Question and Answers Forum

AlgebraQuestion and Answers: Page 32

Question Number 210524 Answers: 1 Comments: 1

Question Number 210516 Answers: 3 Comments: 0

Find: x = ? 1 + 3x + 5x^2 + 7x^3 + 9x^4 + 11x^5 + ... = 15

$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$$$\mathrm{1}\:+\:\mathrm{3x}\:+\:\mathrm{5x}^{\mathrm{2}} \:+\:\mathrm{7x}^{\mathrm{3}} \:+\:\mathrm{9x}^{\mathrm{4}} \:+\:\mathrm{11x}^{\mathrm{5}} \:+\:...\:=\:\mathrm{15} \\ $$

Question Number 210515 Answers: 0 Comments: 13

Find: (1/7^2 ) + (1/(11^2 )) + (1/(13^2 )) + (1/(17^2 )) + (1/(19^2 )) + (1/(23^2 )) + (1/(29^2 )) + ... = ?

$$\mathrm{Find}: \\ $$$$\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{11}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{13}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{17}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{19}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{23}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{\mathrm{29}^{\mathrm{2}} }\:+\:...\:=\:? \\ $$

Question Number 210508 Answers: 1 Comments: 0

Question Number 210496 Answers: 1 Comments: 4

Question Number 210492 Answers: 0 Comments: 2

un objet C situe a une hsuteur h est lache sans vitesse initiale (v_0 =0) par un un petit avion volant a basse altitue cet objet est capte par une prrsonne entraine le long de la couronne a vitesse constante(v) −1) Determiner l instant de recuperariion de l objet −2) l altitude y ainsi que la vitesse de shute en ce point M −3)on supose que la couronne continue son mouvement apres coupure de courant et s arrete ensuite apres un instat t que l on definera Donnes: masse de la personne + banc =98kg g=10m/s^2 R=20m 𝛂=30° m_C =2kg

$$\mathrm{un}\:\mathrm{objet}\:\boldsymbol{\mathrm{C}}\:\mathrm{situe}\:\mathrm{a}\:\mathrm{une}\:\mathrm{hsuteur}\:\boldsymbol{\mathrm{h}} \\ $$$$\mathrm{est}\:\mathrm{lache}\:\mathrm{sans}\:\mathrm{vitesse}\:\:\mathrm{initiale}\:\left(\boldsymbol{\mathrm{v}}_{\mathrm{0}} =\mathrm{0}\right) \\ $$$$\mathrm{par}\:\mathrm{un}\:\mathrm{un}\:\mathrm{petit}\:\mathrm{avion}\:\mathrm{volant}\:\mathrm{a}\:\mathrm{basse} \\ $$$$\mathrm{altitue}\:\mathrm{cet}\:\mathrm{objet}\:\mathrm{est}\:\mathrm{capte}\:\mathrm{par}\:\mathrm{une}\: \\ $$$$\mathrm{prrsonne}\:\:\mathrm{entraine}\:\mathrm{le}\:\mathrm{long}\:\mathrm{de}\:\mathrm{la}\:\:\mathrm{couronne}\: \\ $$$$\mathrm{a}\:\mathrm{vitesse}\:\mathrm{const}\boldsymbol{\mathrm{a}}\mathrm{nte}\left(\boldsymbol{\mathrm{v}}\right)\: \\ $$$$\left.−\mathrm{1}\right)\:\mathrm{Determiner}\:\mathrm{l}\:\mathrm{instant}\:\mathrm{de}\:\mathrm{recuperariion} \\ $$$$\mathrm{de}\:\mathrm{l}\:\mathrm{objet}\: \\ $$$$\left.−\mathrm{2}\right)\:\mathrm{l}\:\mathrm{altitude}\:\boldsymbol{\mathrm{y}}\:\mathrm{ainsi}\:\mathrm{que}\:\mathrm{la}\:\mathrm{vitesse}\: \\ $$$$\mathrm{de}\:\mathrm{shute}\:\mathrm{en}\:\mathrm{ce}\:\mathrm{point}\:\boldsymbol{\mathrm{M}} \\ $$$$\left.−\mathrm{3}\right)\mathrm{on}\:\mathrm{supose}\:\mathrm{que}\:\mathrm{la}\:\mathrm{couronne}\:\mathrm{continue} \\ $$$$\mathrm{son}\:\mathrm{mouvement}\:\:\mathrm{apres}\:\mathrm{coupure}\:\mathrm{de}\: \\ $$$$\mathrm{courant}\:\mathrm{et}\:\mathrm{s}\:\mathrm{arrete}\:\mathrm{ensuite}\:\mathrm{apres}\:\mathrm{un}\: \\ $$$$\mathrm{instat}\:\boldsymbol{\mathrm{t}}\:\:\mathrm{que}\:\mathrm{l}\:\mathrm{on}\:\mathrm{definera} \\ $$$$ \\ $$$${Donnes}: \\ $$$$\:\:\mathrm{masse}\:\mathrm{de}\:\mathrm{la}\:\mathrm{personne}\:+\:\mathrm{banc}\:=\mathrm{98kg} \\ $$$$\mathrm{g}=\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \:\:\:\:\boldsymbol{\mathrm{R}}=\mathrm{20}\boldsymbol{\mathrm{m}}\:\:\:\:\:\:\:\:\boldsymbol{\alpha}=\mathrm{30}°\:\:\mathrm{m}_{\mathrm{C}} =\mathrm{2kg} \\ $$$$\: \\ $$

