Question and Answers Forum

All Questions   Topic List

AlgebraQuestion and Answers: Page 68

Question Number 186330    Answers: 0   Comments: 1

Question Number 186329    Answers: 1   Comments: 0

Question Number 186305    Answers: 0   Comments: 3

log (((3.2^ )/(3.1^ ))) find Characteristic?

$$\mathrm{log}\:\left(\frac{\mathrm{3}.\bar {\mathrm{2}}}{\mathrm{3}.\bar {\mathrm{1}}}\right)\:\:\:\:\:\:\:{find}\:\mathrm{Characteristic}? \\ $$

Question Number 186300    Answers: 1   Comments: 0

solve in R ⌊ 2log_( 8) (x) + (1/3) ⌋ = log_( 4) (x )+ (1/2)

$$\:\:\: \\ $$$$\:\:\:\:\:\mathrm{solve}\:\:\mathrm{in}\:\:\:\mathbb{R} \\ $$$$ \\ $$$$\:\:\:\lfloor\:\:\mathrm{2log}_{\:\mathrm{8}} \left({x}\right)\:+\:\frac{\mathrm{1}}{\mathrm{3}}\:\rfloor\:=\:\mathrm{log}_{\:\mathrm{4}} \left({x}\:\right)+\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$ \\ $$

Question Number 186292    Answers: 0   Comments: 0

(x−p)(x^3 −x−(1/3))=0 x^4 −px^3 −x^2 +(p−(1/3))x+(p/3)=0 (x^2 +ax+h)(x^2 +bx+k)=0 a+b=−p h+k+ab=−1 bh+ak=p−(1/3) hk=(p/3) −−−−−− say ab=t −−−−−− ah+bk+p−(1/3)=p(1+t) bh+ak−(p−(1/3))=0 ⇒ (a−b)(h−k)=pt−p+(2/3) squaring (p^2 −4t){(1+t)^2 −((4p)/3)}=(pt−p+(2/3))^2 say t+1=z (p^2 +4−4z)(z^2 −((4p)/3))=(pz−2p+(2/3))^2 ⇒ −4z^3 +(p^2 +4)z^2 +((16pz)/3)−((4p)/3)(p^2 +4) =p^2 z^2 −4p(p−(1/3))z+4(p−(1/3))^2 ⇒ z^3 −z^2 −p(p+1)z+(p−(1/3))^2 +(p/3)(p^2 +4)=0 .....

$$\left({x}−{p}\right)\left({x}^{\mathrm{3}} −{x}−\frac{\mathrm{1}}{\mathrm{3}}\right)=\mathrm{0} \\ $$$${x}^{\mathrm{4}} −{px}^{\mathrm{3}} −{x}^{\mathrm{2}} +\left({p}−\frac{\mathrm{1}}{\mathrm{3}}\right){x}+\frac{{p}}{\mathrm{3}}=\mathrm{0} \\ $$$$\left({x}^{\mathrm{2}} +{ax}+{h}\right)\left({x}^{\mathrm{2}} +{bx}+{k}\right)=\mathrm{0} \\ $$$${a}+{b}=−{p} \\ $$$${h}+{k}+{ab}=−\mathrm{1} \\ $$$${bh}+{ak}={p}−\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${hk}=\frac{{p}}{\mathrm{3}} \\ $$$$−−−−−− \\ $$$${say}\:{ab}={t} \\ $$$$−−−−−− \\ $$$${ah}+{bk}+{p}−\frac{\mathrm{1}}{\mathrm{3}}={p}\left(\mathrm{1}+{t}\right) \\ $$$${bh}+{ak}−\left({p}−\frac{\mathrm{1}}{\mathrm{3}}\right)=\mathrm{0} \\ $$$$\Rightarrow\:\left({a}−{b}\right)\left({h}−{k}\right)={pt}−{p}+\frac{\mathrm{2}}{\mathrm{3}} \\ $$$${squaring} \\ $$$$\left({p}^{\mathrm{2}} −\mathrm{4}{t}\right)\left\{\left(\mathrm{1}+{t}\right)^{\mathrm{2}} −\frac{\mathrm{4}{p}}{\mathrm{3}}\right\}=\left({pt}−{p}+\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}} \\ $$$${say}\:\:{t}+\mathrm{1}={z} \\ $$$$\left({p}^{\mathrm{2}} +\mathrm{4}−\mathrm{4}{z}\right)\left({z}^{\mathrm{2}} −\frac{\mathrm{4}{p}}{\mathrm{3}}\right)=\left({pz}−\mathrm{2}{p}+\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}} \\ $$$$\Rightarrow \\ $$$$−\mathrm{4}{z}^{\mathrm{3}} +\left({p}^{\mathrm{2}} +\mathrm{4}\right){z}^{\mathrm{2}} +\frac{\mathrm{16}{pz}}{\mathrm{3}}−\frac{\mathrm{4}{p}}{\mathrm{3}}\left({p}^{\mathrm{2}} +\mathrm{4}\right) \\ $$$$\:\:\:\:={p}^{\mathrm{2}} {z}^{\mathrm{2}} −\mathrm{4}{p}\left({p}−\frac{\mathrm{1}}{\mathrm{3}}\right){z}+\mathrm{4}\left({p}−\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} \\ $$$$\Rightarrow\:{z}^{\mathrm{3}} −{z}^{\mathrm{2}} −{p}\left({p}+\mathrm{1}\right){z}+\left({p}−\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:+\frac{{p}}{\mathrm{3}}\left({p}^{\mathrm{2}} +\mathrm{4}\right)=\mathrm{0} \\ $$$$.....\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 186285    Answers: 0   Comments: 2

