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AllQuestion and Answers: Page 279

Question Number 192988 Answers: 2 Comments: 0

Question Number 192987 Answers: 1 Comments: 0

Question Number 192985 Answers: 1 Comments: 0

prove it : lim_(n→∞) Π_(i=1) ^n cos(θ/2^i )=((sinθ)/θ) then show : im_(n→∞) cos(π/4)cos(π/8)...cos(π/2^(n+1) ) =(2/π)

$${prove}\:{it}\:: \\ $$$${lim}_{{n}\rightarrow\infty} \:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}{cos}\frac{\theta}{\mathrm{2}^{{i}} }=\frac{{sin}\theta}{\theta} \\ $$$${then}\:{show}\:: \\ $$$${im}_{{n}\rightarrow\infty} \:{cos}\frac{\pi}{\mathrm{4}}{cos}\frac{\pi}{\mathrm{8}}...{cos}\frac{\pi}{\mathrm{2}^{{n}+\mathrm{1}} }\:=\frac{\mathrm{2}}{\pi} \\ $$$$ \\ $$

Question Number 192979 Answers: 0 Comments: 0

Can this be optimized (getting the minimum) using backprobagation? α(x_i ,y_i ,h_i )=(h_i −x_i )^2 +y_i ^2 β(y_i ,h_i )=y_i h_i ^2 −2uy_i h_i γ(h_i )=h_i ^4 −4uh_i ^3 +4u^2 h_i ^2 Cost=Σ_(i=0) ^m (cα(x_i ,y_i ,h_i )−2c^2 β(y_i ,h_i )+c^3 γ(h_i )) and how?

$$\mathrm{Can}\:\mathrm{this}\:\mathrm{be}\:\mathrm{optimized}\:\left(\mathrm{getting}\:\mathrm{the}\:\mathrm{minimum}\right)\:\mathrm{using}\:\mathrm{backprobagation}? \\ $$$$ \\ $$$$\alpha\left({x}_{{i}} ,{y}_{{i}} ,{h}_{{i}} \right)=\left({h}_{{i}} −{x}_{{i}} \right)^{\mathrm{2}} +{y}_{{i}} ^{\mathrm{2}} \\ $$$$\beta\left({y}_{{i}} ,{h}_{{i}} \right)={y}_{{i}} {h}_{{i}} ^{\mathrm{2}} −\mathrm{2}{uy}_{{i}} {h}_{{i}} \\ $$$$\gamma\left({h}_{{i}} \right)={h}_{{i}} ^{\mathrm{4}} −\mathrm{4}{uh}_{{i}} ^{\mathrm{3}} +\mathrm{4}{u}^{\mathrm{2}} {h}_{{i}} ^{\mathrm{2}} \\ $$$$\mathrm{Cost}=\underset{{i}=\mathrm{0}} {\overset{{m}} {\sum}}\left(\mathrm{c}\alpha\left({x}_{{i}} ,{y}_{{i}} ,{h}_{{i}} \right)−\mathrm{2}{c}^{\mathrm{2}} \beta\left({y}_{{i}} ,{h}_{{i}} \right)+{c}^{\mathrm{3}} \gamma\left({h}_{{i}} \right)\right) \\ $$$$\mathrm{and}\:\mathrm{how}? \\ $$

Question Number 192969 Answers: 2 Comments: 1

Question Number 192966 Answers: 1 Comments: 0

Question Number 192960 Answers: 0 Comments: 0

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Question Number 192959 Answers: 1 Comments: 0

Question Number 192958 Answers: 4 Comments: 0

Question Number 192957 Answers: 4 Comments: 2

bx^3 =10a^2 bx + 3a^3 y , ay^3 = 10ab^2 y + 3b^3 x solve for x and y in terms of (a , b) and solve for a and b in terms of (x , y )

$$ \\ $$$${bx}^{\mathrm{3}} =\mathrm{10}{a}^{\mathrm{2}} {bx}\:+\:\mathrm{3}{a}^{\mathrm{3}} {y}\:,\:{ay}^{\mathrm{3}} =\:\mathrm{10}{ab}^{\mathrm{2}} {y}\:+\:\mathrm{3}{b}^{\mathrm{3}} {x} \\ $$$${solve}\:{for}\:{x}\:{and}\:{y}\:{in}\:{terms}\:{of}\:\left({a}\:,\:{b}\right) \\ $$$${and}\:{solve}\:{for}\:{a}\:{and}\:{b}\:{in}\:{terms}\:{of}\:\:\left({x}\:,\:{y}\:\right) \\ $$

Question Number 192942 Answers: 2 Comments: 1

Question Number 192937 Answers: 0 Comments: 0

Question Number 192936 Answers: 2 Comments: 0

Question Number 192933 Answers: 2 Comments: 0

Question Number 192928 Answers: 1 Comments: 0

2x^2 −6x+k = 0 where k<0 ((α/β) + (β/α))_(max) = ?