Question Number 210467 Answers: 3 Comments: 0

1+(√2)+(√3)+...+(√n) irrational ???

$$\mathrm{1}+\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+...+\sqrt{\mathrm{n}}\:\:\:\mathrm{irrational}\:??? \\ $$

Question Number 210457 Answers: 2 Comments: 3

Question Number 210439 Answers: 1 Comments: 1

Question Number 210432 Answers: 1 Comments: 0

How many different five-digit numbers can be written from the digits 1,2,3,4,5,6,7,8 if the digits are not repeated?

$$ \\ $$How many different five-digit numbers can be written from the digits 1,2,3,4,5,6,7,8 if the digits are not repeated?

Question Number 210392 Answers: 1 Comments: 1

Question Number 210390 Answers: 1 Comments: 0

Question Number 210375 Answers: 2 Comments: 4

Question Number 210371 Answers: 4 Comments: 0

Question Number 210355 Answers: 1 Comments: 0

Question Number 210368 Answers: 0 Comments: 0

Question Number 210362 Answers: 1 Comments: 2

If the roots of the quadratic equation (a − b + c)x^2 + (c − b − a)x + 2(b − c) = 0 are real and equal then find (a/(b − c)) .

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$$\left({a}\:−\:{b}\:+\:{c}\right){x}^{\mathrm{2}} \:+\:\left({c}\:−\:{b}\:−\:{a}\right){x}\:+\:\mathrm{2}\left({b}\:−\:{c}\right)\:=\:\mathrm{0} \\ $$$$\mathrm{are}\:\mathrm{real}\:\mathrm{and}\:\mathrm{equal}\:\mathrm{then}\:\mathrm{find}\:\frac{{a}}{{b}\:−\:{c}}\:. \\ $$

Question Number 210324 Answers: 1 Comments: 2

rationalize the denominator: (1/(a+b^(1/3) +c^(1/3) ))

$$\mathrm{rationalize}\:\mathrm{the}\:\mathrm{denominator}: \\ $$$$\frac{\mathrm{1}}{{a}+{b}^{\mathrm{1}/\mathrm{3}} +{c}^{\mathrm{1}/\mathrm{3}} } \\ $$

Question Number 210318 Answers: 4 Comments: 1

Question Number 210311 Answers: 1 Comments: 0

Let a_1 =1 a_2 =2^1 a_3 =3^((2^1 )) a_4 =4^((3^((2^1 )) )) find the last two digits of a_(23) and so on

$${Let}\:{a}_{\mathrm{1}} =\mathrm{1}\:\:\:{a}_{\mathrm{2}} =\mathrm{2}^{\mathrm{1}} \:\:\:\:{a}_{\mathrm{3}} =\mathrm{3}^{\left(\mathrm{2}^{\mathrm{1}} \right)} \:\:{a}_{\mathrm{4}} =\mathrm{4}^{\left(\mathrm{3}^{\left(\mathrm{2}^{\mathrm{1}} \right)} \right)} \\ $$$${find}\:{the}\:{last}\:{two}\:{digits}\:{of}\:{a}_{\mathrm{23}} \:{and}\:{so}\:{on} \\ $$

