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Question Number 179999 Answers: 1 Comments: 1

Question Number 179993 Answers: 0 Comments: 13

How many 6 digit numbers have different digits and are divisible by 11? (an unsolved old question)

$${How}\:{many}\:\mathrm{6}\:{digit}\:{numbers}\:{have} \\ $$$${different}\:{digits}\:{and}\:{are}\:{divisible}\:{by} \\ $$$$\mathrm{11}? \\ $$$$\left({an}\:{unsolved}\:{old}\:{question}\right) \\ $$

Question Number 179972 Answers: 0 Comments: 5

Question Number 179955 Answers: 1 Comments: 0

Question Number 179950 Answers: 0 Comments: 1

lim_(x→∞) [(1+(1/x))+(1+(2/x))^(2/2) +(1+(3/x))^(1/3) +∙∙∙∙+(1+(x/x))^(1/x) ]=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)+\left(\mathrm{1}+\frac{\mathrm{2}}{{x}}\right)^{\frac{\mathrm{2}}{\mathrm{2}}} +\left(\mathrm{1}+\frac{\mathrm{3}}{{x}}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} +\centerdot\centerdot\centerdot\centerdot+\left(\mathrm{1}+\frac{{x}}{{x}}\right)^{\frac{\mathrm{1}}{{x}}} \right]=? \\ $$

Question Number 179961 Answers: 1 Comments: 0

f(x)∈[0,1],1≤f(x)≤3 how to prove 1≤∫_0 ^1 f(x)dx ∫_0 ^1 (dx/(f(x)))≤(4/3)?

$${f}\left({x}\right)\in\left[\mathrm{0},\mathrm{1}\right],\mathrm{1}\leqslant{f}\left({x}\right)\leqslant\mathrm{3} \\ $$$${how}\:{to}\:{prove}\:\mathrm{1}\leqslant\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right){dx}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{{f}\left({x}\right)}\leqslant\frac{\mathrm{4}}{\mathrm{3}}? \\ $$

Question Number 179938 Answers: 2 Comments: 3

Question Number 179936 Answers: 3 Comments: 0

Question Number 179919 Answers: 1 Comments: 0

Evaluate Ω = lim_( n→∞) ( n− Σ_(k=1) ^n cos ( (( (√k))/( n)) ) ) =?

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{Evaluate}\: \\ $$$$\:\:\:\:\:\:\Omega\:=\:\mathrm{lim}_{\:{n}\rightarrow\infty} \left(\:{n}−\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{cos}\:\left(\:\frac{\:\sqrt{{k}}}{\:{n}}\:\:\right)\:\right)\:=?\:\:\:\:\:\: \\ $$$$\:\:\:\:\: \\ $$

Question Number 179918 Answers: 1 Comments: 0

Question Number 179917 Answers: 1 Comments: 0

Question Number 179916 Answers: 0 Comments: 0

Question Number 179908 Answers: 0 Comments: 2

Some Important notes 1st Someone has solved a question as wrong, and after he see other people have solved it correctly he delete his poste! hmmm by the way, i have some lapses, i′ve never deleted any. My mistakes keep you from making like them. There is no embarrassment, so please, leave things as they are. 2nd I once composed an question, some people had solved it perfectly, and someone write as comment: “You seem don′t know anything about math” I′ve never replied him, because am not interest in introducing my acadimic qualifications to him. But here i would like to do and say that i exchange the qusetions with others, so if you were a student then try to learn, and if you were a professuer so you can note my questions in your book to show them later to your students in real. The bottom line is let′s exchange a variety of questions! 3rd I noticed some people answer qusetions as a comment! Good! now he seems as the 1st one who solved true! Claps! Can you friend respect who had solved before you? Theses were my three points, for this day. Hope you interest in too, and thanks for you all

