Question and Answers Forum

All Questions   Topic List

AlgebraQuestion and Answers: Page 86

Question Number 185122    Answers: 0   Comments: 2

{ (((√(x^2 − (5/9) + (√(y + x^2 − (4/9))))) = y)),(((√(y^2 − (4/9) + (√(x + y^2 − (4/9))))) = x)) :} find: x , y = ?

$$\begin{cases}{\sqrt{\mathrm{x}^{\mathrm{2}} \:−\:\frac{\mathrm{5}}{\mathrm{9}}\:+\:\sqrt{\mathrm{y}\:+\:\mathrm{x}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}}}\:=\:\mathrm{y}}\\{\sqrt{\mathrm{y}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}\:+\:\sqrt{\mathrm{x}\:+\:\mathrm{y}^{\mathrm{2}} \:−\:\frac{\mathrm{4}}{\mathrm{9}}}}\:=\:\mathrm{x}}\end{cases} \\ $$$$\mathrm{find}:\:\:\:\mathrm{x}\:,\:\mathrm{y}\:=\:? \\ $$

Question Number 185109    Answers: 0   Comments: 0

Question Number 185076    Answers: 2   Comments: 0

x^(2x^6 ) =3 x=?

$${x}^{\mathrm{2}{x}^{\mathrm{6}} } =\mathrm{3} \\ $$$${x}=? \\ $$

Question Number 185054    Answers: 1   Comments: 0

If , f(x)= (x/(⌊ x ⌋)) ⇒ D_( f) =?(domain) and R_( f ) = ? (range )

$$ \\ $$$$\:\:\mathrm{I}{f}\:,\:\:\:{f}\left({x}\right)=\:\frac{{x}}{\lfloor\:{x}\:\rfloor}\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\mathrm{D}_{\:{f}} \:=?\left({domain}\right)\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{and}\:\:\:\:\:\:\:\:\:\:\mathrm{R}_{\:{f}\:} =\:?\:\left({range}\:\right) \\ $$

Question Number 185013    Answers: 4   Comments: 3

Question Number 184980    Answers: 2   Comments: 0

(√7) + (√6) = a (√7) − (√6) = ?

$$\sqrt{\mathrm{7}}\:\:+\:\:\sqrt{\mathrm{6}}\:\:=\:\:\mathrm{a} \\ $$$$\sqrt{\mathrm{7}}\:−\:\sqrt{\mathrm{6}}\:=\:? \\ $$

Question Number 184942    Answers: 0   Comments: 2

f(x )= x + ⌊ x + (( ⌊ x_ ^ ⌋)/(⌊ (x^( 2) /(1 +x^( 2) )) ⌋+1)) ⌋ ⇒ f^( −1) (x )=?

$$ \\ $$$$\:\:\:\:{f}\left({x}\:\right)=\:{x}\:+\:\lfloor\:\:{x}\:+\:\frac{\:\lfloor\:\:\underset{} {\overset{} {{x}}}\:\:\rfloor}{\lfloor\:\:\:\frac{{x}^{\:\mathrm{2}} }{\mathrm{1}\:+{x}^{\:\mathrm{2}} }\:\:\:\rfloor+\mathrm{1}}\:\rfloor \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:{f}^{\:−\mathrm{1}} \:\left({x}\:\right)=? \\ $$

Question Number 184941    Answers: 0   Comments: 0

Determiner une relation entre les coeficients de x,y,z pour que z=x+y a_1 x+b_1 y+c_1 z=u a_2 x+b_2 y+c_2 z=v a_3 x+b_3 y+c_3 z=w

$${Determiner}\:{une}\:{relation}\:{entre} \\ $$$${les}\:{coeficients}\:{de}\:{x},{y},{z}\: \\ $$$${pour}\:{que}\:\:{z}={x}+{y} \\ $$$$ \\ $$$${a}_{\mathrm{1}} {x}+{b}_{\mathrm{1}} {y}+{c}_{\mathrm{1}} {z}={u} \\ $$$${a}_{\mathrm{2}} {x}+{b}_{\mathrm{2}} {y}+{c}_{\mathrm{2}} {z}={v} \\ $$$${a}_{\mathrm{3}} {x}+{b}_{\mathrm{3}} {y}+{c}_{\mathrm{3}} {z}={w} \\ $$$$ \\ $$