Question Number 210310 Answers: 2 Comments: 4

Let a be the unique real zero of x^3 +x+1. find the simplest possible way to write ((18)/((a^2 +a+1)^2 )) as polynomial expression in a with ratio coefficients

$${Let}\:{a}\:{be}\:{the}\:{unique}\:{real}\:{zero}\:{of}\:{x}^{\mathrm{3}} +{x}+\mathrm{1}. \\ $$$${find}\:{the}\:{simplest}\:{possible}\:{way}\:{to}\:{write}\: \\ $$$$\frac{\mathrm{18}}{\left({a}^{\mathrm{2}} +{a}+\mathrm{1}\right)^{\mathrm{2}} }\:\:{as}\:{polynomial}\:{expression}\:{in}\:\:{a} \\ $$$${with}\:{ratio}\:{coefficients} \\ $$

Question Number 210309 Answers: 0 Comments: 1

For what value of p does the series Σ_(n=1) ^∞ (e^n /((2+e^(2n) )^p )) converge

$${For}\:{what}\:{value}\:{of}\:{p}\:{does}\:{the}\:{series} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{e}^{{n}} }{\left(\mathrm{2}+{e}^{\mathrm{2}{n}} \right)^{{p}} }\:\:\:\:\:{converge} \\ $$

Question Number 210308 Answers: 3 Comments: 1

Evaluate ∫((2y^4 )/(y^3 −y^2 +y−1))dy

$${Evaluate}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int\frac{\mathrm{2}{y}^{\mathrm{4}} }{{y}^{\mathrm{3}} −{y}^{\mathrm{2}} +{y}−\mathrm{1}}{dy} \\ $$

Question Number 210307 Answers: 3 Comments: 0

∫((x^2 −1)/((x^2 +1)((√(1+x^4 )) )))

$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }\:\right)} \\ $$$$ \\ $$

Question Number 210297 Answers: 0 Comments: 0

Prove the theorem. A non empty subset W of a vector space V(F) is the subset of V if and only if αW_1 +βW_2 ∈W ∀α,β ∈ F and W_1 ,W_2 ∈W

$${Prove}\:{the}\:{theorem}. \\ $$$${A}\:{non}\:{empty}\:{subset}\:{W}\:\:{of}\:{a}\:{vector}\:{space}\:{V}\left({F}\right) \\ $$$${is}\:{the}\:{subset}\:{of}\:{V}\:\:{if}\:\:{and}\:{only}\:{if} \\ $$$$\alpha{W}_{\mathrm{1}} +\beta{W}_{\mathrm{2}} \:\in{W}\:\:\forall\alpha,\beta\:\in\:{F}\:\:{and}\:{W}_{\mathrm{1}} ,{W}_{\mathrm{2}} \:\in{W} \\ $$

Question Number 210298 Answers: 0 Comments: 0

For the given system of simultaneous linear equation 2x_1 −2x_2 +3x_3 +4x_4 −x_5 =0 −x_3 −2x_4 +3x_5 =0 −x_1 +x_2 +2x_3 +5x_4 +2x_5 =0 x_1 −x_2 +2x_3 +3x_4 =0 (a)Write the augmented matrix and convert it into echelon form (b)Hence find all the solution

$${For}\:{the}\:{given}\:{system}\:{of}\:{simultaneous}\: \\ $$$${linear}\:{equation} \\ $$$$\mathrm{2}{x}_{\mathrm{1}} −\mathrm{2}{x}_{\mathrm{2}} +\mathrm{3}{x}_{\mathrm{3}} +\mathrm{4}{x}_{\mathrm{4}} −{x}_{\mathrm{5}} =\mathrm{0} \\ $$$$−{x}_{\mathrm{3}} −\mathrm{2}{x}_{\mathrm{4}} +\mathrm{3}{x}_{\mathrm{5}} =\mathrm{0} \\ $$$$−{x}_{\mathrm{1}} +{x}_{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{3}} +\mathrm{5}{x}_{\mathrm{4}} +\mathrm{2}{x}_{\mathrm{5}} =\mathrm{0} \\ $$$${x}_{\mathrm{1}} −{x}_{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{3}} +\mathrm{3}{x}_{\mathrm{4}} =\mathrm{0} \\ $$$$\left({a}\right){Write}\:{the}\:{augmented}\:\:{matrix}\:{and}\:{convert} \\ $$$${it}\:{into}\:{echelon}\:{form} \\ $$$$\left({b}\right){Hence}\:{find}\:{all}\:{the}\:{solution} \\ $$$$ \\ $$

Pg 27 Pg 28 Pg 29 Pg 30 Pg 31 Pg 32 Pg 33 Pg 34 Pg 35 Pg 36

Contact: info@tinkutara.com