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Question Number 178054    Answers: 2   Comments: 3

Mr. w wants to distribute n+1 different prizes to n friends so that each one gets at least one prize, how many results of this process. I hope to be that one gets 2

$${Mr}.\:{w}\:{wants}\:{to}\:{distribute}\:{n}+\mathrm{1}\:{different}\: \\ $$$${prizes}\:\:{to}\:{n}\:{friends}\:{so}\:{that}\:{each}\:{one}\:{gets} \\ $$$$\:{at}\:{least}\:{one}\:{prize},\:{how}\:{many}\:{results} \\ $$$$\:{of}\:{this}\:{process}.\:{I}\:{hope}\:{to}\:{be}\:{that}\:{one}\:{gets}\:\mathrm{2} \\ $$$$ \\ $$

Question Number 178052    Answers: 0   Comments: 0

Question Number 178051    Answers: 0   Comments: 0

Question Number 178037    Answers: 1   Comments: 1

Question Number 178032    Answers: 0   Comments: 3

• D={z : ∣z∣<1} • H (A→B) denotes the set of holomorfic functions from A to B • We define: W={f∈H (D→R) : ∣∣f∣∣_W <∞ } where ∣∣ ∙ ∣∣_W : { (W,→,R_+ ),(f, ,(Σ_(n=0) ^∞ ((∣f^((n)) (0)∣)/(n!)))) :} Let f∈W Show that ∀g∈H ( f(D^ )), g○f∈W tip: show that ∣∣h∣∣_W ≤cste × Sup_(z∈D) {∣h(z)∣+∣h′′(z)∣} and that W is an algebra then, re−wright f=f_1 +f_2 with f_2 : z Σ_(n=N) ^∞ ((f^((n)) (0))/(n!))z^n with N great enough to make sure that Σ_(n=0) ^∞ ((g^((n)) (0))/(n!))f_2 ^( n) is well defined and converges over W. ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙

$$\bullet\:{D}=\left\{{z}\::\:\mid{z}\mid<\mathrm{1}\right\} \\ $$$$\bullet\:\mathscr{H}\:\left({A}\rightarrow{B}\right)\:\mathrm{denotes}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{holomorfic} \\ $$$$\mathrm{functions}\:\mathrm{from}\:{A}\:\mathrm{to}\:{B} \\ $$$$\bullet\:\mathrm{We}\:\mathrm{define}: \\ $$$${W}=\left\{{f}\in\mathscr{H}\:\left({D}\rightarrow\mathbb{R}\right)\::\:\mid\mid{f}\mid\mid_{{W}} <\infty\:\right\} \\ $$$$\mathrm{where}\:\:\mid\mid\:\centerdot\:\mid\mid_{{W}} \::\:\begin{cases}{{W}}&{\rightarrow}&{\mathbb{R}_{+} }\\{{f}}&{ }&{\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mid{f}^{\left({n}\right)} \left(\mathrm{0}\right)\mid}{{n}!}}\end{cases} \\ $$$$ \\ $$$$\mathrm{Let}\:{f}\in{W} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\forall{g}\in\mathscr{H}\:\left(\:{f}\left(\bar {{D}}\right)\right),\:{g}\circ{f}\in{W} \\ $$$${tip}:\:{show}\:{that} \\ $$$$\:\mid\mid{h}\mid\mid_{{W}} \leqslant{cste}\:×\:\mathrm{Sup}_{{z}\in{D}} \left\{\mid{h}\left({z}\right)\mid+\mid{h}''\left({z}\right)\mid\right\} \\ $$$${and}\:{that}\:{W}\:{is}\:{an}\:{algebra} \\ $$$$ \\ $$$$\mathrm{then},\:\mathrm{re}−\mathrm{wright}\:{f}={f}_{\mathrm{1}} +{f}_{\mathrm{2}} \:\mathrm{with} \\ $$$${f}_{\mathrm{2}} :\:{z}\: \underset{{n}={N}} {\overset{\infty} {\sum}}\frac{{f}^{\left({n}\right)} \left(\mathrm{0}\right)}{{n}!}{z}^{{n}} \\ $$$$\mathrm{with}\:{N}\:\mathrm{great}\:\mathrm{enough}\:\mathrm{to}\:\mathrm{make}\:\mathrm{sure}\:\mathrm{that} \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{g}^{\left({n}\right)} \left(\mathrm{0}\right)}{{n}!}{f}_{\mathrm{2}} ^{\:{n}} \:\mathrm{is}\:\mathrm{well}\:\mathrm{defined}\:\mathrm{and}\:\mathrm{converges} \\ $$$$\mathrm{over}\:{W}. \\ $$$$\:\:\:\:\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot\centerdot \\ $$

