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AlgebraQuestion and Answers: Page 324

Question Number 50016 Answers: 2 Comments: 0

Can you please help me how can i solve this equation x=0.055(1.44x^2 −6.336x+6.9696)

$${Can}\:{you}\:{please}\:{help}\:{me}\: \\ $$$${how}\:{can}\:{i}\:{solve}\:{this}\:{equation}\: \\ $$$${x}=\mathrm{0}.\mathrm{055}\left(\mathrm{1}.\mathrm{44}{x}^{\mathrm{2}} −\mathrm{6}.\mathrm{336}{x}+\mathrm{6}.\mathrm{9696}\right) \\ $$

Question Number 50012 Answers: 0 Comments: 0

help me sir plz

$$\mathrm{help}\:\mathrm{me}\:\mathrm{sir}\:\mathrm{plz} \\ $$$$ \\ $$$$ \\ $$

Question Number 49857 Answers: 1 Comments: 4

Please guide me Sir. I was trying to solve this eq for searching possible values of x. eq is : ∣x − 2∣ < 3∣x + 7∣ the range of x whom i got : −((23)/2) < x < −((19)/4) but the result do not satisfy the eq, instead i put x > −4 , they satisfy the eq. please help me out of this pickle. Not because i didn′t try, yet i always stuck in this type of function.

$$\mathrm{Please}\:\mathrm{guide}\:\mathrm{me}\:\mathrm{Sir}.\:\mathrm{I}\:\mathrm{was}\:\mathrm{trying}\:\mathrm{to}\:\mathrm{solve}\: \\ $$$$\mathrm{this}\:\mathrm{eq}\:\mathrm{for}\:\mathrm{searching}\:\mathrm{possible}\:\mathrm{values}\:\mathrm{of}\:{x}. \\ $$$$\mathrm{eq}\:\mathrm{is}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mid{x}\:−\:\mathrm{2}\mid\:<\:\mathrm{3}\mid{x}\:+\:\mathrm{7}\mid \\ $$$$\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:{x}\:\mathrm{whom}\:\mathrm{i}\:\mathrm{got}\::\:\:\:−\frac{\mathrm{23}}{\mathrm{2}}\:<\:{x}\:<\:−\frac{\mathrm{19}}{\mathrm{4}} \\ $$$$\mathrm{but}\:\mathrm{the}\:\mathrm{result}\:\mathrm{do}\:\mathrm{not}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{eq},\:\mathrm{instead} \\ $$$$\mathrm{i}\:\mathrm{put}\:{x}\:>\:−\mathrm{4}\:,\:\mathrm{they}\:\mathrm{satisfy}\:\mathrm{the}\:\mathrm{eq}.\: \\ $$$$\mathrm{please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{out}\:\mathrm{of}\:\mathrm{this}\:\mathrm{pickle}. \\ $$$$\mathrm{Not}\:\mathrm{because}\:\mathrm{i}\:\mathrm{didn}'\mathrm{t}\:\mathrm{try},\:\mathrm{yet}\:\mathrm{i}\:\mathrm{always} \\ $$$$\mathrm{stuck}\:\mathrm{in}\:\mathrm{this}\:\mathrm{type}\:\mathrm{of}\:\mathrm{function}. \\ $$

Question Number 49851 Answers: 0 Comments: 0

Question Number 49823 Answers: 2 Comments: 0

Complete the square in the expression y^2 +8y+9k and hence find the value of k that makes it a perfect square.

$$\mathrm{Complete}\:\mathrm{the}\:\mathrm{square}\:\mathrm{in}\:\mathrm{the}\:\mathrm{expression} \\ $$$$\mathrm{y}^{\mathrm{2}} +\mathrm{8y}+\mathrm{9k}\:\mathrm{and}\:\mathrm{hence}\:\mathrm{find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{k}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{it}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square}. \\ $$

Question Number 49755 Answers: 1 Comments: 0

Solve simultaneously for s in terms of a and b. h^2 +(b−k)^2 = s^2 .....(i) (h^2 /a^2 )+(k^2 /b^2 ) = 1 .....(ii) (h−(s/2))^2 +(k+b(√(1−(s^2 /(4a^2 )))) )= s^2 ..(iii).

$${Solve}\:{simultaneously}\:{for}\:\boldsymbol{{s}}\:{in}\:{terms} \\ $$$${of}\:\boldsymbol{{a}}\:{and}\:\boldsymbol{{b}}. \\ $$$${h}^{\mathrm{2}} +\left({b}−{k}\right)^{\mathrm{2}} =\:{s}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:.....\left({i}\right) \\ $$$$\frac{{h}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{k}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:=\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....\left({ii}\right) \\ $$$$\left({h}−\frac{{s}}{\mathrm{2}}\right)^{\mathrm{2}} +\left({k}+{b}\sqrt{\mathrm{1}−\frac{{s}^{\mathrm{2}} }{\mathrm{4}{a}^{\mathrm{2}} }}\:\right)=\:{s}^{\mathrm{2}} \:\:\:..\left({iii}\right). \\ $$

