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Question Number 90947 Answers: 0 Comments: 0

if α^(13) =1 and α≠1,find the quadratic equation whose roots are (α+α^3 +α^4 +α^(−4) +α^(−3) +α^(−1) ) and (α^2 +α^5 +α^6 +α^(−6) +α^(−5) +α^(−6) )

$${if}\:\alpha^{\mathrm{13}} =\mathrm{1}\:{and}\:\alpha\neq\mathrm{1},{find}\:{the}\:{quadratic}\:\:{equation} \\ $$$${whose}\:{roots}\:{are}\:\left(\alpha+\alpha^{\mathrm{3}} +\alpha^{\mathrm{4}} +\alpha^{−\mathrm{4}} +\alpha^{−\mathrm{3}} +\alpha^{−\mathrm{1}} \right)\:{and}\:\left(\alpha^{\mathrm{2}} +\alpha^{\mathrm{5}} +\alpha^{\mathrm{6}} +\alpha^{−\mathrm{6}} +\alpha^{−\mathrm{5}} +\alpha^{−\mathrm{6}} \right) \\ $$

Question Number 90940 Answers: 1 Comments: 0

f(x)=(x)^(1/3) is there an inflection point when x=0

$${f}\left({x}\right)=\sqrt[{\mathrm{3}}]{{x}}\:\:{is}\:{there}\:{an}\:{inflection}\:{point} \\ $$$${when}\:{x}=\mathrm{0} \\ $$

Question Number 90709 Answers: 0 Comments: 2

α,β and γ are the roots of x^3 −9x+9=0 find the value of (1) α^(−3) +β^(−3) +γ^(−3) (2) α^(−5) +β^(−5) +γ^(−5)

$$\alpha,\beta\:{and}\:\gamma\:{are}\:{the}\:{roots}\:{of}\:\:{x}^{\mathrm{3}} −\mathrm{9}{x}+\mathrm{9}=\mathrm{0} \\ $$$${find}\:{the}\:{value}\:{of}\:\left(\mathrm{1}\right)\:\alpha^{−\mathrm{3}} +\beta^{−\mathrm{3}} +\gamma^{−\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{2}\right)\:\alpha^{−\mathrm{5}} +\beta^{−\mathrm{5}} +\gamma^{−\mathrm{5}} \\ $$

Question Number 90692 Answers: 1 Comments: 2

Question Number 92777 Answers: 1 Comments: 2

a_(n+1) =(2n+1)a_n a_1 =1 a_n =?

$$\mathrm{a}_{\mathrm{n}+\mathrm{1}} =\left(\mathrm{2n}+\mathrm{1}\right)\mathrm{a}_{\mathrm{n}} \\ $$$$\mathrm{a}_{\mathrm{1}} =\mathrm{1} \\ $$$$\mathrm{a}_{\mathrm{n}} =? \\ $$$$ \\ $$

Question Number 90647 Answers: 0 Comments: 14

Question Number 90581 Answers: 1 Comments: 0

given that α and β are roots of the equation aχ^2 +bχ+c=0. show that λμb^2 =ac(λ+μ)^(2 ) where (α/β)=(λ/μ)

$${given}\:{that}\:\alpha\:{and}\:\beta\:{are}\:{roots}\:{of}\:\:{the}\:{equation}\: \\ $$$${a}\chi^{\mathrm{2}} +{b}\chi+{c}=\mathrm{0}.\:{show}\:{that}\:\lambda\mu{b}^{\mathrm{2}} ={ac}\left(\lambda+\mu\right)^{\mathrm{2}\:} \\ $$$${where}\:\frac{\alpha}{\beta}=\frac{\lambda}{\mu} \\ $$

Question Number 90316 Answers: 1 Comments: 2

determinant ((x,7),(9,(8−x)))= determinant ((7,0,(−3)),((−5),x,(−6)),((−3),(−5),(x−9)))

$$\begin{vmatrix}{{x}}&{\mathrm{7}}\\{\mathrm{9}}&{\mathrm{8}−{x}}\end{vmatrix}=\begin{vmatrix}{\mathrm{7}}&{\mathrm{0}}&{−\mathrm{3}}\\{−\mathrm{5}}&{{x}}&{−\mathrm{6}}\\{−\mathrm{3}}&{−\mathrm{5}}&{{x}−\mathrm{9}}\end{vmatrix} \\ $$$$ \\ $$

