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AlgebraQuestion and Answers: Page 66

Question Number 191061    Answers: 0   Comments: 0

Question Number 191027    Answers: 0   Comments: 0

Question Number 191024    Answers: 1   Comments: 0

Question Number 191022    Answers: 0   Comments: 1

Question Number 191019    Answers: 1   Comments: 0

1−((1−((1−(⋰/5))/5))/5) =?

$$\mathrm{1}−\frac{\mathrm{1}−\frac{\mathrm{1}−\frac{\iddots}{\mathrm{5}}}{\mathrm{5}}}{\mathrm{5}}\:\:=? \\ $$

Question Number 190947    Answers: 1   Comments: 0

Question Number 190942    Answers: 2   Comments: 0

(x+y)(x^2 −xy+y^2 )=2 ((x^3 y^3 )/(x^9 +y^9 −8))=?

$$\left({x}+{y}\right)\left({x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} \right)=\mathrm{2} \\ $$$$\frac{{x}^{\mathrm{3}} {y}^{\mathrm{3}} }{{x}^{\mathrm{9}} +{y}^{\mathrm{9}} −\mathrm{8}}=? \\ $$

Question Number 190938    Answers: 1   Comments: 0

Question Number 190936    Answers: 1   Comments: 0

Determine the value of x such that e^(sinh^(−1) x) =1+e^(cosh^(−1) x)

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\mathrm{e}^{\mathrm{sinh}\:^{−\mathrm{1}} \mathrm{x}} =\mathrm{1}+\mathrm{e}^{\mathrm{cosh}\:^{−\mathrm{1}} \mathrm{x}} \\ $$

Question Number 190935    Answers: 1   Comments: 0

Given that sinh^(−1) y=sech^(−1) y show that y^2 =(((√5)−1)/2)

$$\mathrm{G}{iven}\:{that}\:\:\:\:\:\:\:\:\mathrm{sinh}\:^{−\mathrm{1}} {y}=\mathrm{sech}\:^{−\mathrm{1}} {y}\:\:\:\: \\ $$$${show}\:{that}\:\:\:\:\:\:\:\:\:{y}^{\mathrm{2}} =\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\:\:\: \\ $$$$ \\ $$

Question Number 190916    Answers: 0   Comments: 1

Question Number 190907    Answers: 1   Comments: 0

how is explanotory solution 4^(x^2 +3x+2) +4^(x^2 +3x+7) =4^(2x^2 +6x+9) +1 x=?

$$\mathrm{how}\:\mathrm{is}\:\mathrm{explanotory}\:\mathrm{solution} \\ $$$$\mathrm{4}^{\mathrm{x}^{\mathrm{2}} +\mathrm{3x}+\mathrm{2}} +\mathrm{4}^{\mathrm{x}^{\mathrm{2}} +\mathrm{3x}+\mathrm{7}} =\mathrm{4}^{\mathrm{2x}^{\mathrm{2}} +\mathrm{6x}+\mathrm{9}} +\mathrm{1} \\ $$$$\mathrm{x}=? \\ $$

Question Number 190894    Answers: 2   Comments: 0

f(x)= mx + cos(x) , m>1 , f^( −1) (3)= 2f^( −1) (2 ) find : f ( (1/m) )= ?

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:{mx}\:+\:{cos}\left({x}\right)\:\:,\:\:{m}>\mathrm{1} \\ $$$$\:\:\:\:,\:\:\:{f}^{\:−\mathrm{1}} \left(\mathrm{3}\right)=\:\mathrm{2}{f}^{\:−\mathrm{1}} \left(\mathrm{2}\:\right) \\ $$$$\:\:\:\:\:{find}\::\:\:\:\:\:\:{f}\:\left(\:\frac{\mathrm{1}}{{m}}\:\right)=\:? \\ $$

Question Number 190893    Answers: 2   Comments: 0

if , ((sin(x)−cos(x))/(sin(x)+cos(x))) = (1/4) ⇒ find the value of F = sin^( 6) (x) + cos^( 6) (x)= ?

$$ \\ $$$$\:\:\:\:\:\:\:\:{if}\:,\:\:\frac{{sin}\left({x}\right)−{cos}\left({x}\right)}{{sin}\left({x}\right)+{cos}\left({x}\right)}\:=\:\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\:\:\:\:\:\Rightarrow\:{find}\:\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{F}\:=\:{sin}^{\:\mathrm{6}} \left({x}\right)\:+\:{cos}^{\:\mathrm{6}} \left({x}\right)=\:? \\ $$$$ \\ $$

Question Number 190883    Answers: 2   Comments: 0

Elementary algebra If , x = ((1 +(√(17)))/2) ⇒ Find the value of : E = (( x^8 − x^( 7) + x^( 6) −....− x +1 )/(x^( 6) − x^( 3) + 1)) = ? @nice − mathematics

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Elementary}\:\:\:\mathrm{algebra} \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{If}\:\:,\:\:{x}\:=\:\frac{\mathrm{1}\:+\sqrt{\mathrm{17}}}{\mathrm{2}}\:\:\Rightarrow\:\:\mathrm{Find}\:\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{E}\:=\:\frac{\:{x}^{\mathrm{8}} −\:{x}^{\:\mathrm{7}} \:+\:{x}^{\:\mathrm{6}} −....−\:{x}\:+\mathrm{1}\:}{{x}^{\:\mathrm{6}} \:−\:{x}^{\:\mathrm{3}} \:+\:\mathrm{1}}\:=\:? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:@\mathrm{nice}\:−\:\mathrm{mathematics}\:\:\: \\ $$$$ \\ $$