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{Some}}\:\boldsymbol{{Important}}\:\boldsymbol{{notes}} \\ $$$$\:\mathrm{1}\boldsymbol{{st}}\:{Someone}\:{has}\:{solved}\:{a}\:{question}\:{as}\:{wrong}, \\ $$$$\:{and}\:{after}\:{he}\:{see}\:{other}\:{people}\:{have}\:{solved}\:{it} \\ $$$$\:{correctly}\:{he}\:{delete}\:{his}\:{poste}!\:{hmmm}\:{by}\:{the}\:{way}, \\ $$$$\:{i}\:{have}\:{some}\:{lapses},\:{i}'{ve}\:{never}\:{deleted}\:{any}. \\ $$$$\:{My}\:{mistakes}\:{keep}\:{you}\:{from}\:{making}\:{like}\:{them}. \\ $$$$\:{There}\:{is}\:{no}\:{embarrassment},\:{so}\:{please},\:{leave} \\ $$$$\:{things}\:{as}\:{they}\:{are}. \\ $$$$ \\ $$$$\mathrm{2}\boldsymbol{{nd}}\:{I}\:{once}\:{composed}\:{an}\:{question},\:{some}\:{people} \\ $$$$\:{had}\:{solved}\:{it}\:{perfectly},\:{and}\:{someone}\:{write}\:{as} \\ $$$$\:{comment}: \\ $$$$\:``{You}\:{seem}\:{don}'{t}\:{know}\:{anything}\:{about}\:{math}'' \\ $$$$\:{I}'{ve}\:{never}\:{replied}\:{him},\:{because}\:{am}\:{not}\:{interest} \\ $$$$\:{in}\:{introducing}\:{my}\:{acadimic}\:{qualifications}\:{to}\:{him}. \\ $$$$\:{But}\:{here}\:{i}\:{would}\:{like}\:{to}\:{do}\:{and}\:{say}\:{that} \\ $$$$\:{i}\:{exchange}\:{the}\:{qusetions}\:{with}\:{others},\:{so}\:{if}\:{you} \\ $$$$\:{were}\:{a}\:{student}\:{then}\:{try}\:{to}\:{learn}, \\ $$$$\:{and}\:{if}\:{you}\:{were}\:{a}\:{professuer}\:{so}\:{you}\:{can}\:{note} \\ $$$$\:{my}\:{questions}\:{in}\:{your}\:{book}\:{to}\:{show}\:{them}\:{later} \\ $$$$\:{to}\:{your}\:{students}\:{in}\:{real}. \\ $$$$\:\boldsymbol{{The}}\:\boldsymbol{{bottom}}\:\boldsymbol{{line}}\:{is}\:{let}'{s}\:{exchange} \\ $$$$\:\:\:{a}\:{variety}\:{of}\:{questions}! \\ $$$$ \\ $$$$\mathrm{3}{rd}\:{I}\:{noticed}\:{some}\:{people}\:{answer}\:{qusetions} \\ $$$$\:{as}\:{a}\:{comment}!\:{Good}!\:{now}\:{he}\:{seems} \\ $$$$\:{as}\:{the}\:\mathrm{1}{st}\:{one}\:{who}\:{solved}\:{true}!\:\boldsymbol{{Claps}}! \\ $$$$ \\ $$$$\:{Can}\:{you}\:{friend}\:{respect}\:{who}\:{had}\:{solved}\:{before}\:{you}? \\ $$$$ \\ $$$$\:{Theses}\:{were}\:{my}\:{three}\:{points},\:{for}\:{this}\:{day}. \\ $$$$ \\ $$$$\:{Hope}\:{you}\:{interest}\:{in}\:{too},\:{and}\:{thanks}\:{for}\:{you}\:{all} \\ $$$$ \\ $$

Question Number 179906 Answers: 2 Comments: 0

2 boxes, 1st contains 4 white & 6 black balls 2nd box contains 8 white & 8 black balls We randomly draw a ball, got a black one What′s probability that it was drawn from Box_2 ?

$$\mathrm{2}\:{boxes},\:\mathrm{1}{st}\:{contains}\:\mathrm{4}\:{white}\:\&\:\mathrm{6}\:{black}\:{balls} \\ $$$$\:\mathrm{2}{nd}\:{box}\:{contains}\:\mathrm{8}\:{white}\:\&\:\mathrm{8}\:{black}\:{balls} \\ $$$$\:{We}\:{randomly}\:{draw}\:{a}\:{ball},\:{got}\:{a}\:{black}\:{one} \\ $$$$\:{What}'{s}\:{probability}\:{that}\:{it}\:{was}\:{drawn}\:{from}\:{Box}_{\mathrm{2}} ? \\ $$

Question Number 179900 Answers: 1 Comments: 0

Prove that: f = 5x^4 + 35x^3 + 28x^2 + 14x + 7 is irreducible in Q[x]

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{f}\:=\:\mathrm{5x}^{\mathrm{4}} \:+\:\mathrm{35x}^{\mathrm{3}} \:+\:\mathrm{28x}^{\mathrm{2}} \:+\:\mathrm{14x}\:+\:\mathrm{7}\:\:\mathrm{is}\:\mathrm{irreducible}\:\mathrm{in}\:\:\mathrm{Q}\left[\mathrm{x}\right] \\ $$

Question Number 179890 Answers: 3 Comments: 1

p(x)=(1−x)(1+2x)(1−3x)....(1−15x) find the coefficient of the x^3 term in the expansion.

$${p}\left({x}\right)=\left(\mathrm{1}−{x}\right)\left(\mathrm{1}+\mathrm{2}{x}\right)\left(\mathrm{1}−\mathrm{3}{x}\right)....\left(\mathrm{1}−\mathrm{15}{x}\right) \\ $$$$ \\ $$$${find}\:{the}\:{coefficient}\:{of}\:{the}\:{x}^{\mathrm{3}} \:{term} \\ $$$${in}\:{the}\:{expansion}. \\ $$

Question Number 179886 Answers: 0 Comments: 5