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AlgebraQuestion and Answers: Page 91

Question Number 184828 Answers: 0 Comments: 1

Find x in terms of c ∀ 0<c<(2/(3(√3))) (3x^2 −1)(3x^2 +36x−1)^2 ={4(x^3 −x−c)+9(7x^2 +1)}^2

$${Find}\:{x}\:{in}\:{terms}\:{of}\:\:\:{c}\:\:\forall\:\mathrm{0}<{c}<\frac{\mathrm{2}}{\mathrm{3}\sqrt{\mathrm{3}}} \\ $$$$\left(\mathrm{3}{x}^{\mathrm{2}} −\mathrm{1}\right)\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{36}{x}−\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:=\left\{\mathrm{4}\left({x}^{\mathrm{3}} −{x}−{c}\right)+\mathrm{9}\left(\mathrm{7}{x}^{\mathrm{2}} +\mathrm{1}\right)\right\}^{\mathrm{2}} \\ $$

Question Number 184823 Answers: 1 Comments: 0

Lim_( x→ 0^( +) ) (( 1− cos ( 1− cos((√x) )))/x^( 4) )

$$ \\ $$$$\:\:\:\mathrm{Lim}_{\:{x}\rightarrow\:\mathrm{0}^{\:+} } \:\:\frac{\:\:\mathrm{1}−\:\:\mathrm{cos}\:\left(\:\mathrm{1}−\:\mathrm{cos}\left(\sqrt{{x}}\:\right)\right)}{{x}^{\:\mathrm{4}} } \\ $$

Question Number 184757 Answers: 2 Comments: 2

Which function has a crisis point? a)y=x^3 +2x+6 b)y=(x)^(1/4) c)y=((15)/x) d)y=e^x e)y=(x)^(1/3)

$$\mathrm{Which}\:\mathrm{function}\:\mathrm{has}\:\mathrm{a}\:\mathrm{crisis}\:\mathrm{point}? \\ $$$$\left.\mathrm{a}\right)\mathrm{y}=\mathrm{x}^{\mathrm{3}} +\mathrm{2x}+\mathrm{6} \\ $$$$\left.\mathrm{b}\right)\mathrm{y}=\sqrt[{\mathrm{4}}]{\mathrm{x}} \\ $$$$\left.\mathrm{c}\right)\mathrm{y}=\frac{\mathrm{15}}{\mathrm{x}} \\ $$$$\left.\mathrm{d}\right)\mathrm{y}=\mathrm{e}^{\boldsymbol{\mathrm{x}}} \\ $$$$\left.\mathrm{e}\right)\mathrm{y}=\sqrt[{\mathrm{3}}]{\mathrm{x}} \\ $$

Question Number 184753 Answers: 1 Comments: 0

Question Number 184739 Answers: 1 Comments: 1

Number of linear functions be defined f:[−1, 1]→[0,2] is a)1 b)2 c)3 d)4

$${Number}\:{of}\:{linear}\:{functions}\: \\ $$$${be}\:{defined}\:{f}:\left[−\mathrm{1},\:\mathrm{1}\right]\rightarrow\left[\mathrm{0},\mathrm{2}\right]\:{is} \\ $$$$\left.{a}\left.\right)\left.\mathrm{1}\left.\:\:\:\:{b}\right)\mathrm{2}\:\:\:\:{c}\right)\mathrm{3}\:\:\:{d}\right)\mathrm{4} \\ $$

Question Number 184738 Answers: 1 Comments: 0

α , β are roots of , x^( 2) −x−1=0 ( α > β ) and , t_( n) = ((α^( n) − β^( n) )/(α−β)) ( n ∈ N ), if , b_1 =1 , b_( n) = t_( n−1) +t_( n−2) ( n ≥2 ) find the value of S = Σ_(n=1) ^∞ (( b_( n) )/(10^( n) )) =?

$$ \\ $$$$\alpha\:\:,\:\beta\:\:{are}\:{roots}\:{of}\:\:,\:{x}^{\:\mathrm{2}} −{x}−\mathrm{1}=\mathrm{0} \\ $$$$\left(\:\:\alpha\:>\:\beta\:\right)\:{and}\:,\:\:{t}_{\:{n}} =\:\frac{\alpha^{\:{n}} −\:\beta^{\:{n}} }{\alpha−\beta} \\ $$$$\:\left(\:{n}\:\in\:\mathbb{N}\:\right),\:{if}\:,\:{b}_{\mathrm{1}} =\mathrm{1}\:,\:{b}_{\:{n}} =\:{t}_{\:{n}−\mathrm{1}} +{t}_{\:{n}−\mathrm{2}} \\ $$$$\:\:\:\left(\:{n}\:\geqslant\mathrm{2}\:\right)\:{find}\:{the}\:{value}\:{of} \\ $$$$\:\:\:\:\:\:\:\:\mathrm{S}\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{b}_{\:{n}} }{\mathrm{10}^{\:{n}} }\:=? \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 184728 Answers: 5 Comments: 0

x^( 2) − 3x +1=0 α , β are roots : ( α^( 3) +(1/β) )^( 3) + ( β^^( 3) +(1/α) )^( 3) = ?