Prove that: R (m , n) ≤ C_(m+n) ^m Here R states the Ramsey theory

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{R}\:\left(\mathrm{m}\:,\:\mathrm{n}\right)\:\leqslant\:\mathrm{C}_{\boldsymbol{\mathrm{m}}+\boldsymbol{\mathrm{n}}} ^{\boldsymbol{\mathrm{m}}} \\ $$$$\mathrm{Here}\:\:\mathrm{R}\:\:\mathrm{states}\:\mathrm{the}\:\:\mathrm{Ramsey}\:\:\mathrm{theory} \\ $$

Question Number 186265    Answers: 1   Comments: 0

f(x)= (√( x −a)) + (√(3a −x)) with ( a>0) is given .If , f_( max) . f_( min) = (√(32)) find , ” a ” = ?

$$ \\ $$$$\:\:\:{f}\left({x}\right)=\:\sqrt{\:{x}\:−{a}}\:\:+\:\sqrt{\mathrm{3}{a}\:−{x}}\:\:\:{with}\:\left(\:{a}>\mathrm{0}\right) \\ $$$$\:\:\:\:{is}\:\:{given}\:.{If}\:\:,\:\:{f}_{\:{max}} \:.\:{f}_{\:{min}} \:=\:\sqrt{\mathrm{32}} \\ $$$$\:\:\:\:\:{find}\:\:,\:\:\:\:\:\:\:''\:\:\:{a}\:\:''\:\:=\:? \\ $$

Question Number 186256    Answers: 0   Comments: 1

Prove that: R (m , n) ≤ C_(m+n) ^m

$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathbb{R}\:\left(\mathrm{m}\:,\:\mathrm{n}\right)\:\leqslant\:\mathbb{C}_{\boldsymbol{\mathrm{m}}+\boldsymbol{\mathrm{n}}} ^{\boldsymbol{\mathrm{m}}} \\ $$$$ \\ $$

Question Number 186253    Answers: 1   Comments: 1

Question Number 186249    Answers: 0   Comments: 0

Question Number 186248    Answers: 0   Comments: 0

Question Number 186241    Answers: 2   Comments: 3

x+(1/x)=((−1+(√5))/2) x?

$${x}+\frac{\mathrm{1}}{{x}}=\frac{−\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${x}? \\ $$

Question Number 186232    Answers: 1   Comments: 0

1+(x/(1+(x/(1+(x/∙_∙_∙ )))))=5 x=?

$$\mathrm{1}+\frac{{x}}{\mathrm{1}+\frac{{x}}{\mathrm{1}+\frac{{x}}{\centerdot_{\centerdot_{\centerdot} } }}}=\mathrm{5}\:\:\:\:\:\:\:\:\:{x}=? \\ $$

Question Number 186163    Answers: 3   Comments: 0

Question Number 186146    Answers: 0   Comments: 0

Question Number 186124    Answers: 1   Comments: 1

Question Number 186123    Answers: 0   Comments: 0

Question Number 186105    Answers: 3   Comments: 0

a^2 + 1 = a a^(12) + a^6 + 1 = ?

$$\:{a}^{\mathrm{2}} \:+\:\mathrm{1}\:\:=\:{a} \\ $$$$\:{a}^{\mathrm{12}} \:+\:{a}^{\mathrm{6}} \:+\:\mathrm{1}\:=\:?\: \\ $$

Question Number 186099    Answers: 1   Comments: 0

1. Solve for the linear system: x−2y+3z=5 2x+y−4z=0 3x+4y−11z=−5 2. Ghana railways co−operation has 20 trains for it′s operations. It is observed that x trains can accommodate 2 passengers, y trains 3 passengers and z trains 5 passengers. Howeer, the totsl number of passrngers always present at Ghana railways are 64. During market day, 3 of x trains, 2 of y trains and 4 of z trains for a total of 10 trains were used. Determine the values of x, y and z.