Question Number 90138 Answers: 0 Comments: 2

∫x(√(3x^3 +7)) dx

$$\int{x}\sqrt{\mathrm{3}{x}^{\mathrm{3}} +\mathrm{7}}\:{dx} \\ $$

Question Number 90099 Answers: 0 Comments: 2

given the polar equation r = a^2 sin2θ show the tangents at the poles of this polar equation is. θ = {(π/4),((3π)/4),((5π)/4),((7π)/4)}

$$\:\mathrm{given}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{equation} \\ $$$$\:{r}\:=\:{a}^{\mathrm{2}} \:\mathrm{sin2}\theta\:\:\mathrm{show}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{at}\: \\ $$$$\mathrm{the}\:\mathrm{poles}\:\mathrm{of}\:\mathrm{this}\:\mathrm{polar}\:\mathrm{equation}\:\mathrm{is}. \\ $$$$\:\theta\:=\:\left\{\frac{\pi}{\mathrm{4}},\frac{\mathrm{3}\pi}{\mathrm{4}},\frac{\mathrm{5}\pi}{\mathrm{4}},\frac{\mathrm{7}\pi}{\mathrm{4}}\right\} \\ $$

Question Number 90046 Answers: 0 Comments: 0

bhz

$${bhz} \\ $$

Question Number 90024 Answers: 0 Comments: 2

sinh^(−1) [ln(x + (√(x^2 + 1)) )] = ?

$$\mathrm{sinh}^{−\mathrm{1}} \left[\mathrm{ln}\left({x}\:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\mathrm{1}}\:\right)\right]\:=\:? \\ $$

Question Number 90023 Answers: 1 Comments: 0

∫ e^(∣x∣) dx = ???

$$\:\int\:{e}^{\mid{x}\mid} \:{dx}\:=\:??? \\ $$

Question Number 90019 Answers: 1 Comments: 0

find the gcd(2467, 1367)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{gcd}\left(\mathrm{2467},\:\mathrm{1367}\right) \\ $$

Question Number 90018 Answers: 1 Comments: 2

expand , ln(1 + sin x) right up to the term in x^3

$$\mathrm{expand}\:,\:\mathrm{ln}\left(\mathrm{1}\:+\:\mathrm{sin}\:{x}\right)\:\mathrm{right}\:\mathrm{up}\:\mathrm{to}\:\mathrm{the}\:\mathrm{term}\:\mathrm{in}\:{x}^{\mathrm{3}} \\ $$

Question Number 89986 Answers: 0 Comments: 3

∫_0 ^1 (−1)^(⌊(1/x)⌋) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(−\mathrm{1}\right)^{\lfloor\frac{\mathrm{1}}{{x}}\rfloor} \:{dx} \\ $$

Question Number 89980 Answers: 0 Comments: 2

Question Number 89953 Answers: 0 Comments: 1

solvethefollowingequation 5^(2x+y) =625and2^(4x∤2y) =(1/6)

$$\mathrm{solvethefollowingequation} \\ $$$$\mathrm{5}^{\mathrm{2x}+\mathrm{y}} =\mathrm{625and2}^{\mathrm{4x}\nmid\mathrm{2y}} =\frac{\mathrm{1}}{\mathrm{6}} \\ $$

Question Number 89956 Answers: 0 Comments: 1

simplifyκgivingκyourκanswerκinκindexκform (√((ac^2 )/(9a^2 c^4 )))

$$\mathrm{simplify}\kappa\mathrm{giving}\kappa\mathrm{your}\kappa\mathrm{answer}\kappa\mathrm{in}\kappa\mathrm{index}\kappa\mathrm{form} \\ $$$$\sqrt{\frac{\mathrm{ac}^{\mathrm{2}} }{\mathrm{9a}^{\mathrm{2}} \mathrm{c}^{\mathrm{4}} }} \\ $$