Question Number 178039    Answers: 0   Comments: 0

Question Number 178026    Answers: 1   Comments: 2

Question Number 178021    Answers: 1   Comments: 0

Let S={1, 2, 3, 4, 5} , we want to make a group H of numbers have the following properties: 1. Each number has different digits and taken from S 2. Each number is greater than 20 000 3. None of them is multiple of five How many items of H?

$$ \\ $$$${Let}\:{S}=\left\{\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\mathrm{5}\right\}\:,\:{we}\:{want}\:{to}\:{make}\:{a}\: \\ $$$$\:{group}\:{H}\:{of}\:{numbers}\:{have}\:{the}\:{following}\: \\ $$$$\:{properties}: \\ $$$$\:\mathrm{1}.\:{Each}\:{number}\:{has}\:{different}\:{digits}\:{and} \\ $$$$\:{taken}\:{from}\:{S} \\ $$$$\:\mathrm{2}.\:{Each}\:{number}\:{is}\:{greater}\:{than}\:\mathrm{20}\:\mathrm{000} \\ $$$$\:\mathrm{3}.\:{None}\:{of}\:{them}\:{is}\:{multiple}\:{of}\:{five} \\ $$$$ \\ $$$${How}\:{many}\:{items}\:{of}\:{H}? \\ $$

Question Number 178019    Answers: 0   Comments: 0

Give the IUPAC name of the following (a)H_3 PO_4 (b)H_2 CO_3 (c)HCIO (d) HNO_2 (e)HNO_3 (f)Al_2 (SO_4 )_3 (g)Ca_3 (PO_4 )_2 (h)MgO_2 (i)HF

$$\mathrm{Give}\:\mathrm{the}\:\mathrm{IUPAC}\:\mathrm{name}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{following} \\ $$$$\left(\mathrm{a}\right)\mathrm{H}_{\mathrm{3}} \mathrm{PO}_{\mathrm{4}} \\ $$$$\left(\mathrm{b}\right)\mathrm{H}_{\mathrm{2}} \mathrm{CO}_{\mathrm{3}} \\ $$$$\left(\mathrm{c}\right)\mathrm{HCIO} \\ $$$$\left(\mathrm{d}\right)\:\mathrm{HNO}_{\mathrm{2}} \\ $$$$\left(\mathrm{e}\right)\mathrm{HNO}_{\mathrm{3}} \\ $$$$\left(\mathrm{f}\right)\mathrm{Al}_{\mathrm{2}} \left(\mathrm{SO}_{\mathrm{4}} \right)_{\mathrm{3}} \\ $$$$\left(\mathrm{g}\right)\mathrm{Ca}_{\mathrm{3}} \left(\mathrm{PO}_{\mathrm{4}} \right)_{\mathrm{2}} \\ $$$$\left(\mathrm{h}\right)\mathrm{MgO}_{\mathrm{2}} \\ $$$$\left(\mathrm{i}\right)\mathrm{HF} \\ $$

Question Number 178018    Answers: 2   Comments: 0

8.1g of a compound Q contain magnessium and oxygen.if mass of magnessium is 4.9g Determine the empirical formular of compound Q. [given Mg=24 O=16]

$$\mathrm{8}.\mathrm{1g}\:\mathrm{of}\:\mathrm{a}\:\mathrm{compound}\:\mathrm{Q}\:\mathrm{contain} \\ $$$$\mathrm{magnessium}\:\mathrm{and}\:\mathrm{oxygen}.\mathrm{if} \\ $$$$\mathrm{mass}\:\mathrm{of}\:\mathrm{magnessium}\:\mathrm{is}\:\mathrm{4}.\mathrm{9g} \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{empirical}\:\mathrm{formular} \\ $$$$\mathrm{of}\:\mathrm{compound}\:\mathrm{Q}. \\ $$$$\left[\mathrm{given}\:\mathrm{Mg}=\mathrm{24}\:\:\:\mathrm{O}=\mathrm{16}\right] \\ $$