$$\mathrm{1}.\:{Solve}\:{for}\:{the}\:{linear}\:{system}: \\ $$$${x}−\mathrm{2}{y}+\mathrm{3}{z}=\mathrm{5} \\ $$$$\mathrm{2}{x}+{y}−\mathrm{4}{z}=\mathrm{0} \\ $$$$\mathrm{3}{x}+\mathrm{4}{y}−\mathrm{11}{z}=−\mathrm{5} \\ $$$$\mathrm{2}.\:{Ghana}\:{railways}\:{co}−{operation}\:{has}\:\mathrm{20}\: \\ $$$${trains}\:{for}\:{it}'{s}\:{operations}.\:{It}\:{is}\:{observed}\:{that} \\ $$$${x}\:{trains}\:{can}\:{accommodate}\:\mathrm{2}\:{passengers}, \\ $$$${y}\:{trains}\:\mathrm{3}\:{passengers}\:{and}\:{z}\:{trains}\:\mathrm{5}\: \\ $$$${passengers}.\:{Howeer},\:{the}\:{totsl}\:{number}\:{of} \\ $$$${passrngers}\:{always}\:{present}\:{at}\:{Ghana}\: \\ $$$${railways}\:{are}\:\mathrm{64}.\:{During}\:{market}\:{day},\:\mathrm{3}\:{of} \\ $$$${x}\:{trains},\:\mathrm{2}\:{of}\:{y}\:{trains}\:{and}\:\mathrm{4}\:{of}\:{z}\:{trains}\:{for}\: \\ $$$${a}\:{total}\:{of}\:\mathrm{10}\:{trains}\:{were}\:{used}.\:{Determine}\: \\ $$$${the}\:{values}\:{of}\:{x},\:{y}\:{and}\:{z}. \\ $$

Question Number 186053    Answers: 2   Comments: 0

Question Number 186025    Answers: 0   Comments: 1

P(x) = −3x^2 +5x^3 +5x^2 −5x−2 division euclidienne par x^2 −1

$$\boldsymbol{\mathrm{P}}\left(\boldsymbol{{x}}\right)\:=\:−\mathrm{3}\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{3}} +\mathrm{5}\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{\mathrm{x}}−\mathrm{2} \\ $$$${division}\:{euclidienne}\:{par}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{1} \\ $$$$ \\ $$

Question Number 186022    Answers: 0   Comments: 5

prove that(using Epsilon−Delta definition) (a) lim_(x→3) ( 2x^2 +1)=19 (b) lim_(x→2) x^3 =8

$${prove}\:\:{that}\left({using}\:{Epsilon}−{Delta}\:{definition}\right) \\ $$$$\left({a}\right)\:\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\left(\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{19} \\ $$$$\left({b}\right)\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:{x}^{\mathrm{3}} =\mathrm{8} \\ $$

Question Number 186021    Answers: 1   Comments: 0

prove that(using Epsilon−Delta definition) (a) lim_(x→1) (6x−2)=4 (b)lim_(x→6) (√(3x−2))=4

$${prove}\:{that}\left({using}\:{Epsilon}−{Delta}\:{definition}\right) \\ $$$$\left({a}\right)\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\left(\mathrm{6}{x}−\mathrm{2}\right)=\mathrm{4} \\ $$$$\left({b}\right)\underset{{x}\rightarrow\mathrm{6}} {\mathrm{lim}}\sqrt{\mathrm{3}{x}−\mathrm{2}}=\mathrm{4} \\ $$

Question Number 186002    Answers: 1   Comments: 1

Question Number 185982    Answers: 1   Comments: 0

Question Number 185981    Answers: 1   Comments: 0

solve in R ⌊ 2x ⌋ + ⌊ 3x ⌋ = 1 ⌊ x ⌋ := greatest integer number more than or equal to ” x ”

$$ \\ $$$$\:\:\:\:\:\:\:{solve}\:\:{in}\:\:\:\mathbb{R} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\lfloor\:\:\mathrm{2}{x}\:\rfloor\:\:+\:\lfloor\:\:\mathrm{3}{x}\:\rfloor\:=\:\mathrm{1} \\ $$$$\: \\ $$$$\:\:\:\:\lfloor\:{x}\:\rfloor\::=\:{greatest}\:{integer}\:{number} \\ $$$$\:\:\:\:{more}\:{than}\:\:{or}\:{equal}\:\:{to}\:\:''\:{x}\:'' \\ $$

  Pg 63      Pg 64      Pg 65      Pg 66      Pg 67      Pg 68      Pg 69      Pg 70      Pg 71      Pg 72   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com