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AlgebraQuestion and Answers: Page 312

Question Number 57932    Answers: 1   Comments: 0

7+g=24

$$\mathrm{7}+{g}=\mathrm{24} \\ $$$$ \\ $$

Question Number 57930    Answers: 1   Comments: 0

solve 2.3((2/(11))+3)

$$\mathrm{solve}\:\mathrm{2}.\mathrm{3}\left(\frac{\mathrm{2}}{\mathrm{11}}+\mathrm{3}\right) \\ $$

Question Number 57902    Answers: 1   Comments: 1

prove that the equation Z^n =1 have exacly n roots given by Z_k =e^(i((2kπ)/n)) k∈[[0,n−1]]

$${prove}\:{that}\:{the}\:{equation}\:{Z}^{{n}} =\mathrm{1}\:\:{have}\:{exacly}\:{n}\:{roots}\:\:{given}\:{by} \\ $$$${Z}_{{k}} ={e}^{{i}\frac{\mathrm{2}{k}\pi}{{n}}} \:\:\:\:{k}\in\left[\left[\mathrm{0},{n}−\mathrm{1}\right]\right] \\ $$

Question Number 57881    Answers: 0   Comments: 0

calculate(2/(13))×2(1/4)

$$\mathrm{calculate}\frac{\mathrm{2}}{\mathrm{13}}×\mathrm{2}\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 57880    Answers: 0   Comments: 0

6×2

$$\mathrm{6}×\mathrm{2} \\ $$

Question Number 57818    Answers: 1   Comments: 0

Question Number 57791    Answers: 3   Comments: 0

If a + b + c = 1 a^2 + b^2 + c^2 = 2 a^3 + b^3 + c^3 = 3 then a^5 + b^5 + c^(5 ) = ?

$$\:\mathrm{If}\:\:\:\:\:\mathrm{a}\:+\:\mathrm{b}\:+\:\mathrm{c}\:\:=\:\:\mathrm{1}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{c}^{\mathrm{3}} \:\:=\:\:\mathrm{3}\:\: \\ $$$$\mathrm{then}\:\:\:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \:+\:\mathrm{c}^{\mathrm{5}\:\:} =\:\:? \\ $$

Question Number 57635    Answers: 1   Comments: 2

Find the sum of the cubes of first n even number, and first n odd number.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{cubes}\:\mathrm{of}\:\mathrm{first}\:\mathrm{n}\:\mathrm{even}\:\mathrm{number},\:\:\mathrm{and} \\ $$$$\mathrm{first}\:\mathrm{n}\:\mathrm{odd}\:\mathrm{number}. \\ $$

Question Number 57585    Answers: 2   Comments: 0

knowing that x+y=1. what is the result of (y/x)+(x/y)

$${knowing}\:{that}\:{x}+{y}=\mathrm{1}.\:{what}\:{is}\:{the}\:{result}\:{of}\:\frac{{y}}{{x}}+\frac{{x}}{{y}} \\ $$

Question Number 57521    Answers: 2   Comments: 1

Question Number 57513    Answers: 0   Comments: 4

There are 128 players in the first round of a knockout competition. Half of the players were knocked out in each round. How many players took part in the fourth round? How many rounds were there in this competion?

$$\mathrm{There}\:\mathrm{are}\:\mathrm{128}\:\mathrm{players}\:\mathrm{in}\:\mathrm{the}\:\mathrm{first}\:\mathrm{round} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{knockout}\:\mathrm{competition}.\:\mathrm{Half}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{players}\:\mathrm{were}\:\mathrm{knocked}\:\mathrm{out}\:\mathrm{in}\:\mathrm{each}\:\mathrm{round}. \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{players}\:\mathrm{took}\:\mathrm{part}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{fourth}\:\mathrm{round}?\:\mathrm{How}\:\mathrm{many}\:\mathrm{rounds}\:\mathrm{were}\:\mathrm{there} \\ $$$$\mathrm{in}\:\mathrm{this}\:\mathrm{competion}? \\ $$

Question Number 57480    Answers: 0   Comments: 2

if F(x,y)=F(y,x) and x+y=c (constant) prove that F_(max or min) =F((c/2),(c/2)).

$${if}\:{F}\left({x},{y}\right)={F}\left({y},{x}\right)\:{and}\:{x}+{y}={c}\:\left({constant}\right) \\ $$$${prove}\:{that}\:{F}_{{max}\:{or}\:{min}} ={F}\left(\frac{{c}}{\mathrm{2}},\frac{{c}}{\mathrm{2}}\right). \\ $$