Question Number 178013    Answers: 4   Comments: 0

Using Electronic diagrams show the bonding in the following (a)Magnesium chloride (b)Sodium chloride

$$\mathrm{Using}\:\mathrm{Electronic}\:\mathrm{diagrams}\:\mathrm{show} \\ $$$$\mathrm{the}\:\mathrm{bonding}\:\mathrm{in}\:\mathrm{the}\:\mathrm{following} \\ $$$$\left(\mathrm{a}\right)\mathrm{Magnesium}\:\mathrm{chloride} \\ $$$$\left(\mathrm{b}\right)\mathrm{Sodium}\:\mathrm{chloride} \\ $$

Question Number 178011    Answers: 3   Comments: 0

Hydrocarbon contain 80% by mass of carbon and the rest is for hydrogen.calculate the empirical formula of the compound [given H=1 C=12]

$$\mathrm{Hydrocarbon}\:\mathrm{contain}\:\mathrm{80\%}\:\mathrm{by} \\ $$$$\mathrm{mass}\:\mathrm{of}\:\mathrm{carbon}\:\mathrm{and}\:\mathrm{the}\:\mathrm{rest} \\ $$$$\mathrm{is}\:\mathrm{for}\:\mathrm{hydrogen}.\mathrm{calculate}\:\mathrm{the} \\ $$$$\mathrm{empirical}\:\mathrm{formula}\:\mathrm{of}\:\mathrm{the}\:\mathrm{compound} \\ $$$$\left[\mathrm{given}\:\mathrm{H}=\mathrm{1}\:\:\mathrm{C}=\mathrm{12}\right] \\ $$

Question Number 178009    Answers: 3   Comments: 2

Question Number 178008    Answers: 1   Comments: 0

Question Number 178007    Answers: 1   Comments: 0

Question Number 178001    Answers: 1   Comments: 1

Question Number 177996    Answers: 0   Comments: 1

Question Number 177990    Answers: 0   Comments: 0

Question Number 177980    Answers: 1   Comments: 0

Question Number 177978    Answers: 3   Comments: 0

Question Number 177976    Answers: 0   Comments: 1

Question Number 177975    Answers: 1   Comments: 0

Question Number 177964    Answers: 3   Comments: 1

(1/(sec15 sin15 cos30))=?

$$\frac{\mathrm{1}}{{sec}\mathrm{15}\:{sin}\mathrm{15}\:{cos}\mathrm{30}}=? \\ $$

Question Number 177957    Answers: 2   Comments: 0

let a > 0 find the sum of the infinite series 1 + (((loga)^2 )/(2!)) + (((loga)^4 )/(4!)) + (((loga)^6 )/(6!))...

$$\mathrm{let}\:\:\mathrm{a}\:>\:\mathrm{0}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{infinite}\: \\ $$$$\mathrm{series} \\ $$$$\:\mathrm{1}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{2}} \:}{\mathrm{2}!}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{4}} \:}{\mathrm{4}!}\:+\:\frac{\left(\mathrm{loga}\right)^{\mathrm{6}} \:}{\mathrm{6}!}... \\ $$

Question Number 177933    Answers: 2   Comments: 0

If 1+sin x+sin^2 x+sin^3 x+...∞ =4+2(√3) ,0<x<π Find the value of x

$$\mathrm{If}\:\mathrm{1}+\mathrm{sin}\:\mathrm{x}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+...\infty \\ $$$$=\mathrm{4}+\mathrm{2}\sqrt{\mathrm{3}}\:\:,\mathrm{0}<\mathrm{x}<\pi\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$ \\ $$

Question Number 177932    Answers: 1   Comments: 0

If a,b,c are in A.P show that (1/( (√b)+(√c))),(1/( (√c) +(√a))),(1/( (√b)+(√a))),are in A.P

$$\mathrm{If}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}\:\mathrm{show}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}}+\sqrt{\mathrm{c}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{c}}\:+\sqrt{\mathrm{a}}},\frac{\mathrm{1}}{\:\sqrt{\mathrm{b}}+\sqrt{\mathrm{a}}},\mathrm{are}\:\mathrm{in}\:\mathrm{A}.\mathrm{P} \\ $$

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