Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 193

Question Number 201857    Answers: 1   Comments: 1

If a,b,c,d,e are thr roots of 2x^5 −3x^3 +2x−7=0 , find the value of Π_(cyc) (a^3 −1)

$$\:\:\mathrm{If}\:{a},{b},{c},{d},{e}\:\mathrm{are}\:\mathrm{thr}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$$\:\:\mathrm{2x}^{\mathrm{5}} −\mathrm{3x}^{\mathrm{3}} +\mathrm{2x}−\mathrm{7}=\mathrm{0}\:,\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\:\mathrm{value}\:\mathrm{of}\:\underset{\mathrm{cyc}} {\prod}\left({a}^{\mathrm{3}} −\mathrm{1}\right)\: \\ $$

Question Number 201854    Answers: 0   Comments: 3

Question Number 201852    Answers: 0   Comments: 0

Question Number 201853    Answers: 1   Comments: 0

Question Number 201850    Answers: 0   Comments: 0

Question Number 201897    Answers: 0   Comments: 0

Question: The congruence equation ′′ ( 5a +3 )x ≡^(3a + 4) 19 ′′ is given. Find the sum of digits of the smallest three −digit natural number ” a ” such that the assumed equation has no solution in ” Z ”.

$$ \\ $$$$\:\:\:\:\:\mathrm{Q}{uestion}:\:\:{The}\:{congruence} \\ $$$$\:\:\:\:\:\:\:{equation}\:\:\:''\:\:\:\:\left(\:\mathrm{5}{a}\:+\mathrm{3}\:\right){x}\:\:\overset{\mathrm{3}{a}\:+\:\mathrm{4}} {\equiv}\:\mathrm{19}\:\:\:''\:\:{is}\:{given}. \\ $$$$\:\:\:\:\:\:\:{Find}\:{the}\:{sum}\:{of}\:{digits}\:{of}\:\: \\ $$$$\:\:\:\:\:\:\:{the}\:{smallest}\:\:{three}\:−{digit}\:{natural}\:{number}\:\:''\:{a}\:''\: \\ $$$$\:\:\:\:\:\:\:{such}\:{that}\:{the}\:{assumed}\:{equation}\:{has}\: \\ $$$$\:\:\:\:\:\:\:\:\:{no}\:\:{solution}\:\:{in}\:\:\:''\:\:\:\mathbb{Z}\:\:''. \\ $$$$ \\ $$

Question Number 201848    Answers: 1   Comments: 0

Question Number 201846    Answers: 0   Comments: 1

$$\:\: \\ $$$$ \\ $$

Question Number 201839    Answers: 0   Comments: 1

Question Number 201837    Answers: 0   Comments: 0

y′′′−y′′+y′=sec(t),−(π/2)<t<(π/2)

$${y}'''−{y}''+{y}'={sec}\left({t}\right),−\frac{\pi}{\mathrm{2}}<{t}<\frac{\pi}{\mathrm{2}} \\ $$

Question Number 201982    Answers: 0   Comments: 0

Question Number 201977    Answers: 0   Comments: 1

Question Number 201980    Answers: 1   Comments: 0

Question Number 201979    Answers: 2   Comments: 1

Question Number 201972    Answers: 1   Comments: 0

Question Number 201969    Answers: 2   Comments: 0

A dice is cast twice, and the sum of the appearing numbers is 10. The probability that the number 5 has appeared at least once is.

$$\mathrm{A}\:\mathrm{dice}\:\mathrm{is}\:\mathrm{cast}\:\mathrm{twice},\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{appearing}\:\mathrm{numbers}\:\mathrm{is}\:\mathrm{10}. \\ $$$$\mathrm{The}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{the}\:\mathrm{number}\:\mathrm{5}\:\mathrm{has}\: \\ $$$$\mathrm{appeared}\:\mathrm{at}\:\mathrm{least}\:\mathrm{once}\:\mathrm{is}. \\ $$

Question Number 201966    Answers: 2   Comments: 0

solve ((x^2 +3x+2))^(1/3) (((x+1))^(1/3) −((x+2))^(1/3) )= 1

$$ \\ $$$$\:\:\:\:\:\:\:{solve}\: \\ $$$$\:\: \\ $$$$\:\:\:\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}}\:\left(\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}\:−\sqrt[{\mathrm{3}}]{{x}+\mathrm{2}}\:\right)=\:\mathrm{1} \\ $$$$ \\ $$

Question Number 201965    Answers: 1   Comments: 0

m−h=2p p(m−h)=k−q mk−qh=(1/3) k−2q=1+ph Assume one find the rest! ✓

$${m}−{h}=\mathrm{2}{p} \\ $$$${p}\left({m}−{h}\right)={k}−{q} \\ $$$${mk}−{qh}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${k}−\mathrm{2}{q}=\mathrm{1}+{ph} \\ $$$${Assume}\:{one}\:{find}\:{the}\:{rest}! \\ $$$$\checkmark \\ $$

Question Number 201832    Answers: 1   Comments: 0

Question Number 201831    Answers: 0   Comments: 0

Question Number 201829    Answers: 2   Comments: 0

shortest distance from (−6,0)to x^2 −y^2 +16=0

$${shortest}\:{distance}\:{from}\:\left(−\mathrm{6},\mathrm{0}\right){to}\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} +\mathrm{16}=\mathrm{0} \\ $$