Question Number 50924 Answers: 1 Comments: 0

factor the expression: E=x^5 +x^4 +1

$$\mathrm{factor}\:\mathrm{the}\:\mathrm{expression}: \\ $$$$\mathrm{E}={x}^{\mathrm{5}} +{x}^{\mathrm{4}} +\mathrm{1} \\ $$

Question Number 49647 Answers: 1 Comments: 3

let p(x) =x^(2n) −x^n +1 1) determine the roots of p(x) 2) factorize inside C[x] the polynom p(x) . 3)solve p(x)=0 and p(x) =2

$${let}\:{p}\left({x}\right)\:={x}^{\mathrm{2}{n}} \:−{x}^{{n}} \:+\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{p}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{inside}\:{C}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right)\:. \\ $$$$\left.\mathrm{3}\right){solve}\:{p}\left({x}\right)=\mathrm{0}\:\:{and}\:{p}\left({x}\right)\:=\mathrm{2} \\ $$

Question Number 49642 Answers: 1 Comments: 0

if a+b =s and a^3 +b^3 =t find a^2 +b^2 and a^4 +b^4 interms of s and t .

$${if}\:\:{a}+{b}\:={s}\:{and}\:{a}^{\mathrm{3}} \:+{b}^{\mathrm{3}} \:={t}\:\:{find}\:{a}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \:\:{and}\:{a}^{\mathrm{4}} \:+{b}^{\mathrm{4}} \:{interms}\:{of}\:{s}\:{and}\:{t}\:. \\ $$

Question Number 49604 Answers: 2 Comments: 0

Show that: (((a + b)^2 )/2) ≤ a^2 + b^2

$$\mathrm{Show}\:\mathrm{that}:\:\:\:\:\:\:\:\:\:\:\:\frac{\left(\mathrm{a}\:+\:\mathrm{b}\right)^{\mathrm{2}} }{\mathrm{2}}\:\:\leqslant\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \\ $$

Question Number 49570 Answers: 1 Comments: 0

Eliminate t from this equation: (1) x = 1 + t, y = 1 + (1/t) (2) x = 3 + t^3 , y = 2 + (1/t)

$$\mathrm{Eliminate}\:\:\boldsymbol{\mathrm{t}}\:\:\mathrm{from}\:\mathrm{this}\:\mathrm{equation}:\:\:\left(\mathrm{1}\right)\:\:\:\mathrm{x}\:=\:\mathrm{1}\:+\:\mathrm{t},\:\:\:\mathrm{y}\:=\:\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$$$\left(\mathrm{2}\right)\:\:\mathrm{x}\:=\:\mathrm{3}\:+\:\mathrm{t}^{\mathrm{3}} \:,\:\:\:\:\:\mathrm{y}\:=\:\mathrm{2}\:+\:\frac{\mathrm{1}}{\mathrm{t}} \\ $$

Question Number 49555 Answers: 0 Comments: 0

Find 4 plz help me sir

$$\mathrm{Find}\:\mathrm{4}\:\: \\ $$$$\mathrm{plz}\:\mathrm{help}\:\mathrm{me}\:\mathrm{sir} \\ $$

Question Number 49331 Answers: 1 Comments: 2

Find : arg( (((2(√3)+2i)^8 )/((1−i)^6 )) + (((1+i)^6 )/((2(√3)−2i)^8 ))) ?

$${Find}\:: \\ $$$${arg}\left(\:\frac{\left(\mathrm{2}\sqrt{\mathrm{3}}+\mathrm{2}{i}\right)^{\mathrm{8}} }{\left(\mathrm{1}−{i}\right)^{\mathrm{6}} }\:\:+\:\frac{\left(\mathrm{1}+{i}\right)^{\mathrm{6}} }{\left(\mathrm{2}\sqrt{\mathrm{3}}−\mathrm{2}{i}\right)^{\mathrm{8}} }\right)\:? \\ $$

Question Number 49272 Answers: 2 Comments: 0

ZεC satisfies the condition ∣Z∣≥3. Then find the least value of ∣Z+(1/Z)∣ ?

$${Z}\epsilon\mathbb{C}\:{satisfies}\:{the}\:{condition}\:\mid{Z}\mid\geqslant\mathrm{3}. \\ $$$${Then}\:{find}\:{the}\:{least}\:{value}\:{of}\:\mid{Z}+\frac{\mathrm{1}}{{Z}}\mid\:? \\ $$

