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Question Number 182374 Answers: 2 Comments: 1

Question Number 182012 Answers: 1 Comments: 0

f(x)=9^x −m∙3^x +m+6 ∃x∈R, f(x)+f(−x)=0 find the range of m.

$${f}\left({x}\right)=\mathrm{9}^{{x}} −{m}\centerdot\mathrm{3}^{{x}} +{m}+\mathrm{6} \\ $$$$\exists{x}\in\mathbb{R},\:{f}\left({x}\right)+{f}\left(−{x}\right)=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\:\mathrm{range}\:\mathrm{of}\:{m}. \\ $$

Question Number 182011 Answers: 1 Comments: 1

Is this true for complex number: 4Re(z_1 z_2 ^(−) )=∣z_1 +z_2 ^(−) ∣^2 −∣z_1 −z_2 ^(−) ∣^2

$${Is}\:{this}\:{true}\:{for}\:{complex}\:{number}: \\ $$$$\mathrm{4}\mathscr{R}{e}\left({z}_{\mathrm{1}} \overline {{z}_{\mathrm{2}} }\right)=\mid{z}_{\mathrm{1}} +\overline {{z}_{\mathrm{2}} }\mid^{\mathrm{2}} −\mid{z}_{\mathrm{1}} −\overline {{z}_{\mathrm{2}} }\mid^{\mathrm{2}} \\ $$

Question Number 182006 Answers: 1 Comments: 2

Question Number 182000 Answers: 0 Comments: 1

if a−2b+3c−4d+5e−6f=0, find the maximum of ((∣a+b+c+d+e+f∣)/( (√(a^2 +b^2 +c^2 +d^2 +e^2 +f^2 )))).

$${if}\:\boldsymbol{{a}}−\mathrm{2}\boldsymbol{{b}}+\mathrm{3}\boldsymbol{{c}}−\mathrm{4}\boldsymbol{{d}}+\mathrm{5}\boldsymbol{{e}}−\mathrm{6}\boldsymbol{{f}}=\mathrm{0},\:{find} \\ $$$${the}\:{maximum}\:{of} \\ $$$$\frac{\mid\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}+\boldsymbol{{d}}+\boldsymbol{{e}}+\boldsymbol{{f}}\mid}{\:\sqrt{\boldsymbol{{a}}^{\mathrm{2}} +\boldsymbol{{b}}^{\mathrm{2}} +\boldsymbol{{c}}^{\mathrm{2}} +\boldsymbol{{d}}^{\mathrm{2}} +\boldsymbol{{e}}^{\mathrm{2}} +\boldsymbol{{f}}^{\mathrm{2}} }}. \\ $$

Question Number 181998 Answers: 1 Comments: 0

Question Number 181987 Answers: 3 Comments: 0

Question Number 182004 Answers: 3 Comments: 0

f(x)=2^x +3^x −6^x Find f(x)_(max)

$${f}\left({x}\right)=\mathrm{2}^{{x}} +\mathrm{3}^{{x}} −\mathrm{6}^{{x}} \\ $$$$\mathrm{Find}\:{f}\left({x}\right)_{\mathrm{max}} \\ $$

Question Number 182003 Answers: 0 Comments: 0

u_(xx) −u_x u_y −u_(yy) +2u_y −2u_x =e^(2x+3y) +sin(2x+y)+xy

$$\mathrm{u}_{\mathrm{xx}} −\mathrm{u}_{\mathrm{x}} \mathrm{u}_{\mathrm{y}} −\mathrm{u}_{\mathrm{yy}} +\mathrm{2u}_{\mathrm{y}} −\mathrm{2u}_{\mathrm{x}} =\mathrm{e}^{\mathrm{2x}+\mathrm{3y}} +\mathrm{sin}\left(\mathrm{2x}+\mathrm{y}\right)+\mathrm{xy} \\ $$

Question Number 182001 Answers: 2 Comments: 1

Question Number 181978 Answers: 0 Comments: 0

Question Number 181977 Answers: 0 Comments: 0

Question Number 181976 Answers: 3 Comments: 0

Question Number 181973 Answers: 0 Comments: 1

please how can I get the proofs of the Putnam competition in pdf format?

$$ \\ $$please how can I get the proofs of the Putnam competition in pdf format?

Question Number 181971 Answers: 1 Comments: 0

How many words can be formed from different letters of the “Your answer is wrong” with not repeating? So that they shouldn′t start with ′o′ neither ′w′ and shouldn′t end with ′w′, and should be′r′ & ′s′ adjacents. Oya...n, Wen...y, Iog...w , Yourws...e : are invalid Enrsow...g : is valid Q.180162

$${How}\:{many}\:{words}\:{can}\:{be}\:{formed}\:{from}\:{different} \\ $$$${letters}\:{of}\:{the}\:``{Your}\:{answer}\:{is}\:{wrong}''\:{with}\:{not} \\ $$$${repeating}?\:{So}\:{that}\:{they}\:{shouldn}'{t}\:{start}\:{with}\:'{o}'\: \\ $$$$\:{neither}\:'{w}'\:{and}\:{shouldn}'{t}\:{end}\:{with}\:'{w}',\:{and} \\ $$$$\:{should}\:{be}'{r}'\:\&\:'{s}'\:{adjacents}. \\ $$$$ \\ $$$$\:\cancel{{O}ya}...{n},\:\cancel{{W}en}...{y},\:{Iog}...\cancel{{w}}\:,\:{You}\cancel{{r}w}\cancel{{s}}...{e}\:\::\:{are}\:{invalid} \\ $$$$\:{Enrsow}...{g}\::\:{is}\:{valid} \\ $$$${Q}.\mathrm{180162} \\ $$

Question Number 181945 Answers: 1 Comments: 0