$$\mathrm{2}{x}^{\mathrm{2}} −\mathrm{6}{x}+{k}\:=\:\mathrm{0}\:{where}\:{k}<\mathrm{0}\: \\ $$$$\left(\frac{\alpha}{\beta}\:+\:\frac{\beta}{\alpha}\right)_{\mathrm{max}} \:=\:? \\ $$

Question Number 192927 Answers: 2 Comments: 0

Question Number 192925 Answers: 1 Comments: 0

Find: x = ? 1. 2^(x+1) + 0,5^(x−2) = 9 2. 4^(3x) = 12 3. 6^(x+2) = 18

$$\mathrm{Find}:\:\:\:\mathrm{x}\:=\:? \\ $$$$\mathrm{1}.\:\mathrm{2}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:+\:\mathrm{0},\mathrm{5}^{\boldsymbol{\mathrm{x}}−\mathrm{2}} \:=\:\mathrm{9} \\ $$$$\mathrm{2}.\:\mathrm{4}^{\mathrm{3}\boldsymbol{\mathrm{x}}} \:=\:\mathrm{12} \\ $$$$\mathrm{3}.\:\mathrm{6}^{\boldsymbol{\mathrm{x}}+\mathrm{2}} \:=\:\mathrm{18} \\ $$

Question Number 192924 Answers: 2 Comments: 0

1•determiner: tan (x/2) en fonction de tan x 2•on donne tan x=(1/8) tan (x/2)=? 3• la valeur proche de x?

$$\mathrm{1}\bullet\mathrm{determiner}:\:\mathrm{tan}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\:\:\mathrm{en}\:\mathrm{fonction}\:\mathrm{de}\:\mathrm{tan}\:\boldsymbol{\mathrm{x}} \\ $$$$\mathrm{2}\bullet\mathrm{on}\:\mathrm{donne}\:\:\mathrm{tan}\:\boldsymbol{\mathrm{x}}=\frac{\mathrm{1}}{\mathrm{8}}\:\:\:\:\mathrm{tan}\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}=? \\ $$$$\mathrm{3}\bullet\:\:\mathrm{la}\:\mathrm{valeur}\:\mathrm{proche}\:\mathrm{de}\:\boldsymbol{\mathrm{x}}? \\ $$

Question Number 192918 Answers: 1 Comments: 0

Question Number 192917 Answers: 1 Comments: 0

Question Number 192916 Answers: 2 Comments: 0

Question Number 192914 Answers: 1 Comments: 0

x^2 (x^2 −1)=(1−(c/x))^3 +((c/x))^3

$${x}^{\mathrm{2}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)=\left(\mathrm{1}−\frac{{c}}{{x}}\right)^{\mathrm{3}} +\left(\frac{{c}}{{x}}\right)^{\mathrm{3}} \\ $$

Question Number 192909 Answers: 0 Comments: 0

let P(x) is polinomial with integer coefficient s.t P(6)P(38)P(57)+19 is divided by 114. P(-13)=479 and P≥0 what is minimum value of P(0)?

$$\: \\ $$$$\:{let}\:{P}\left({x}\right)\:{is}\:{polinomial}\:{with}\:{integer} \\ $$$$\:{coefficient}\:{s}.{t}\:{P}\left(\mathrm{6}\right){P}\left(\mathrm{38}\right){P}\left(\mathrm{57}\right)+\mathrm{19}\:{is} \\ $$$$\:{divided}\:{by}\:\mathrm{114}.\:{P}\left(-\mathrm{13}\right)=\mathrm{479}\:{and}\:{P}\geqslant\mathrm{0} \\ $$$$\:{what}\:{is}\:{minimum}\:{value}\:{of}\:{P}\left(\mathrm{0}\right)? \\ $$$$ \\ $$

Question Number 192901 Answers: 2 Comments: 0

Question Number 192898 Answers: 0 Comments: 1

Solve for x x^3 −7x−2=0

$$\mathrm{Solve}\:\mathrm{for}\:{x} \\ $$$${x}^{\mathrm{3}} −\mathrm{7}{x}−\mathrm{2}=\mathrm{0} \\ $$

Question Number 192893 Answers: 1 Comments: 0

Q : Find the remainder of dividing the following number by 7 . N = 3^( 10^( 1) ) + 3^( 10^( 2) ) + 3^( 10^( 3) ) + ... + 3^( 10^( 10) ) ... @ nice − mathematics ...

$$ \\ $$$$\:\:\:\:\:\:\mathrm{Q}\::\:\mathrm{Find}\:\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{of}\:\:\mathrm{dividing} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{the}\:\mathrm{following}\:\mathrm{number}\:\mathrm{by}\:\:\mathrm{7}\:. \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{N}\:=\:\mathrm{3}^{\:\mathrm{10}^{\:\mathrm{1}} } \:+\:\mathrm{3}^{\:\mathrm{10}^{\:\mathrm{2}} \:} \:+\:\mathrm{3}^{\:\mathrm{10}^{\:\mathrm{3}} \:} \:+\:...\:+\:\mathrm{3}^{\:\mathrm{10}^{\:\mathrm{10}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\:\:@\:\mathrm{nice}\:−\:\mathrm{mathematics}\:... \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$

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