Question Number 89937 Answers: 0 Comments: 1

Prove that for all complex such as ∣z∣<1= Σ_(n=1) ^∞ (z^n /((z^n −1)^2 )) +Σ_(n=1) ^∞ ((nz^n )/(z^n −1)) = 0

$${Prove}\:{that}\:{for}\:{all}\:{complex}\:{such}\:{as}\:\mid{z}\mid<\mathrm{1}= \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{z}^{{n}} }{\left({z}^{{n}} −\mathrm{1}\right)^{\mathrm{2}} }\:+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{nz}^{{n}} }{{z}^{{n}} −\mathrm{1}}\:=\:\mathrm{0}\: \\ $$

Question Number 89936 Answers: 1 Comments: 0

Prove that Σ_(p≥1,q≥1) (1/(pq(p+q−1))) =(π^2 /3)

$${Prove}\:{that}\:\underset{{p}\geqslant\mathrm{1},{q}\geqslant\mathrm{1}} {\sum}\:\:\frac{\mathrm{1}}{{pq}\left({p}+{q}−\mathrm{1}\right)}\:=\frac{\pi^{\mathrm{2}} }{\mathrm{3}}\: \\ $$

Question Number 89934 Answers: 0 Comments: 0

Let x∈]0;1[ Prove that Σ_(n=1) ^∞ (x^n /(1+x^n )) +Σ_(n=1) ^∞ (((−x)^n )/(1−x^n )) = 0

$$\left.{Let}\:{x}\in\right]\mathrm{0};\mathrm{1}\left[\:\:{Prove}\:{that}\right. \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} }{\mathrm{1}+{x}^{{n}} }\:+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−{x}\right)^{{n}} }{\mathrm{1}−{x}^{{n}} }\:=\:\mathrm{0} \\ $$

Question Number 89745 Answers: 0 Comments: 2

f(x) = f(x+((3π)/8)) , ∀x∈ R if ∫_0 ^(3π/8) f(x) dx = t , then ∫_π ^(5π/2) f(x−π) dx = A. 2t B. 3t C. 4t D. 6t E. 8t

$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{f}\left(\mathrm{x}+\frac{\mathrm{3}\pi}{\mathrm{8}}\right)\:,\:\forall\mathrm{x}\in\:\mathbb{R} \\ $$$$\mathrm{if}\:\underset{\mathrm{0}} {\overset{\mathrm{3}\pi/\mathrm{8}} {\int}}\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:\mathrm{t}\:,\:\mathrm{then}\: \\ $$$$\underset{\pi} {\overset{\mathrm{5}\pi/\mathrm{2}} {\int}}\mathrm{f}\left(\mathrm{x}−\pi\right)\:\mathrm{dx}\:=\: \\ $$$$\mathrm{A}.\:\mathrm{2t}\:\:\:\:\:\:\:\mathrm{B}.\:\mathrm{3t}\:\:\:\:\:\:\:\mathrm{C}.\:\mathrm{4t}\:\:\:\:\:\:\:\mathrm{D}.\:\mathrm{6t} \\ $$$$\mathrm{E}.\:\mathrm{8t}\: \\ $$

Question Number 89728 Answers: 1 Comments: 0

Find the area bounded by 3x+4y=12 and the coordinate axes?

$${Find}\:{the}\:{area}\:{bounded}\:{by}\:\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{12} \\ $$$${and}\:{the}\:{coordinate}\:{axes}? \\ $$

Question Number 89661 Answers: 0 Comments: 3

The Area of the triangle is 9x^2 −12x+4. compute its perimeter?

$${The}\:{Area}\:{of}\:{the}\:{triangle}\:{is}\:\mathrm{9}{x}^{\mathrm{2}} \:−\mathrm{12}{x}+\mathrm{4}. \\ $$$${compute}\:{its}\:{perimeter}? \\ $$

Question Number 89626 Answers: 0 Comments: 1

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