Question Number 49279 Answers: 2 Comments: 1

Question Number 49256 Answers: 2 Comments: 0

Question Number 49253 Answers: 2 Comments: 0

Question Number 49251 Answers: 5 Comments: 1

Question Number 49248 Answers: 1 Comments: 0

1) solve z^4 =1+i(√3) 2) factorize p(x)=x^4 −1−i(√3)inside C[x] 3)factorze inside R[x] the polynom p(x).

$$\left.\mathrm{1}\right)\:{solve}\:{z}^{\mathrm{4}} =\mathrm{1}+{i}\sqrt{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{1}−{i}\sqrt{\mathrm{3}}{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right){factorze}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right). \\ $$

Question Number 49244 Answers: 1 Comments: 0

let w from C and w^n =1 find the value of S =Σ_(k=0) ^(n−1) C_n ^k w^k .

$${let}\:{w}\:{from}\:{C}\:{and}\:{w}^{{n}} \:=\mathrm{1}\:{find}\:{the}\:{value}\:{of}\: \\ $$$${S}\:=\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{C}_{{n}} ^{{k}} \:{w}^{{k}} \:. \\ $$

Question Number 49246 Answers: 0 Comments: 0

simplify Π_(k=0) ^(n−1) (e^(i((4kπ)/n)) −2cosθ e^((i2π)/n) +1)

$${simplify}\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left({e}^{{i}\frac{\mathrm{4}{k}\pi}{{n}}} \:−\mathrm{2}{cos}\theta\:{e}^{\frac{{i}\mathrm{2}\pi}{{n}}} \:+\mathrm{1}\right) \\ $$

Question Number 49245 Answers: 0 Comments: 0

solve inside C: 1+(z−1)^3 +(z−1)^6 =0

$${solve}\:{inside}\:{C}:\:\mathrm{1}+\left({z}−\mathrm{1}\right)^{\mathrm{3}} \:+\left({z}−\mathrm{1}\right)^{\mathrm{6}} =\mathrm{0} \\ $$

Question Number 49242 Answers: 0 Comments: 0

let z from C and θ from R and z^2 +2zcosθ +1 =0 find the value of z^(2n) +2zcos(nθ)+1 .

$${let}\:{z}\:{from}\:{C}\:{and}\:\theta\:{from}\:{R}\:{and}\:{z}^{\mathrm{2}} \:+\mathrm{2}{zcos}\theta\:+\mathrm{1}\:=\mathrm{0}\:{find}\:{the}\:{value}\:{of} \\ $$$${z}^{\mathrm{2}{n}} \:+\mathrm{2}{zcos}\left({n}\theta\right)+\mathrm{1}\:. \\ $$$$ \\ $$

Question Number 49241 Answers: 0 Comments: 0

let z =r e^(iθ) find the value of P_n =(z+z^− )(z^2 +z^−^2 ).....(z^n +z^−^n ) .

$${let}\:{z}\:={r}\:{e}^{{i}\theta} \:\:\:{find}\:{the}\:{value}\:{of}\: \\ $$$${P}_{{n}} =\left({z}+\overset{−} {{z}}\right)\left({z}^{\mathrm{2}} \:+\overset{−^{\mathrm{2}} } {{z}}\right).....\left({z}^{{n}} \:+\overset{−^{{n}} } {{z}}\right)\:. \\ $$

Question Number 49249 Answers: 0 Comments: 0

smplify A_(np) =Σ_(k=0) ^(n−1) cos(pk) and B_(np) =Σ_(k=0) ^(n−1) sin(pk) with p fromN

$${smplify}\:{A}_{{np}} =\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{cos}\left({pk}\right)\:\:{and}\:{B}_{{np}} \:=\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{sin}\left({pk}\right)\:{with}\:{p}\:{fromN} \\ $$

Question Number 49238 Answers: 0 Comments: 3

Find the maximum common divisor of the folllwing polynomials: •f(x)=x^4 +5x^3 −4x^2 −2x and g(x)=−3x^4 −x^3 +4x^2 in Q[x]. •f(x)=2x^2 −2 and g(x)=x^4 −3x^3 +x^2 +3x−2 in R[x]

$${Find}\:{the}\:{maximum}\:{common}\:{divisor} \\ $$$${of}\:{the}\:{folllwing}\:{polynomials}: \\ $$$$\bullet{f}\left({x}\right)={x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} −\mathrm{2}{x}\:{and}\: \\ $$$${g}\left({x}\right)=−\mathrm{3}{x}^{\mathrm{4}} −{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} \:{in}\:{Q}\left[{x}\right]. \\ $$$$\bullet{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}\:{and}\:{g}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{2}\:{in}\:{R}\left[{x}\right] \\ $$

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