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Question Number 192039    Answers: 0   Comments: 0

let x,y,z be positive real number such that x^4 +y^4 +z^4 = 1 find the minimum value of (x^3 /(1−x^8 )) + (y^3 /(1−y^8 )) + (z^3 /(1−z^8 ))

$$\mathrm{let}\:{x},{y},{z}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} \:=\:\mathrm{1}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of} \\ $$$$\:\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{8}} }\:+\:\frac{{y}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{8}} }\:+\:\frac{{z}^{\mathrm{3}} }{\mathrm{1}−{z}^{\mathrm{8}} } \\ $$

Question Number 192015    Answers: 1   Comments: 0

Question Number 192013    Answers: 0   Comments: 0

∫e^(at^b ) dt with a,b as a constant how to evaluate this

$$ \\ $$$$\:\int{e}^{{at}^{{b}} } {dt} \\ $$$$\:{with}\:{a},{b}\:{as}\:{a}\:{constant} \\ $$$$\:{how}\:{to}\:{evaluate}\:{this} \\ $$$$ \\ $$

Question Number 192009    Answers: 2   Comments: 0

if a>1 , show ((Σ_(k=1) ^(a^2 −1) (√(a+(√k))))/(Σ_(k=1) ^(a^2 −1) (√(a−(√k))))) = (√2) + 1

$$\:\:\:\:\:{if}\:\:{a}>\mathrm{1}\:,\:{show} \\ $$$$\:\:\:\:\:\frac{\underset{{k}=\mathrm{1}} {\overset{{a}^{\mathrm{2}} −\mathrm{1}} {\sum}}\:\:\sqrt{{a}+\sqrt{{k}}}}{\underset{{k}=\mathrm{1}} {\overset{{a}^{\mathrm{2}} −\mathrm{1}} {\sum}}\:\:\sqrt{{a}−\sqrt{{k}}}}\:\:\:=\:\:\:\sqrt{\mathrm{2}}\:\:+\:\:\mathrm{1} \\ $$

Question Number 192001    Answers: 2   Comments: 1

Question Number 191997    Answers: 1   Comments: 2

Show that C={−1,1,−ı,ı} where ı=(√(−1)) with addition operation is a group. Help!

$$\mathrm{Show}\:\mathrm{that}\:\mathbb{C}=\left\{−\mathrm{1},\mathrm{1},−\imath,\imath\right\}\:\mathrm{where} \\ $$$$\imath=\sqrt{−\mathrm{1}}\:\mathrm{with}\:\mathrm{addition}\:\mathrm{operation}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{group}. \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 191993    Answers: 0   Comments: 0

Question Number 191986    Answers: 1   Comments: 0

Ques. 1 Let (G,∗) be a group, then show that for each a∈G, ∃ a unique element e∈G ∣ a∗e=e∗a=a Ques. 2 If a∈G ⇒ x∈G and x is unique show that if x∗a=e, then a∗x=e. Hello!

$$\mathrm{Ques}.\:\mathrm{1} \\ $$$$\mathrm{Let}\:\left(\mathrm{G},\ast\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{group},\:\mathrm{then}\:\mathrm{show} \\ $$$$\mathrm{that}\:\mathrm{for}\:\mathrm{each}\:\mathrm{a}\in\mathrm{G},\:\exists\:\mathrm{a}\:\mathrm{unique}\: \\ $$$$\mathrm{element}\:\mathrm{e}\in\mathrm{G}\:\mid\:\mathrm{a}\ast\mathrm{e}=\mathrm{e}\ast\mathrm{a}=\mathrm{a} \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{2} \\ $$$$\mathrm{If}\:\mathrm{a}\in\mathrm{G}\:\Rightarrow\:\mathrm{x}\in\mathrm{G}\:\mathrm{and}\:\mathrm{x}\:\mathrm{is}\:\mathrm{unique} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{x}\ast\mathrm{a}=\mathrm{e},\:\mathrm{then}\:\mathrm{a}\ast\mathrm{x}=\mathrm{e}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Hello}! \\ $$

Question Number 191966    Answers: 1   Comments: 0

Question Number 191962    Answers: 1   Comments: 0

Question Number 191961    Answers: 0   Comments: 0

Question Number 191960    Answers: 2   Comments: 0

Question Number 191958    Answers: 1   Comments: 2

Question Number 191950    Answers: 1   Comments: 0

(√a) = 1 + (1/a) find: a^2 −a−(√a) = ?

$$\sqrt{\mathrm{a}}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:\:\:\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{2}} −\mathrm{a}−\sqrt{\mathrm{a}}\:=\:? \\ $$

Question Number 191946    Answers: 1   Comments: 0

((fof^(−1) (5)+fof^(−1) (15))/(fof^(−1) (5)))=?

$$\frac{\mathrm{fof}^{−\mathrm{1}} \left(\mathrm{5}\right)+\mathrm{fof}^{−\mathrm{1}} \left(\mathrm{15}\right)}{\mathrm{fof}^{−\mathrm{1}} \left(\mathrm{5}\right)}=? \\ $$