Question Number 201822    Answers: 0   Comments: 4

Do Not Use sin(θ)∼θ (θ is small Enough) θ^ +(g/ℓ)sin(θ)=0 y′′(t)+(g/ℓ) sin(y(t))=0 y′′(t)y′(t)+(g/ℓ)sin(y(t))y′(t)=0 y′(t)y′′(t)=(1/2)∙((d )/dt)(y′(t))^2 (g/ℓ)sin(y(t))y′(t)=−(g/ℓ)∙((d )/dt)cos(y(t)) ∴ ((d )/dt)[(1/2)(y′(t))^2 −(g/ℓ)cos(y(t))]=0 ∴(1/2)(y′(t))^2 −(g/ℓ)cos(y(t))=c_1 Const y′′(t)+(g/ℓ)sin(y(t))=0→(y′(t))^2 −((2g)/ℓ)cos(y(t))=c_1 and... I can′t Sove Diff Equa..

$$\mathrm{Do}\:\mathrm{Not}\:\mathrm{Use}\:\mathrm{sin}\left(\theta\right)\sim\theta\:\left(\theta\:\:\mathrm{is}\:\mathrm{small}\:\mathrm{Enough}\right) \\ $$$$\ddot {\theta}+\frac{\mathrm{g}}{\ell}\mathrm{sin}\left(\theta\right)=\mathrm{0} \\ $$$${y}''\left({t}\right)+\frac{\mathrm{g}}{\ell}\:\mathrm{sin}\left({y}\left({t}\right)\right)=\mathrm{0} \\ $$$${y}''\left({t}\right){y}'\left({t}\right)+\frac{\mathrm{g}}{\ell}\mathrm{sin}\left({y}\left({t}\right)\right){y}'\left({t}\right)=\mathrm{0} \\ $$$${y}'\left({t}\right){y}''\left({t}\right)=\frac{\mathrm{1}}{\mathrm{2}}\centerdot\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}\left({y}'\left({t}\right)\right)^{\mathrm{2}} \\ $$$$\frac{\mathrm{g}}{\ell}\mathrm{sin}\left({y}\left({t}\right)\right){y}'\left({t}\right)=−\frac{\mathrm{g}}{\ell}\centerdot\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}\mathrm{cos}\left({y}\left({t}\right)\right) \\ $$$$\therefore\:\frac{\mathrm{d}\:\:}{\mathrm{d}{t}}\left[\frac{\mathrm{1}}{\mathrm{2}}\left({y}'\left({t}\right)\right)^{\mathrm{2}} −\frac{\mathrm{g}}{\ell}\mathrm{cos}\left({y}\left({t}\right)\right)\right]=\mathrm{0} \\ $$$$\therefore\frac{\mathrm{1}}{\mathrm{2}}\left({y}'\left({t}\right)\right)^{\mathrm{2}} −\frac{\mathrm{g}}{\ell}\mathrm{cos}\left({y}\left({t}\right)\right)={c}_{\mathrm{1}} \:\:\boldsymbol{\mathrm{Const}} \\ $$$${y}''\left({t}\right)+\frac{\mathrm{g}}{\ell}\mathrm{sin}\left({y}\left({t}\right)\right)=\mathrm{0}\rightarrow\left({y}'\left({t}\right)\right)^{\mathrm{2}} −\frac{\mathrm{2g}}{\ell}\mathrm{cos}\left({y}\left({t}\right)\right)={c}_{\mathrm{1}} \\ $$$$\mathrm{and}...\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{Sove}\:\mathrm{Diff}\:\:\mathrm{Equa}.. \\ $$

Question Number 201820    Answers: 1   Comments: 0

((∣3x+1∣−∣x+2∣)/(3−∣2x∣)) ≥ 0 find the solution set.

$$\:\:\:\frac{\mid\mathrm{3x}+\mathrm{1}\mid−\mid\mathrm{x}+\mathrm{2}\mid}{\mathrm{3}−\mid\mathrm{2x}\mid}\:\geqslant\:\mathrm{0}\: \\ $$$$\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set}. \\ $$

Question Number 201819    Answers: 0   Comments: 0

If xyz ∈R^+ , xyz=1 , prove that the following inequality holds: (x/(2x^5 +x+4))+(y/(2y^5 +y+4))+(z/(2z^5 +z+4))≥(3/7). Solution please with an advice to get better at inequalities and which book would you recommend. Thanks in advance!

$$\mathrm{If}\:{xyz}\:\in\mathbb{R}^{+} \:,\:{xyz}=\mathrm{1}\:,\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following}\:\mathrm{inequality}\:\mathrm{holds}: \\ $$$$\frac{{x}}{\mathrm{2}{x}^{\mathrm{5}} +{x}+\mathrm{4}}+\frac{{y}}{\mathrm{2}{y}^{\mathrm{5}} +{y}+\mathrm{4}}+\frac{{z}}{\mathrm{2}{z}^{\mathrm{5}} +{z}+\mathrm{4}}\geqslant\frac{\mathrm{3}}{\mathrm{7}}. \\ $$$$\boldsymbol{\mathrm{Solution}}\:\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{an}}\:\boldsymbol{\mathrm{advice}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{get}}\:\boldsymbol{\mathrm{better}} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{inequalities}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{which}}\:\boldsymbol{\mathrm{book}}\:\boldsymbol{\mathrm{would}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{recommend}}. \\ $$$$\boldsymbol{\mathrm{Thanks}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{advance}}! \\ $$$$\: \\ $$

Question Number 201817    Answers: 1   Comments: 0

Question Number 201808    Answers: 1   Comments: 1

  Pg 188      Pg 189      Pg 190      Pg 191      Pg 192      Pg 193      Pg 194      Pg 195      Pg 196      Pg 197   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com