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Question Number 194140 Answers: 1 Comments: 0

prove it : ((n),(k) )^( 2) ≥ ((( n)),((k−1)) ) × ((( n)),((k+1)) ) ; 1≤k≤n−1

$${prove}\:{it}\:: \\ $$$$\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}^{\:\mathrm{2}} \geqslant\:\begin{pmatrix}{\:\:\:\:{n}}\\{{k}−\mathrm{1}}\end{pmatrix}\:×\begin{pmatrix}{\:\:{n}}\\{{k}+\mathrm{1}}\end{pmatrix}\:\:\:\:\:;\:\:\:\mathrm{1}\leqslant{k}\leqslant{n}−\mathrm{1} \\ $$$$ \\ $$

Question Number 194139 Answers: 1 Comments: 1

Question Number 194135 Answers: 3 Comments: 0

determinant (((((23!−23)/(1.1!+2.2!+3.3!+...+21.21!)) =?)))

$$\:\:\:\:\:\:\begin{array}{|c|}{\frac{\mathrm{23}!−\mathrm{23}}{\mathrm{1}.\mathrm{1}!+\mathrm{2}.\mathrm{2}!+\mathrm{3}.\mathrm{3}!+...+\mathrm{21}.\mathrm{21}!}\:=?}\\\hline\end{array} \\ $$

Question Number 194131 Answers: 1 Comments: 1

Question Number 194128 Answers: 1 Comments: 0

Question Number 194127 Answers: 2 Comments: 0

Question Number 194116 Answers: 1 Comments: 0

Question Number 194113 Answers: 1 Comments: 0

Question Number 194105 Answers: 1 Comments: 0

x , y , z are positive real numbers if x^4 +y^4 +z^4 =1 Then find the minimum value of (x^3 /(1−x^8 ))+(y^3 /(1−y^8 ))+(z^3 /(1−z^8 ))

$$ \\ $$$${x}\:,\:{y}\:,\:{z}\:{are}\:{positive}\:{real}\:{numbers}\:{if}\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} =\mathrm{1} \\ $$$${Then}\:{find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{8}} }+\frac{{y}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{8}} }+\frac{{z}^{\mathrm{3}} }{\mathrm{1}−{z}^{\mathrm{8}} } \\ $$

Question Number 194089 Answers: 1 Comments: 3

Determiner le rayon r

$$\mathrm{Determiner}\:\mathrm{le}\:\mathrm{rayon}\:\boldsymbol{\mathrm{r}} \\ $$

Question Number 194088 Answers: 3 Comments: 0

Question Number 194086 Answers: 1 Comments: 1

f(x)=2y^2 +4y+3 then a_(0 ) equle to a) p(5) b) 7 c) 3 d) not defined

$${f}\left({x}\right)=\mathrm{2}{y}^{\mathrm{2}} +\mathrm{4}{y}+\mathrm{3}\:\:{then}\:{a}_{\mathrm{0}\:} {equle}\:{to} \\ $$$$\left.{a}\left.\right)\:\:\:{p}\left(\mathrm{5}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{b}\right)\:\:\:\:\mathrm{7} \\ $$$$\left.{c}\left.\right)\:\:\:\:\:\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}\right)\:{not}\:{defined} \\ $$

Question Number 194085 Answers: 2 Comments: 0

f(x)−f(x−1)=x+1 f′(6)=? solution??

$$\mathrm{f}\left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{x}+\mathrm{1} \\ $$$$\mathrm{f}'\left(\mathrm{6}\right)=? \\ $$$$\mathrm{solution}?? \\ $$

Question Number 194073 Answers: 2 Comments: 0

Question Number 194067 Answers: 2 Comments: 0

Question Number 194065 Answers: 0 Comments: 0

Question Number 194064 Answers: 1 Comments: 0

Question Number 194059 Answers: 0 Comments: 0

Question Number 194058 Answers: 0 Comments: 0

Ques. 1 Let G = C_5 × C_(25) × C_(625) . Determine the number of elements of each order in G Ques. 2 List the abelian groups of order 16 and of order 27 up to Isomorphism. Ques. 3 Describe a Sylow 2−subgroup in S_5 , and how many Sylow 2−subgroups are in S_5 ?

$$\mathrm{Ques}.\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Let}\:\mathrm{G}\:=\:\mathrm{C}_{\mathrm{5}} \:×\:\mathrm{C}_{\mathrm{25}} \:×\:\mathrm{C}_{\mathrm{625}} .\:\mathrm{Determine} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{each}\:\mathrm{order}\:\mathrm{in}\:\mathrm{G} \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{List}\:\mathrm{the}\:\mathrm{abelian}\:\mathrm{groups}\:\mathrm{of}\:\mathrm{order}\:\mathrm{16} \\ $$$$\mathrm{and}\:\mathrm{of}\:\mathrm{order}\:\mathrm{27}\:\mathrm{up}\:\mathrm{to}\:\mathrm{Isomorphism}. \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{3}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Describe}\:\mathrm{a}\:\mathrm{Sylow}\:\mathrm{2}−\mathrm{subgroup}\:\mathrm{in}\:\mathrm{S}_{\mathrm{5}} , \\ $$$$\mathrm{and}\:\mathrm{how}\:\mathrm{many}\:\mathrm{Sylow}\:\mathrm{2}−\mathrm{subgroups}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{S}_{\mathrm{5}} \:? \\ $$

Question Number 194057 Answers: 0 Comments: 0

find all functions such that f(x)f(y) = x^a f((y/2))+y^b f((x/2))

$${find}\:{all}\:{functions}\:{such}\:{that} \\ $$$${f}\left({x}\right){f}\left({y}\right)\:=\:{x}^{{a}} {f}\left(\frac{{y}}{\mathrm{2}}\right)+{y}^{{b}} {f}\left(\frac{{x}}{\mathrm{2}}\right) \\ $$

Question Number 194037 Answers: 3 Comments: 0

Let a_1 ,a_2 ....a_n ∈R^+ , a_1 +a_2 +.....a_n =1 prove that: (a_1 /(2−a_1 ))+(a_2 /(2−a_2 )).......(a_n /(2−a_n ))≥(n/(2n−1))

$$ \\ $$$${Let}\:{a}_{\mathrm{1}} ,{a}_{\mathrm{2}} ....{a}_{{n}} \in{R}^{+} ,\:{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +.....{a}_{{n}} =\mathrm{1} \\ $$$${prove}\:{that}: \\ $$$$\frac{{a}_{\mathrm{1}} }{\mathrm{2}−{a}_{\mathrm{1}} }+\frac{{a}_{\mathrm{2}} }{\mathrm{2}−{a}_{\mathrm{2}} }.......\frac{{a}_{{n}} }{\mathrm{2}−{a}_{{n}} }\geqslant\frac{{n}}{\mathrm{2}{n}−\mathrm{1}} \\ $$

Question Number 194034 Answers: 0 Comments: 0