Question Number 184938    Answers: 2   Comments: 0

If , { (( f : [ (√2) , +∞ ) → R )),(( f (x ) = x^( 2) + ⌊ (( 1)/(1 − ⌊ x^( 2) ⌋)) ⌋ )) :} ⇒ ⌊ f^( −1) ( π ) ⌋ = ?

$$ \\ $$$$\:\:\:\:\:\mathrm{If}\:\:,\:\:\begin{cases}{\:\:{f}\:\::\:\:\left[\:\sqrt{\mathrm{2}}\:,\:+\infty\:\right)\:\rightarrow\:\mathbb{R}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\\{\:\:\:{f}\:\left({x}\:\right)\:=\:{x}^{\:\mathrm{2}} \:\:+\:\lfloor\:\frac{\:\mathrm{1}}{\mathrm{1}\:−\:\lfloor\:{x}^{\:\mathrm{2}} \:\rfloor}\:\rfloor\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{cases} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:\:\:\lfloor\:\:{f}^{\:−\mathrm{1}} \:\left(\:\pi\:\right)\:\rfloor\:=\:? \\ $$$$ \\ $$$$ \\ $$

Question Number 184927    Answers: 2   Comments: 0

s=(2/(11^0 ))+(6/(11))+((10)/(11^2 ))+((14)/(11^3 ))+((18)/(11^4 ))+∙∙∙∙ s=?

$${s}=\frac{\mathrm{2}}{\mathrm{11}^{\mathrm{0}} }+\frac{\mathrm{6}}{\mathrm{11}}+\frac{\mathrm{10}}{\mathrm{11}^{\mathrm{2}} }+\frac{\mathrm{14}}{\mathrm{11}^{\mathrm{3}} }+\frac{\mathrm{18}}{\mathrm{11}^{\mathrm{4}} }+\centerdot\centerdot\centerdot\centerdot \\ $$$${s}=? \\ $$

Question Number 184914    Answers: 0   Comments: 1

Lindsey randomly selects 2 distinct days each lveek to go to the gym. Jess randomly selects 3 distinct days each tveek to go to the same gym. What is the probability that Lindsey and Jess will both be at the gym on the same day at least once in any given week? Express your anslver as a common fraction.

$$ \\ $$ Lindsey randomly selects 2 distinct days each lveek to go to the gym. Jess randomly selects 3 distinct days each tveek to go to the same gym. What is the probability that Lindsey and Jess will both be at the gym on the same day at least once in any given week? Express your anslver as a common fraction.

Question Number 184893    Answers: 1   Comments: 0

find the set of critical points for: 1: f (x) = (x/(⌊ x ⌋+⌊ −x⌋)) −x 2 : g(x) = (x/(⌊ x ⌋ +⌊ −x ⌋)) +x

$$ \\ $$$$\:\:\:\:{find}\:{the}\:{set}\:{of}\: \\ $$$$\:\:\:\:{critical}\:{points}\:{for}: \\ $$$$\:\:\:\mathrm{1}:\:\:\:{f}\:\left({x}\right)\:=\:\frac{{x}}{\lfloor\:{x}\:\rfloor+\lfloor\:−{x}\rfloor}\:−{x}\:\:\:\: \\ $$$$\:\:\:\:\mathrm{2}\::\:\:{g}\left({x}\right)\:=\:\frac{{x}}{\lfloor\:{x}\:\rfloor\:+\lfloor\:−{x}\:\rfloor}\:+{x} \\ $$

Question Number 184877    Answers: 1   Comments: 0

Find the sum of the last ten digits: 5^(23) ∙ 2^(2022) − 2023

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{ten}\:\mathrm{digits}: \\ $$$$\mathrm{5}^{\mathrm{23}} \:\centerdot\:\mathrm{2}^{\mathrm{2022}} \:−\:\mathrm{2023} \\ $$