Question Number 57435    Answers: 0   Comments: 0

Question Number 57434    Answers: 0   Comments: 0

is there a way to find the sum to infinity of a product operator e.g product of 1.2.3.4.5 ... [1, infinity]

$$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{way}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{to}\:\mathrm{infinity}\:\mathrm{of}\:\mathrm{a}\:\mathrm{product}\:\mathrm{operator} \\ $$$$\:\:\mathrm{e}.\mathrm{g}\:\:\:\:\:\mathrm{product}\:\mathrm{of}\:\:\:\:\:\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}.\mathrm{5}\:...\:\:\left[\mathrm{1},\:\mathrm{infinity}\right] \\ $$

Question Number 57328    Answers: 1   Comments: 0

Question Number 57251    Answers: 1   Comments: 0

Question Number 57245    Answers: 1   Comments: 0

((a^8 +a^4 +1)/(a^4 +a^2 +1))=?

$$\frac{\boldsymbol{\mathrm{a}}^{\mathrm{8}} +\boldsymbol{\mathrm{a}}^{\mathrm{4}} +\mathrm{1}}{\boldsymbol{\mathrm{a}}^{\mathrm{4}} +\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\mathrm{1}}=? \\ $$

Question Number 57244    Answers: 0   Comments: 1

Question Number 57222    Answers: 1   Comments: 0

Express 5.27 in form of a series and show that is equal to 5 (5/(18))

$$\mathrm{Express}\:\:\:\mathrm{5}.\mathrm{27}\:\:\mathrm{in}\:\mathrm{form}\:\mathrm{of}\:\mathrm{a}\:\mathrm{series}\:\mathrm{and}\:\mathrm{show}\:\mathrm{that}\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\:\:\mathrm{5}\:\frac{\mathrm{5}}{\mathrm{18}} \\ $$

Question Number 57234    Answers: 0   Comments: 0

let tbe fraction F(x)=(1/(x^n −1)) with n from n and n≥2 1) find the poles of F and decompose it inside C(x) 2)decompose F(x)inside R(x) 3) calculate ∫_2 ^3 F(x)dx .

$${let}\:{tbe}\:{fraction}\:{F}\left({x}\right)=\frac{\mathrm{1}}{{x}^{{n}} −\mathrm{1}}\:\:{with}\:{n}\:{from}\:{n}\:{and}\:{n}\geqslant\mathrm{2} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{poles}\:{of}\:{F}\:{and}\:{decompose}\:{it}\:{inside}\:{C}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){decompose}\:{F}\left({x}\right){inside}\:{R}\left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{2}} ^{\mathrm{3}} {F}\left({x}\right){dx}\:. \\ $$

Question Number 57163    Answers: 0   Comments: 0

Question Number 57127    Answers: 0   Comments: 24

{cos1°}+{cos2°}+{cos3°}+....+{cos270}=?

$$\left\{\boldsymbol{\mathrm{cos}}\mathrm{1}°\right\}+\left\{\boldsymbol{\mathrm{cos}}\mathrm{2}°\right\}+\left\{\boldsymbol{\mathrm{cos}}\mathrm{3}°\right\}+....+\left\{\boldsymbol{\mathrm{cos}}\mathrm{270}\right\}=? \\ $$

Question Number 57024    Answers: 0   Comments: 1

If f(x−1)=2x^3 −3x^2 +7x+10. Find f(3).

$$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{2x}^{\mathrm{3}} −\mathrm{3x}^{\mathrm{2}} +\mathrm{7x}+\mathrm{10}.\:\mathrm{Find}\:\mathrm{f}\left(\mathrm{3}\right). \\ $$

Question Number 57000    Answers: 3   Comments: 1

If (x+2)^2 is a factor of the polynomial f(x)=mx^3 +x^2 +x+n, find; the values of m and n.

$$\mathrm{If}\:\left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{factor}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{mx}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{n},\:\mathrm{find}; \\ $$$$\:\mathrm{the}\:\mathrm{values}\:\mathrm{of}\:\mathrm{m}\:\mathrm{and}\:\mathrm{n}. \\ $$

Question Number 56991    Answers: 0   Comments: 4

x! − x^2 = 8 , Find x

$$\:\:\mathrm{x}!\:−\:\mathrm{x}^{\mathrm{2}} \:\:=\:\:\mathrm{8}\:,\:\:\:\:\mathrm{Find}\:\:\mathrm{x} \\ $$$$ \\ $$

Question Number 56904    Answers: 1   Comments: 0

If α and β are the roots of of the equation 3x^2 −x−3=0, find thevalue of (α^2 −β^2 ) if α>β.

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{3x}^{\mathrm{2}} −\mathrm{x}−\mathrm{3}=\mathrm{0},\:\mathrm{find}\:\mathrm{thevalue}\:\mathrm{of}\:\left(\alpha^{\mathrm{2}} −\beta^{\mathrm{2}} \right) \\ $$$$\mathrm{if}\:\alpha>\beta. \\ $$

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