Question Number 190882    Answers: 1   Comments: 2

Question Number 190820    Answers: 1   Comments: 0

Question Number 190802    Answers: 1   Comments: 0

log_x x=x^(5x−10) x=?

$${log}_{{x}} {x}={x}^{\mathrm{5}{x}−\mathrm{10}} \:\:\:\:\:{x}=? \\ $$

Question Number 190784    Answers: 0   Comments: 0

If , 0 ⇢ M′ ⇢^f M⇢^g M′′⇢0 is a short exact sequence and M′ , M′′ are two finitely generated R −modules then prove M is finitely generated. Hint: f , g are two R − homomorphism.

$$ \\ $$$$\:\:\mathrm{If}\:,\:\mathrm{0}\:\dashrightarrow\:\mathrm{M}'\:\overset{{f}} {\dashrightarrow}\mathrm{M}\overset{{g}} {\dashrightarrow}\mathrm{M}''\dashrightarrow\mathrm{0}\:\mathrm{is} \\ $$$$\:\:\:\:\mathrm{a}\:\mathrm{short}\:\mathrm{exact}\:\mathrm{sequence}\:\:\mathrm{and}\:\:\mathrm{M}'\:,\:\mathrm{M}''\:\mathrm{are} \\ $$$$\:\:\:\mathrm{two}\:\:\mathrm{finitely}\:\mathrm{generated}\:\:\mathrm{R}\:−\mathrm{modules} \\ $$$$\:\:\:\mathrm{then}\:\:\mathrm{prove}\:\:\:\mathrm{M}\:\:\mathrm{is}\:\:\mathrm{finitely}\:\mathrm{generated}.\: \\ $$$$\:\:\:\mathrm{Hint}:\:\:{f}\:\:,\:\:{g}\:\:\:{are}\:\:{two}\:\:\:{R}\:−\:{homomorphism}. \\ $$

Question Number 190774    Answers: 0   Comments: 0

Question Number 190765    Answers: 1   Comments: 0

Question Number 190746    Answers: 2   Comments: 0

Question Number 190705    Answers: 1   Comments: 0

Question Number 190704    Answers: 1   Comments: 0

f(x+y)=f(x)+f(y)+x∙y f(4)=10 finde f(2022)=?

$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+{x}\centerdot{y} \\ $$$${f}\left(\mathrm{4}\right)=\mathrm{10}\:\:{finde}\:{f}\left(\mathrm{2022}\right)=? \\ $$

Question Number 190677    Answers: 0   Comments: 0

If x ∈ R a_1 ,a_2 ,a_3 , b_1 ,b_2 ,b_3 > 0 Then prove that: a_1 ^(sin^2 x) b_1 ^(cos^2 x) + a_2 ^(sin^2 x) b_2 ^(cos^2 x) + a_3 ^(sin^2 x) b_3 ^(cos^2 x) ≤ ≤ (a_1 + a_2 + a_3 )^(sin^2 x) (b_1 + b_2 + b_3 )^(cos^2 x)

$$\mathrm{If}\:\:\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\:\:\:\:\:\mathrm{a}_{\mathrm{1}} ,\mathrm{a}_{\mathrm{2}} ,\mathrm{a}_{\mathrm{3}} \:,\:\mathrm{b}_{\mathrm{1}} ,\mathrm{b}_{\mathrm{2}} ,\mathrm{b}_{\mathrm{3}} \:>\:\mathrm{0} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mathrm{a}_{\mathrm{1}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{1}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:+\:\mathrm{a}_{\mathrm{2}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{2}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:+\:\mathrm{a}_{\mathrm{3}} ^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\mathrm{b}_{\mathrm{3}} ^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\leqslant \\ $$$$\leqslant\:\left(\mathrm{a}_{\mathrm{1}} +\:\mathrm{a}_{\mathrm{2}} +\:\mathrm{a}_{\mathrm{3}} \right)^{\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \:\left(\mathrm{b}_{\mathrm{1}} +\:\mathrm{b}_{\mathrm{2}} +\:\mathrm{b}_{\mathrm{3}} \right)^{\boldsymbol{\mathrm{cos}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}} \\ $$

Question Number 190659    Answers: 0   Comments: 0

Prove that: ((cos (π/9)))^(1/3) − ((cos ((2π)/9)))^(1/3) − ((cos ((4π)/9)))^(1/3) = ((3 − (3/2) (9)^(1/3) ))^(1/3)

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{2}\pi}{\mathrm{9}}}\:−\:\sqrt[{\mathrm{3}}]{\mathrm{cos}\:\frac{\mathrm{4}\pi}{\mathrm{9}}} \\ $$$$=\:\sqrt[{\mathrm{3}}]{\mathrm{3}\:−\:\frac{\mathrm{3}}{\mathrm{2}}\:\sqrt[{\mathrm{3}}]{\mathrm{9}}}\: \\ $$

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