$$ \\ $$$$\:\:\:\:\:\:{x}^{\:\mathrm{2}} −\:\mathrm{3}{x}\:+\mathrm{1}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\alpha\:,\:\beta\:{are}\:{roots}\:: \\ $$$$\:\:\:\left(\:\alpha^{\:\mathrm{3}} \:+\frac{\mathrm{1}}{\beta}\:\right)^{\:\mathrm{3}} \:+\:\left(\:\beta^{\:^{\:\mathrm{3}} } \:+\frac{\mathrm{1}}{\alpha}\:\right)^{\:\mathrm{3}} =\:? \\ $$$$ \\ $$

Question Number 184669 Answers: 0 Comments: 3

Question Number 184668 Answers: 0 Comments: 0

Question Number 184622 Answers: 1 Comments: 0

Solve for real numbers: sinx (√(1 − sin^2 x)) = 1 + cosy (√(1 − cos^2 y))

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{sinx}\:\sqrt{\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:=\:\mathrm{1}\:+\:\mathrm{cosy}\:\sqrt{\mathrm{1}\:−\:\mathrm{cos}^{\mathrm{2}} \mathrm{y}}\: \\ $$

Question Number 184607 Answers: 0 Comments: 3

solve { ((x^2 −xy+y^2 =16)),((y^2 −yz+z^2 =25)),((z^2 −zx+x^2 =49)) :}

$${solve} \\ $$$$\begin{cases}{{x}^{\mathrm{2}} −{xy}+{y}^{\mathrm{2}} =\mathrm{16}}\\{{y}^{\mathrm{2}} −{yz}+{z}^{\mathrm{2}} =\mathrm{25}}\\{{z}^{\mathrm{2}} −{zx}+{x}^{\mathrm{2}} =\mathrm{49}}\end{cases} \\ $$

Question Number 184590 Answers: 0 Comments: 0

Question Number 184573 Answers: 4 Comments: 2

Question Number 184567 Answers: 1 Comments: 0

Resoudre dans Z^+ (√a) +(√b) =z (a,b,z)∈N^3 a,b ?

$${Resoudre}\:{dans}\:\mathbb{Z}^{+} \\ $$$$\sqrt{{a}}\:\:+\sqrt{{b}}\:={z}\:\:\:\:\left({a},{b},{z}\right)\in\mathbb{N}^{\mathrm{3}} \\ $$$${a},{b}\:? \\ $$

Question Number 184555 Answers: 3 Comments: 6

Suppose that the sum of the square of complex numbers x or y is 7 , and the sum of their cubes is 10. Find the largest true value of the sum x+y that satisfies these conditions. A)4 B)5 C)6 D)7 E)8

$$\mathrm{Suppose}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{square}\:\mathrm{of} \\ $$$$\mathrm{complex}\:\mathrm{numbers}\:\:\boldsymbol{\mathrm{x}}\:\mathrm{or}\:\boldsymbol{\mathrm{y}}\:\mathrm{is}\:\mathrm{7}\:,\:\mathrm{and}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{cubes}\:\mathrm{is}\:\mathrm{10}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{largest} \\ $$$$\mathrm{true}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{sum}\:\:\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{y}}\:\:\mathrm{that}\:\mathrm{satisfies} \\ $$$$\mathrm{these}\:\mathrm{conditions}. \\ $$$$\left.\mathrm{A}\left.\right)\left.\mathrm{4}\left.\:\left.\:\:\mathrm{B}\right)\mathrm{5}\:\:\:\mathrm{C}\right)\mathrm{6}\:\:\:\mathrm{D}\right)\mathrm{7}\:\:\:\mathrm{E}\right)\mathrm{8} \\ $$

Question Number 184551 Answers: 1 Comments: 0

Resoudre dans Z^+ x+y+(√(xy)) =39

$${Resoudre}\:{dans}\:\mathbb{Z}^{+} \\ $$$${x}+{y}+\sqrt{{xy}}\:\:\:\:=\mathrm{39} \\ $$

