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AlgebraQuestion and Answers: Page 71

Question Number 185204 Answers: 1 Comments: 1

1+(1/(2+(1/(3+(1/(4+(1/⋱)))))))=???

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}+\frac{\mathrm{1}}{\mathrm{3}+\frac{\mathrm{1}}{\mathrm{4}+\frac{\mathrm{1}}{\ddots}}}}=??? \\ $$

Question Number 185198 Answers: 0 Comments: 2

Question Number 185192 Answers: 0 Comments: 2

Question Number 185191 Answers: 1 Comments: 0

y = sin (1/x) ⇒ y^′ = ?

$$\mathrm{y}\:=\:\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{x}}\:\:\Rightarrow\:\:\mathrm{y}^{'} \:=\:? \\ $$

Question Number 185164 Answers: 0 Comments: 0

Question Number 185163 Answers: 0 Comments: 0

Question Number 185151 Answers: 1 Comments: 0

Question Number 185143 Answers: 0 Comments: 0

Question Number 185136 Answers: 0 Comments: 0

Question Number 185137 Answers: 2 Comments: 0

Question Number 185153 Answers: 0 Comments: 0

Question Number 185126 Answers: 0 Comments: 0

(∣y∣−∣x∣−2,8)(∣x∣−∣y∣−1,8) = 0 ∣y∣ = a ∣x∣ + a ∣∣x∣ − 1,1∣ + 5 At what value of a does the equation have 4 roots?

$$\left(\mid\mathrm{y}\mid−\mid\mathrm{x}\mid−\mathrm{2},\mathrm{8}\right)\left(\mid\mathrm{x}\mid−\mid\mathrm{y}\mid−\mathrm{1},\mathrm{8}\right)\:=\:\mathrm{0} \\ $$$$\mid\mathrm{y}\mid\:=\:\mathrm{a}\:\mid\mathrm{x}\mid\:+\:\mathrm{a}\:\mid\mid\mathrm{x}\mid\:−\:\mathrm{1},\mathrm{1}\mid\:+\:\mathrm{5} \\ $$$$\mathrm{At}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\:\boldsymbol{\mathrm{a}}\:\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{have}\:\:\mathrm{4}\:\:\mathrm{roots}? \\ $$

Question Number 185127 Answers: 0 Comments: 3

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

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

Question Number 185128 Answers: 1 Comments: 0

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

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

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