and} \\ $$$${goat}\:{were}\:{counted}\:{by}\:{the}\:{farmer}. \\ $$

Question Number 157752    Answers: 1   Comments: 0

A sum of two−digit number is 14. The tens digit is the square of a number which is two less than the unit digit. Find the two−digit numbers.

$$ \\ $$$${A}\:{sum}\:{of}\:{two}−{digit}\:{number} \\ $$$${is}\:\mathrm{14}.\:{The}\:{tens}\:{digit}\:{is}\:{the}\:{square} \\ $$$${of}\:{a}\:{number}\:{which}\:{is}\:{two}\:{less}\:{than} \\ $$$${the}\:{unit}\:{digit}.\:{Find}\:{the}\:{two}−{digit}\:{numbers}. \\ $$

Question Number 157744    Answers: 1   Comments: 0

∫_0 ^( 1) (( Li_( 2) (−x ) )/(1+ x))dx=?

$$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:\:\mathrm{Li}_{\:\mathrm{2}} \:\left(−\mathrm{x}\:\right)\:}{\mathrm{1}+\:\mathrm{x}}\mathrm{dx}=? \\ $$$$ \\ $$$$ \\ $$

Question Number 157795    Answers: 1   Comments: 0

{a_n } is a natural number sequence for n ≥ 0 that satisfy recurrence relation a_(m+n) + a_(m−n) −m+n = 1 + (1/2) (a_(2m) +a_(2n) ) , for ∀ m,n nonnegative integers . Find a_(2016) .

$$\left\{{a}_{{n}} \right\}\:{is}\:{a}\:\:{natural}\:\:{number}\:\:{sequence}\:\:{for}\:\:{n}\:\geqslant\:\mathrm{0}\:\:{that}\:\:{satisfy} \\ $$$${recurrence}\:\:{relation}\:\:{a}_{{m}+{n}} \:+\:{a}_{{m}−{n}} \:−{m}+{n}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\:\left({a}_{\mathrm{2}{m}} \:+{a}_{\mathrm{2}{n}} \right)\:,\:\: \\ $$$${for}\:\:\forall\:{m},{n}\:\:{nonnegative}\:\:{integers}\:. \\ $$$${Find}\:\:{a}_{\mathrm{2016}} \:. \\ $$

Question Number 157742    Answers: 0   Comments: 0

Find: 𝛀 =∫_( 0) ^( 1) ((tan^(-1) x ∙ Li_2 (((1-x)/(1+x))))/((1+x)^2 )) dx

$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\frac{\mathrm{tan}^{-\mathrm{1}} \mathrm{x}\:\centerdot\:\mathrm{Li}_{\mathrm{2}} \left(\frac{\mathrm{1}-\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 157792    Answers: 0   Comments: 0

Question Number 157739    Answers: 1   Comments: 1

two parallel paths 26m apart run east−west through the woods. one person east on one path at 3 kmph and another west on other path at 4 kmph. if they pass each other at time t =0 , i)how far apart are they 8 sec later? ii) how fast is the distance between them changing at that mlment? iii)find the distance L between them at 8 sec and (dL/dt)?

$${two}\:{parallel}\:{paths}\:\mathrm{26}{m}\:{apart}\:{run} \\ $$$${east}−{west}\:{through}\:{the}\:{woods}. \\ $$$${one}\:{person}\:{east}\:{on}\:{one}\:{path}\:{at}\: \\ $$$$\mathrm{3}\:{kmph}\:{and}\:{another}\:{west}\:{on}\:{other}\: \\ $$$${path}\:{at}\:\mathrm{4}\:{kmph}.\:{if}\:{they}\:{pass}\:{each}\: \\ $$$${other}\:{at}\:{time}\:{t}\:=\mathrm{0}\:,\: \\ $$$$\left.{i}\right){how}\:{far}\:{apart}\:{are}\:{they} \\ $$$$\mathrm{8}\:{sec}\:{later}?\: \\ $$$$\left.{ii}\right)\:{how}\:{fast}\:{is}\:{the}\: \\ $$$${distance}\:{between}\:{them}\:{changing}\: \\ $$$${at}\:{that}\:{mlment}?\: \\ $$$$\left.{iii}\right){find}\:{the}\:{distance}\:{L} \\ $$$${between}\:{them}\:{at}\:\mathrm{8}\:{sec}\:{and}\:\frac{{dL}}{{dt}}? \\ $$

Question Number 157730    Answers: 0   Comments: 8

Good day Mr.W, I would have loved to send this privately to you but there′s nomeans of doing that. You assisted me in solving a problem and the answers are really correct; I was also understandinv the approach however some points got me lost. I′ll be most grateful if you could help me amplify the solution. I always appreciate you since I was here in 2014. Thank you now and always. here are some of the issues i have with the solution. I thought that in the composite system the axial load would be shared among the steel and concrete thus having a portion of the load in the steel and the rest in the concrete, yet you solved for the stress in concrete and used the general axial load and total area and yet your answer was very correct but i really dont understand why and how you had to use the general area and load for just concrete. I was also shocked about how the area of the steel became had α in it. I thought it would just be ((nπd^2 )/4). I would lie if I say I dont marvel at your calculation skills sir. please explain this method for me. It is really short and concise.The other method I know also gave me the answer you got but its a really long journey. Please sir, explain in detail to me. I′m most grateful. Thanks in advance. I′ll post the auestion and your previous workings.

