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AlgebraQuestion and Answers: Page 29

Question Number 211617 Answers: 1 Comments: 0

Ato starts a business with $1,250.00. Ama joins the business later with a capital of 1,875.00. At the end of the first year, profits are shared equally between Ato and Ama. When did Ama join the business?

$$\mathrm{Ato}\:\:\mathrm{starts}\:\mathrm{a}\:\mathrm{business}\:\mathrm{with}\:\$\mathrm{1},\mathrm{250}.\mathrm{00}.\:\mathrm{Ama}\:\mathrm{joins}\:\mathrm{the}\:\mathrm{business} \\ $$$$\mathrm{later}\:\mathrm{with}\:\mathrm{a}\:\mathrm{capital}\:\mathrm{of}\:\mathrm{1},\mathrm{875}.\mathrm{00}.\:\mathrm{At}\:\mathrm{the}\: \\ $$$$\mathrm{end}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{year},\:\mathrm{profits}\:\mathrm{are}\:\mathrm{shared}\:\mathrm{equally} \\ $$$$\mathrm{between}\:\mathrm{Ato}\:\mathrm{and}\:\mathrm{Ama}.\:\mathrm{When}\:\mathrm{did}\:\mathrm{Ama} \\ $$$$\mathrm{join}\:\mathrm{the}\:\mathrm{business}? \\ $$

Question Number 211605 Answers: 1 Comments: 1

Let a_1 ,a_2 ,…a_n Is n real numbers. All fall in the interval (−1,1) ________________________ (1)Prove that: Π_(1≤i,j≤n) ((1+a_i a_j )/(1−a_i a_j ))≥1 (2) Determine the necessary andsufficient conditions forl equaity in the inequality.

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Let}\:\boldsymbol{{a}}_{\mathrm{1}} ,\boldsymbol{{a}}_{\mathrm{2}} ,\ldots\boldsymbol{{a}}_{\boldsymbol{{n}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Is}\:\mathrm{n}\:\mathrm{real}\:\mathrm{numbers}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{All}\:\mathrm{fall}\:\mathrm{in}\:\mathrm{the}\:\mathrm{interval}\:\left(−\mathrm{1},\mathrm{1}\right) \\ $$$$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ $$$$\left(\mathrm{1}\right)\mathrm{Prove}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{1}\leq\boldsymbol{{i}},\boldsymbol{{j}}\leq\boldsymbol{{n}}} {\prod}\frac{\mathrm{1}+\boldsymbol{{a}}_{\boldsymbol{{i}}} \boldsymbol{{a}}_{\boldsymbol{{j}}} }{\mathrm{1}−\boldsymbol{{a}}_{\boldsymbol{{i}}} \boldsymbol{{a}}_{\boldsymbol{{j}}} }\geq\mathrm{1} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{necessary}\: \\ $$$$\mathrm{andsufficient}\:\mathrm{conditions}\:\mathrm{forl} \\ $$$$\mathrm{equaity}\:\mathrm{in}\:\mathrm{the}\:\mathrm{inequality}. \\ $$$$ \\ $$

Question Number 211601 Answers: 0 Comments: 0

set 𝛂(2)^(1/3) ,ask Q(𝛂)Upper irreducible cubic equation: x^3 −3x+1=0 All the roots of

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{set}\:\boldsymbol{\alpha}\sqrt[{\mathrm{3}}]{\mathrm{2}},\mathrm{ask}\:\mathbb{Q}\left(\boldsymbol{\alpha}\right)\mathrm{Upper}\:\mathrm{irreducible}\:\mathrm{cubic}\:\mathrm{equation}: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{3}\boldsymbol{{x}}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{All}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of} \\ $$$$ \\ $$

Question Number 211598 Answers: 2 Comments: 0

{ ((x^2 −4x+3<0)),((((2x−1)/(x+2))≥1)) :}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\begin{cases}{\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{{x}}+\mathrm{3}<\mathrm{0}}\\{\frac{\mathrm{2}\boldsymbol{{x}}−\mathrm{1}}{\boldsymbol{{x}}+\mathrm{2}}\geq\mathrm{1}}\end{cases} \\ $$$$ \\ $$

Question Number 211597 Answers: 1 Comments: 0

2x^4 −4x^3 −22x^2 +24x+36=0

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\boldsymbol{{x}}^{\mathrm{4}} −\mathrm{4}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{22}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{24}\boldsymbol{{x}}+\mathrm{36}=\mathrm{0} \\ $$$$ \\ $$

Question Number 211574 Answers: 1 Comments: 0

{ ((x^2 +y^2 =25)),((x+2y−3=0)) :}