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AlgebraQuestion and Answers: Page 327

Question Number 43471 Answers: 1 Comments: 0

Question Number 43449 Answers: 1 Comments: 0

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Question Number 43391 Answers: 1 Comments: 0

x^2 +x=y^4 +y^3 +y^2 +y x^4 +(x+1)^4 =y^2 +(y+1)^2 find x and y of is…

$${x}^{\mathrm{2}} +{x}={y}^{\mathrm{4}} +{y}^{\mathrm{3}} +{y}^{\mathrm{2}} +{y} \\ $$$${x}^{\mathrm{4}} +\left({x}+\mathrm{1}\right)^{\mathrm{4}} ={y}^{\mathrm{2}} +\left({y}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\mathrm{find}\:{x}\:\mathrm{and}\:{y}\:\:\mathrm{of}\:\mathrm{is}\ldots \\ $$$$ \\ $$

Question Number 43363 Answers: 3 Comments: 1

If z= cos θ + isin θ , 0<θ<(π/6) , then prove that argument of 1−z^4 = 2θ − (π/2) .

$$\mathrm{If}\:\mathrm{z}=\:\mathrm{cos}\:\theta\:+\:\mathrm{isin}\:\theta\:,\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{6}}\:,\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{argument}\:\mathrm{of}\:\:\mathrm{1}−\mathrm{z}^{\mathrm{4}} \:=\:\mathrm{2}\theta\:−\:\frac{\pi}{\mathrm{2}}\:. \\ $$

Question Number 43353 Answers: 2 Comments: 1

Given the functions f(x)=2x−1 and f•g(x)=x^2 −x+2, find g(x)

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{functions}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}−\mathrm{1}\:\mathrm{and}\:\mathrm{f}\bullet\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{2}, \\ $$$$\mathrm{find}\:\mathrm{g}\left(\mathrm{x}\right) \\ $$

Question Number 43349 Answers: 2 Comments: 0

Question Number 43341 Answers: 1 Comments: 0

write 2×7+3×8 4×9+5×10+6×11 using the sigma notation

$$\mathrm{write}\:\mathrm{2}×\mathrm{7}+\mathrm{3}×\mathrm{8}\:\mathrm{4}×\mathrm{9}+\mathrm{5}×\mathrm{10}+\mathrm{6}×\mathrm{11}\:\mathrm{using}\:\mathrm{the}\:\mathrm{sigma} \\ $$$$\mathrm{notation} \\ $$

Question Number 42910 Answers: 1 Comments: 0

whatshouldbesubtructedfrom(2a+8b+90)toget(−3a+7b+16)?

$${whatshouldbesubtructedfrom}\left(\mathrm{2}{a}+\mathrm{8}{b}+\mathrm{90}\right){toget}\left(−\mathrm{3}{a}+\mathrm{7}{b}+\mathrm{16}\right)? \\ $$

Question Number 42906 Answers: 3 Comments: 0

x^x +y^y =31 x+y = 5 Find x and y

$${x}^{{x}} +{y}^{{y}} =\mathrm{31} \\ $$$${x}+{y}\:=\:\mathrm{5} \\ $$$${Find}\:{x}\:{and}\:{y} \\ $$

Question Number 42776 Answers: 1 Comments: 0

Solve: q^4 − 40q^2 + q + 384 = 0

$$\mathrm{Solve}:\:\:\:\:\:\mathrm{q}^{\mathrm{4}} \:−\:\mathrm{40q}^{\mathrm{2}} \:+\:\mathrm{q}\:+\:\mathrm{384}\:=\:\mathrm{0} \\ $$

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33(√(67))

$$\mathrm{33}\sqrt{\mathrm{67}} \\ $$

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Question Number 42671 Answers: 0 Comments: 0

If pqr = 1 Hence evaluate: (1/(1 + e + f^(−1) )) + (1/(1 + f + g^(−1) )) + (1/(1 + g + e^(−1) ))

$$\mathrm{If}\:\mathrm{pqr}\:=\:\mathrm{1} \\ $$$$\mathrm{Hence}\:\mathrm{evaluate}:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{e}\:+\:\mathrm{f}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{f}\:+\:\mathrm{g}^{−\mathrm{1}} }\:\:+\:\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{g}\:+\:\mathrm{e}^{−\mathrm{1}} } \\ $$

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Question Number 42516 Answers: 1 Comments: 1

(x−(1/2)a),(x−(5/2)a)=? Solve Please.

$$\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a}\right),\left(\mathrm{x}−\frac{\mathrm{5}}{\mathrm{2}}\mathrm{a}\right)=? \\ $$$$\mathrm{Solve}\:\mathrm{Please}. \\ $$

Question Number 42514 Answers: 1 Comments: 0

calculate d(x!)/dx= ?

$${calculate}\:\:{d}\left({x}!\right)/{dx}=\:? \\ $$

Question Number 42507 Answers: 0 Comments: 2

let j =e^((i2π)/3) and p(x) =(1+xj)^n −(1−xj)^n 1) find the roots of p(x) and factorize inside C[x] p(x) 2) decompose inside C(x) the fration F(x) =(1/(p(x))) .

$${let}\:{j}\:={e}^{\frac{{i}\mathrm{2}\pi}{\mathrm{3}}} \:\:\:{and}\:\:\:{p}\left({x}\right)\:=\left(\mathrm{1}+{xj}\right)^{{n}} \:−\left(\mathrm{1}−{xj}\right)^{{n}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{roots}\:{of}\:{p}\left({x}\right)\:{and}\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{decompose}\:{inside}\:{C}\left({x}\right)\:{the}\:{fration}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{{p}\left({x}\right)}\:. \\ $$

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Question Number 42473 Answers: 0 Comments: 0

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