Question Number 184875    Answers: 1   Comments: 0

Question Number 184861    Answers: 0   Comments: 0

x ∈ [−0,5 ; 0,5] find the product of all x′s 3(cos^2 πx + sinπy) + 2 = 9 + 3 ∣sinπx ∙ sinπy∣−sinπy

$$\mathrm{x}\:\in\:\left[−\mathrm{0},\mathrm{5}\:\:;\:\:\mathrm{0},\mathrm{5}\right] \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\:\boldsymbol{\mathrm{x}}'\mathrm{s} \\ $$$$\mathrm{3}\left(\mathrm{cos}^{\mathrm{2}} \pi\mathrm{x}\:+\:\mathrm{sin}\pi\mathrm{y}\right)\:+\:\mathrm{2}\:=\:\mathrm{9}\:+\:\mathrm{3}\:\mid\mathrm{sin}\pi\mathrm{x}\:\centerdot\:\mathrm{sin}\pi\mathrm{y}\mid−\mathrm{sin}\pi\mathrm{y} \\ $$

Question Number 184859    Answers: 2   Comments: 0

Lim_( x→∞) x^( 4) ( 1− cos (1− cos((2/x))))=?

$$ \\ $$$$\:\mathrm{Lim}_{\:{x}\rightarrow\infty} \:{x}^{\:\mathrm{4}} \:\left(\:\mathrm{1}−\:{cos}\:\left(\mathrm{1}−\:{cos}\left(\frac{\mathrm{2}}{{x}}\right)\right)\right)=? \\ $$$$ \\ $$

Question Number 184856    Answers: 0   Comments: 0

f(x)= (√( ∣ x_ ^ ∣ −∣ x−_ ^ ⌊ax⌋ ∣)) ; a ∈ [ 3 , 4 ) find : { (( D_( f) =? (domain ))),(( R_( f) =? (range ))) :}

$$ \\ $$$$\:\:\:\:\:{f}\left({x}\right)=\:\sqrt{\:\mid\:\underset{} {\overset{} {{x}}}\:\:\mid\:−\mid\:\:{x}\underset{} {\overset{} {−}}\lfloor{ax}\rfloor\:\mid} \\ $$$$\:\:\:\:\:\:;\:\:\:{a}\:\in\:\left[\:\mathrm{3}\:,\:\mathrm{4}\:\right) \\ $$$$\:\:\:\:\:{find}\::\:\:\:\begin{cases}{\:\:{D}_{\:{f}} \:=?\:\left({domain}\:\right)}\\{\:\:\mathcal{R}_{\:{f}} \:=?\:\left({range}\:\right)}\end{cases} \\ $$$$ \\ $$

Question Number 184845    Answers: 0   Comments: 0

x ∈ [−0,5 ; 0,5] find the product of all x′s 1. 4sin^2 πx−4sinπx + 2 = 2sin^2 πy−1 2. 4sinπx = 4sinπy − 7 − (1/(sin^2 πx))

$$\mathrm{x}\:\in\:\left[−\mathrm{0},\mathrm{5}\:;\:\mathrm{0},\mathrm{5}\right] \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{all}\:\:\boldsymbol{\mathrm{x}}'\mathrm{s} \\ $$$$\mathrm{1}.\:\mathrm{4sin}^{\mathrm{2}} \pi\mathrm{x}−\mathrm{4sin}\pi\mathrm{x}\:+\:\mathrm{2}\:=\:\mathrm{2sin}^{\mathrm{2}} \pi\mathrm{y}−\mathrm{1} \\ $$$$\mathrm{2}.\:\mathrm{4sin}\pi\mathrm{x}\:=\:\mathrm{4sin}\pi\mathrm{y}\:−\:\mathrm{7}\:−\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} \pi\mathrm{x}} \\ $$

Question Number 184843    Answers: 0   Comments: 0

Question Number 184841    Answers: 1   Comments: 0

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) )) =?

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

  Pg 81      Pg 82      Pg 83      Pg 84      Pg 85      Pg 86      Pg 87      Pg 88      Pg 89      Pg 90   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com