Question Number 191947    Answers: 2   Comments: 0

prove that (√(a+b(√(a−b(√(a+b(√(a−b(√(...)))))))))) = (((√(4a−3b^2 ))+b)/2)

$${prove}\:{that} \\ $$$$\sqrt{{a}+{b}\sqrt{{a}−{b}\sqrt{{a}+{b}\sqrt{{a}−{b}\sqrt{...}}}}}\:\:=\:\:\frac{\sqrt{\mathrm{4}{a}−\mathrm{3}{b}^{\mathrm{2}} }+{b}}{\mathrm{2}} \\ $$

Question Number 191937    Answers: 1   Comments: 0

Check whether (Q, ∙) is a group or not Hello bosses!

$$\mathrm{Check}\:\mathrm{whether}\:\left(\mathrm{Q},\:\centerdot\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{group}\:\mathrm{or} \\ $$$$\mathrm{not} \\ $$$$ \\ $$$$\mathrm{Hello}\:\mathrm{bosses}! \\ $$

Question Number 191935    Answers: 2   Comments: 0

Question Number 191934    Answers: 1   Comments: 0

Question Number 195092    Answers: 1   Comments: 0

lim_(x→1^+ ) ((4x+5)/(x−x^2 ))=?

$$\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\:\frac{\mathrm{4}{x}+\mathrm{5}}{{x}−{x}^{\mathrm{2}} }=? \\ $$

Question Number 191930    Answers: 1   Comments: 2

What is the value of inside Area of (ABCDEF)? Such that: ∡AOB=120 ∡ANB=60;°R=ON (OA=OB=32cm) ArcAE=ArcBF(r=12cm) BASE is circulare (Aider le tailleur a savoir la surface du tissu necessaire pour couvrir l ′espace indique dans la figure?)

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{inside}\:\mathrm{Area}\:\mathrm{of} \\ $$$$\left(\mathrm{ABCDEF}\right)? \\ $$$$\mathrm{Such}\:\mathrm{that}:\:\measuredangle\mathrm{AOB}=\mathrm{120}\:\:\:\measuredangle\mathrm{ANB}=\mathrm{60};°\mathrm{R}=\mathrm{ON} \\ $$$$\:\left(\mathrm{OA}=\mathrm{OB}=\mathrm{32cm}\right)\:\mathrm{ArcAE}=\mathrm{ArcBF}\left(\mathrm{r}=\mathrm{12cm}\right) \\ $$$$\mathrm{BASE}\:\mathrm{is}\:\mathrm{circulare} \\ $$$$\left({Aider}\:{le}\:{tailleur}\:{a}\:{savoir}\:{la}\:{surface}\right. \\ $$$${du}\:{tissu}\:{necessaire}\:{pour}\:{couvrir}\: \\ $$$$\left.\:{l}\:'\mathrm{e}{space}\:{indique}\:{dans}\:{la}\:{figure}?\right) \\ $$

Question Number 191901    Answers: 3   Comments: 0

if 0<θ<45^0 which is bigger ? 2tanθ or tan2θ

$${if}\:\:\mathrm{0}<\theta<\mathrm{45}^{\mathrm{0}} \:\:{which}\:{is}\:{bigger}\:? \\ $$$$\mathrm{2}{tan}\theta\:\:{or}\:\:{tan}\mathrm{2}\theta \\ $$

Question Number 191897    Answers: 2   Comments: 0

if we combine 100gr Na with 180 Cl_2 then how much NaCl will produce?

$${if}\:{we}\:{combine}\:\mathrm{100}{gr}\:{Na}\:{with}\:\mathrm{180}\:{Cl}_{\mathrm{2}} \\ $$$${then}\:{how}\:{much}\:{NaCl}\:{will}\:{produce}? \\ $$

Question Number 191927    Answers: 0   Comments: 1

What is the value of laterale Shaded Area (couronne circulaire coloree?) R=10cm 20cm≤ h≤24cm ∡COD=45°

$$\boldsymbol{\mathrm{W}}\mathrm{hat}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{laterale}\:\mathrm{Shaded} \\ $$$$\:\mathrm{Area}\:\:\left(\boldsymbol{\mathrm{couronne}}\:\boldsymbol{\mathrm{circulaire}}\:\:\boldsymbol{\mathrm{coloree}}?\right) \\ $$$$\:\:\boldsymbol{\mathrm{R}}=\mathrm{10}\boldsymbol{\mathrm{cm}}\:\:\:\mathrm{20}\boldsymbol{\mathrm{cm}}\leqslant\:\boldsymbol{\mathrm{h}}\leqslant\mathrm{24}\boldsymbol{\mathrm{cm}}\:\:\measuredangle\mathrm{COD}=\mathrm{45}° \\ $$$$\:\: \\ $$

Question Number 191926    Answers: 2   Comments: 0

Question Number 191921    Answers: 1   Comments: 0

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