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Question Number 196870 Answers: 1 Comments: 0

let b_i ∧ a_i >0 where i∈{1,2,3,...,n}& Σ_(i=1) ^n (b_i )=λ Prove that ((λ−(b_1 +b_2 ))/((b_1 +b_2 )))(a_1 +a_2 )+((λ−(b_1 +b_3 ))/((b_1 +b_3 )))(a_1 +a_3 )+....+((λ−(b_2 +b_3 ))/((b_2 +b_3 )))(a_2 +a_3 )+...((λ−(b_(n−1) +b_n ))/((b_(n−1) +b_n )))(a_(n−1) +a_n ) ≥(√(((n(n−1)(n−2)^2 )/4)×ΣΣ_(1≤i<j≤n) (a_i a_j )))

$${let}\:{b}_{{i}} \wedge\:{a}_{{i}} >\mathrm{0}\:{where}\:{i}\in\left\{\mathrm{1},\mathrm{2},\mathrm{3},...,{n}\right\}\&\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left({b}_{{i}} \right)=\lambda\:{Prove}\:{that} \\ $$$$\frac{\lambda−\left({b}_{\mathrm{1}} +{b}_{\mathrm{2}} \right)}{\left({b}_{\mathrm{1}} +{b}_{\mathrm{2}} \right)}\left({a}_{\mathrm{1}} +{a}_{\mathrm{2}} \right)+\frac{\lambda−\left({b}_{\mathrm{1}} +{b}_{\mathrm{3}} \right)}{\left({b}_{\mathrm{1}} +{b}_{\mathrm{3}} \right)}\left({a}_{\mathrm{1}} +{a}_{\mathrm{3}} \right)+....+\frac{\lambda−\left({b}_{\mathrm{2}} +{b}_{\mathrm{3}} \right)}{\left({b}_{\mathrm{2}} +{b}_{\mathrm{3}} \right)}\left({a}_{\mathrm{2}} +{a}_{\mathrm{3}} \right)+...\frac{\lambda−\left({b}_{{n}−\mathrm{1}} +{b}_{{n}} \right)}{\left({b}_{{n}−\mathrm{1}} +{b}_{{n}} \right)}\left({a}_{{n}−\mathrm{1}} +{a}_{{n}} \right) \\ $$$$\geqslant\sqrt{\frac{{n}\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{4}}×\underset{\mathrm{1}\leqslant{i}<{j}\leqslant{n}} {\Sigma\Sigma}\left({a}_{{i}} {a}_{{j}} \right)} \\ $$$$ \\ $$

Question Number 196861 Answers: 0 Comments: 0

Question Number 196860 Answers: 0 Comments: 0

Question Number 196852 Answers: 1 Comments: 0

Question Number 196850 Answers: 0 Comments: 0

Question Number 196848 Answers: 0 Comments: 1

Question Number 196846 Answers: 1 Comments: 0

2xy′′ + (1−4x)y′ + (2x−1)y = y

$$\mathrm{2}{xy}''\:+\:\left(\mathrm{1}−\mathrm{4}{x}\right){y}'\:+\:\left(\mathrm{2}{x}−\mathrm{1}\right){y}\:=\:{y} \\ $$

Question Number 196845 Answers: 0 Comments: 0

Question Number 196843 Answers: 1 Comments: 0

Question Number 196832 Answers: 0 Comments: 1

∫xe^(1/(2x)) dx=?

$$\int{x}\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}{x}}} {dx}=? \\ $$

Question Number 196829 Answers: 1 Comments: 0

Question Number 196828 Answers: 2 Comments: 0

Question Number 196817 Answers: 1 Comments: 0

Question Number 196816 Answers: 1 Comments: 0

Question Number 196815 Answers: 1 Comments: 0

!6×(((!5+9!!!!!+7!!!−16))^(1/4) /(!10))=?

$$!\mathrm{6}×\frac{\sqrt[{\mathrm{4}}]{!\mathrm{5}+\mathrm{9}!!!!!+\mathrm{7}!!!−\mathrm{16}}}{!\mathrm{10}}=? \\ $$

Question Number 196836 Answers: 1 Comments: 1

Question Number 196806 Answers: 2 Comments: 0

lim_(x→0) ( ((((√(2x−2x^2 )))^(1/3) − x)/(2x+ ((1−((x^3 +1))^(1/3) ))^(1/3) )) ) .

$$\:\:\:\: \\ $$$$ \underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\:\frac{\sqrt[{\mathrm{3}}]{\sqrt{\mathrm{2x}−\mathrm{2x}^{\mathrm{2}} }}\:−\:\mathrm{x}}{\mathrm{2x}+\:\sqrt[{\mathrm{3}}]{\mathrm{1}−\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{3}} +\mathrm{1}}}}\:\right)\:. \\ $$

Question Number 196793 Answers: 1 Comments: 0

Question Number 196761 Answers: 0 Comments: 0

A tightly wound toroidal coil with a square cross section and an inner radius of 15cm has 500 turns of copper wire and carries an insulated filamentary ccurrent of 0.800A. what is the strength of the magnetic field inside the toroid at the inner radius?

$$\mathrm{A}\:\mathrm{tightly}\:\mathrm{wound}\:\mathrm{toroidal}\:\mathrm{coil}\:\mathrm{with}\:\mathrm{a}\:\mathrm{square} \\ $$$$\mathrm{cross}\:\mathrm{section}\:\mathrm{and}\:\mathrm{an}\:\mathrm{inner}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{15cm}\:\mathrm{has} \\ $$$$\mathrm{500}\:\mathrm{turns}\:\mathrm{of}\:\mathrm{copper}\:\mathrm{wire}\:\mathrm{and}\:\mathrm{carries}\:\mathrm{an}\:\mathrm{insulated} \\ $$$$\mathrm{filamentary}\:\mathrm{ccurrent}\:\mathrm{of}\:\mathrm{0}.\mathrm{800A}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{strength}\:\mathrm{of}\:\mathrm{the}\:\mathrm{magnetic}\:\mathrm{field}\:\mathrm{inside}\:\mathrm{the} \\ $$$$\mathrm{toroid}\:\mathrm{at}\:\mathrm{the}\:\mathrm{inner}\:\mathrm{radius}? \\ $$

Question Number 196760 Answers: 0 Comments: 0

f: R→R f(f(x+y))=f(x)+f(y) Find f(x)=¿

$${f}:\:{R}\rightarrow{R} \\ $$$${f}\left({f}\left({x}+{y}\right)\right)={f}\left({x}\right)+{f}\left({y}\right) \\ $$$${Find}\:{f}\left({x}\right)=¿ \\ $$

Question Number 196758 Answers: 1 Comments: 0

Question Number 196757 Answers: 1 Comments: 0

Question Number 196756 Answers: 0 Comments: 0

Question Number 196755 Answers: 0 Comments: 0

Question Number 196738 Answers: 0 Comments: 13

Question Number 196735 Answers: 2 Comments: 0

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