Question Number 184535 Answers: 6 Comments: 0

If a, b>0 such that 2a+b=2, then find the minimum value of: 1) (4a^2 +1)(b^2 +1) 2) ((2a^2 −b+4)/(a+1))+((b^2 −2a−2)/(b+4))

$$\mathrm{If}\:{a},\:{b}>\mathrm{0}\:\mathrm{such}\:\mathrm{that}\:\mathrm{2}{a}+{b}=\mathrm{2}, \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}: \\ $$$$\left.\mathrm{1}\right)\:\:\left(\mathrm{4}{a}^{\mathrm{2}} +\mathrm{1}\right)\left({b}^{\mathrm{2}} +\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:\:\frac{\mathrm{2}{a}^{\mathrm{2}} −{b}+\mathrm{4}}{{a}+\mathrm{1}}+\frac{{b}^{\mathrm{2}} −\mathrm{2}{a}−\mathrm{2}}{{b}+\mathrm{4}} \\ $$

Question Number 184503 Answers: 1 Comments: 0

Question Number 184478 Answers: 1 Comments: 0

Question Number 184477 Answers: 3 Comments: 2

Question Number 184475 Answers: 1 Comments: 0

If A = 20° and B = 25° Find (1 + tanA)(1 + tanB)

$$\mathrm{If}\:\:\:\mathrm{A}\:=\:\mathrm{20}°\:\:\:\mathrm{and}\:\:\:\mathrm{B}\:=\:\mathrm{25}° \\ $$$$\mathrm{Find}\:\:\:\left(\mathrm{1}\:+\:\mathrm{tanA}\right)\left(\mathrm{1}\:+\:\mathrm{tanB}\right) \\ $$

Question Number 184473 Answers: 1 Comments: 0

Choose 4 random points in a sphere to form a tetrahedron inside the sphere. What is the probability that this tetrahedron contain the centre point of the sphere?

Question Number 184472 Answers: 4 Comments: 0

solve in R^3 { ((x+(1/y)=3)),((y+(1/z)=4)),((z+(1/x)=5)) :}

$${solve}\:{in}\:\mathbb{R}^{\mathrm{3}} \\ $$$$\begin{cases}{{x}+\frac{\mathrm{1}}{{y}}=\mathrm{3}}\\{{y}+\frac{\mathrm{1}}{{z}}=\mathrm{4}}\\{{z}+\frac{\mathrm{1}}{{x}}=\mathrm{5}}\end{cases} \\ $$

Question Number 184438 Answers: 3 Comments: 0

If a − (4/( (√a))) = 17 Find a − 4 (√a) = ?

$$\mathrm{If}\:\:\:\mathrm{a}\:−\:\frac{\mathrm{4}}{\:\sqrt{\mathrm{a}}}\:=\:\mathrm{17} \\ $$$$\mathrm{Find}\:\:\:\mathrm{a}\:−\:\mathrm{4}\:\sqrt{\mathrm{a}}\:=\:? \\ $$

Question Number 184434 Answers: 2 Comments: 0

(2a−b)b+(5/(3a))−7b^2 +3a=0 Evaluer b en fonction de a

$$\left(\mathrm{2}{a}−{b}\right){b}+\frac{\mathrm{5}}{\mathrm{3}{a}}−\mathrm{7}{b}^{\mathrm{2}} +\mathrm{3}{a}=\mathrm{0} \\ $$$${Evaluer}\:\:\boldsymbol{{b}}\:{en}\:{fonction}\:{de}\:\boldsymbol{{a}} \\ $$

Question Number 184401 Answers: 2 Comments: 3

U_n = ((((−4)^(n+1) −1)/(1−(−4)^n )))U_(n−1) with U_0 =1 find U_(n ) in terms of n (question Q173132 reposted)

$${U}_{{n}} \:=\:\left(\frac{\left(−\mathrm{4}\right)^{{n}+\mathrm{1}} −\mathrm{1}}{\mathrm{1}−\left(−\mathrm{4}\right)^{{n}} }\right){U}_{{n}−\mathrm{1}} \:{with}\:{U}_{\mathrm{0}} =\mathrm{1} \\ $$$${find}\:{U}_{{n}\:} \:{in}\:{terms}\:{of}\:{n}\:\: \\ $$$$ \\ $$$$\left({question}\:{Q}\mathrm{173132}\:{reposted}\right) \\ $$

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