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AlgebraQuestion and Answers: Page 312

Question Number 58246 Answers: 1 Comments: 0

show that P=x^(9999) +x^(8888) +x^(7777) +x^(6666) +x^(5555) +x^(4444) +x^(3333) +x^(2222) +x^(1111) +1 Q=x^9 +x^8 +x^7 +x^6 +x^5 +x^4 +x^3 +x^2 +x+1 prove P is divisible by Q

$${show}\:{that} \\ $$$${P}={x}^{\mathrm{9999}} +{x}^{\mathrm{8888}} +{x}^{\mathrm{7777}} +{x}^{\mathrm{6666}} +{x}^{\mathrm{5555}} +{x}^{\mathrm{4444}} +{x}^{\mathrm{3333}} +{x}^{\mathrm{2222}} +{x}^{\mathrm{1111}} +\mathrm{1} \\ $$$${Q}={x}^{\mathrm{9}} +{x}^{\mathrm{8}} +{x}^{\mathrm{7}} +{x}^{\mathrm{6}} +{x}^{\mathrm{5}} +{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +{x}+\mathrm{1} \\ $$$${prove}\:\:{P}\:\:{is}\:{divisible}\:{by}\:{Q} \\ $$

Question Number 58210 Answers: 0 Comments: 5

find two possible number such that 1) xy=(x/y)=x−y 2)xy=((2x)/y)=3(x−y) 3) xy=(x/y)=2(x−y).

$$\mathrm{find}\:\mathrm{two}\:\mathrm{possible}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\left.\mathrm{1}\right)\:\:\mathrm{xy}=\frac{\mathrm{x}}{\mathrm{y}}=\mathrm{x}−\mathrm{y} \\ $$$$\left.\mathrm{2}\right)\mathrm{xy}=\frac{\mathrm{2x}}{\mathrm{y}}=\mathrm{3}\left(\mathrm{x}−\mathrm{y}\right) \\ $$$$\left.\mathrm{3}\right)\:\:\mathrm{xy}=\frac{\mathrm{x}}{\mathrm{y}}=\mathrm{2}\left(\mathrm{x}−\mathrm{y}\right). \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 58156 Answers: 1 Comments: 0

Jaiden buys 334 cupcakes.He got 14 more cupcakes.How many cupcakes did he got altogether?

$$\mathrm{Jaiden}\:\mathrm{buys}\:\mathrm{334}\:\mathrm{cupcakes}.\mathrm{He}\:\mathrm{got}\:\mathrm{14}\:\mathrm{more}\:\mathrm{cupcakes}.\mathrm{How}\:\mathrm{many}\:\mathrm{cupcakes}\:\mathrm{did}\:\mathrm{he}\:\mathrm{got}\:\mathrm{altogether}? \\ $$

Question Number 58154 Answers: 1 Comments: 0

A(1,1+i),B((√2)+i,2),C(1−3i,1−i) are given. find angle between: AB and AC .

Question Number 58153 Answers: 1 Comments: 0

arctan((√2)−i)=? [i=(√(−1))]

$$\boldsymbol{\mathrm{arctan}}\left(\sqrt{\mathrm{2}}−\boldsymbol{\mathrm{i}}\right)=?\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{\mathrm{i}}=\sqrt{−\mathrm{1}}\right] \\ $$

Question Number 58145 Answers: 1 Comments: 0

how to factorize a^3 b^2 +a^2 b^3

$${how}\:{to}\:{factorize} \\ $$$${a}^{\mathrm{3}} {b}^{\mathrm{2}} +{a}^{\mathrm{2}} {b}^{\mathrm{3}} \: \\ $$

Question Number 58135 Answers: 1 Comments: 0

Question Number 58092 Answers: 3 Comments: 0

6x^3 +5x^2 −6x−5=0

$$\mathrm{6}{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{5}=\mathrm{0} \\ $$

Question Number 58084 Answers: 0 Comments: 3

Question Number 58077 Answers: 1 Comments: 0

(3/(10))×2

$$\frac{\mathrm{3}}{\mathrm{10}}×\mathrm{2} \\ $$

Question Number 58046 Answers: 2 Comments: 0

3x^4 −4x^3 −7x^2 −4x+5=0 x=?

$$\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{4}} −\mathrm{4}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{7}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{x}}+\mathrm{5}=\mathrm{0} \\ $$$$\boldsymbol{\mathrm{x}}=? \\ $$

Question Number 57988 Answers: 0 Comments: 5

list all subset of {2,4,6,7,8}

$${list}\:{all}\:{subset}\:{of}\: \\ $$$$\left\{\mathrm{2},\mathrm{4},\mathrm{6},\mathrm{7},\mathrm{8}\right\} \\ $$

Question Number 57984 Answers: 0 Comments: 0

Question Number 58045 Answers: 1 Comments: 0

(x+1)^4 <5x^3 +21x^2 +17x+61 find the root x?

$$\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{4}} <\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\mathrm{21}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{17}\boldsymbol{\mathrm{x}}+\mathrm{61} \\ $$$$\boldsymbol{\mathrm{find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{root}}\:\:\:\boldsymbol{\mathrm{x}}? \\ $$

Question Number 57977 Answers: 0 Comments: 0

2[(4×5)−(4×3)]=2×[20−(4×3)]=2×[(20−12)]=2×8=16

$$\mathrm{2}\left[\left(\mathrm{4}×\mathrm{5}\right)−\left(\mathrm{4}×\mathrm{3}\right)\right]=\mathrm{2}×\left[\mathrm{20}−\left(\mathrm{4}×\mathrm{3}\right)\right]=\mathrm{2}×\left[\left(\mathrm{20}−\mathrm{12}\right)\right]=\mathrm{2}×\mathrm{8}=\mathrm{16} \\ $$

Question Number 57960 Answers: 1 Comments: 0

Find maximum n such that 12^n divides 100!.

$${Find}\:{maximum}\:{n}\:{such}\:{that}\:\mathrm{12}^{{n}} \:{divides} \\ $$$$\mathrm{100}!. \\ $$

Question Number 57955 Answers: 1 Comments: 1

Question Number 57947 Answers: 0 Comments: 0

let P(x)=(1+ix)^n −1−ni with x real and n integr natural 1) find the roots of P(x) 2) factorize P(x) inside C[x] 3) factorize P(x) inside R[x] 4) decompose the fraction F(x) =((P^((1)) (x))/(P(x))) inside C(x) P^((1)) is the derivative of P .

$${let}\:{P}\left({x}\right)=\left(\mathrm{1}+{ix}\right)^{{n}} −\mathrm{1}−{ni}\:\:\:\:{with}\:{x}\:{real}\:{and}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{P}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{P}\left({x}\right)\:{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right)\:{factorize}\:{P}\left({x}\right)\:{inside}\:{R}\left[{x}\right] \\ $$$$\left.\mathrm{4}\right)\:{decompose}\:{the}\:{fraction}\:{F}\left({x}\right)\:=\frac{{P}^{\left(\mathrm{1}\right)} \left({x}\right)}{{P}\left({x}\right)}\:{inside}\:{C}\left({x}\right) \\ $$$${P}^{\left(\mathrm{1}\right)} \:{is}\:{the}\:{derivative}\:{of}\:{P}\:. \\ $$

Question Number 57946 Answers: 0 Comments: 0