$${Good}\:{day}\:{Mr}.{W},\:{I}\:{would}\:{have}\:{loved} \\ $$$${to}\:{send}\:{this}\:{privately}\:{to}\:{you}\:{but} \\ $$$${there}'{s}\:{nomeans}\:{of}\:{doing}\:{that}.\:{You} \\ $$$${assisted}\:{me}\:{in}\:{solving}\:{a}\:{problem} \\ $$$${and}\:{the}\:{answers}\:{are}\:{really}\:{correct};\:{I} \\ $$$${was}\:{also}\:{understandinv}\:{the}\:{approach} \\ $$$${however}\:{some}\:{points}\:{got}\:{me}\:{lost}. \\ $$$${I}'{ll}\:{be}\:{most}\:{grateful}\:{if}\:{you}\:{could} \\ $$$${help}\:{me}\:{amplify}\:{the}\:{solution}.\: \\ $$$$ \\ $$$${I}\:{always}\:{appreciate}\:{you}\:{since}\:{I}\:{was} \\ $$$${here}\:{in}\:\mathrm{2014}. \\ $$$${Thank}\:{you}\:{now}\:{and}\:{always}.\: \\ $$$$ \\ $$$$\boldsymbol{{here}}\:\boldsymbol{{are}}\:\boldsymbol{{some}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{issues}} \\ $$$$\boldsymbol{{i}}\:\boldsymbol{{have}}\:\boldsymbol{{with}}\:\boldsymbol{{the}}\:\boldsymbol{{solution}}. \\ $$$$ \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{thought}}\:\boldsymbol{{that}}\:\boldsymbol{{in}}\:\boldsymbol{{the}}\:\boldsymbol{{composite}} \\ $$$$\boldsymbol{{system}}\:\boldsymbol{{the}}\:\boldsymbol{{axial}}\:\boldsymbol{{load}}\:\boldsymbol{{would}}\:\boldsymbol{{be}} \\ $$$$\boldsymbol{{shared}}\:\boldsymbol{{among}}\:\boldsymbol{{the}}\:\boldsymbol{{steel}}\:\boldsymbol{{and}} \\ $$$$\boldsymbol{{concrete}}\:\boldsymbol{{thus}}\:\boldsymbol{{having}}\:\boldsymbol{{a}}\:\boldsymbol{{portion}} \\ $$$$\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{load}}\:\boldsymbol{{in}}\:\boldsymbol{{the}}\:\boldsymbol{{steel}}\:\boldsymbol{{and}}\: \\ $$$$\boldsymbol{{the}}\:\boldsymbol{{rest}}\:\boldsymbol{{in}}\:\boldsymbol{{the}}\:\boldsymbol{{concrete}},\:{yet} \\ $$$${you}\:{solved}\:{for}\:{the}\:{stress}\:{in} \\ $$$${concrete}\:{and}\:{used}\:{the}\:{general}\:{axial}\:{load}\:{and} \\ $$$${total}\:{area}\:{and}\:{yet}\:{your}\:{answer} \\ $$$${was}\:{very}\:{correct}\:{but}\:{i}\:{really}\:{dont} \\ $$$${understand}\:{why}\:{and}\:{how}\:{you}\:{had}\:{to}\: \\ $$$${use}\:{the}\:{general}\:{area}\:{and}\:{load}\:{for} \\ $$$${just}\:{concrete}. \\ $$$$ \\ $$$$ \\ $$$${I}\:{was}\:{also}\:{shocked}\:{about}\:{how}\:{the} \\ $$$${area}\:{of}\:{the}\:{steel}\:{became}\:{had}\:\alpha\:{in} \\ $$$${it}.\:{I}\:{thought}\:{it}\:{would}\:{just}\:{be}\:\frac{{n}\pi{d}^{\mathrm{2}} }{\mathrm{4}}. \\ $$$${I}\:{would}\:{lie}\:{if}\:{I}\:{say}\:{I}\:{dont}\:{marvel} \\ $$$${at}\:{your}\:{calculation}\:{skills}\:{sir}. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$${please}\:{explain}\:{this}\:{method}\:{for}\:{me}. \\ $$$${It}\:{is}\:{really}\:{short}\:{and}\:{concise}.{The} \\ $$$${other}\:{method}\:{I}\:{know}\:{also}\:{gave}\:{me} \\ $$$${the}\:{answer}\:{you}\:{got}\:{but}\:{its}\:{a}\:{really}\:{long} \\ $$$${journey}.\:{Please}\:{sir},\:{explain}\:{in}\:{detail} \\ $$$${to}\:{me}.\:{I}'{m}\:{most}\:{grateful}.\: \\ $$$$ \\ $$$${Thanks}\:{in}\:{advance}. \\ $$$$ \\ $$$${I}'{ll}\:{post}\:{the}\:{auestion}\:{and}\:{your}\:{previous}\:{workings}. \\ $$

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