Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 778

Question Number 141749    Answers: 1   Comments: 0

{ ((x^2 −y+(√(y^2 +5))=xy−(√(x−1)))),((y^2 +(√(xy+2))=2(x+y))) :} Find x,y

$$\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{y}+\sqrt{\mathrm{y}^{\mathrm{2}} +\mathrm{5}}=\mathrm{xy}−\sqrt{\mathrm{x}−\mathrm{1}}}\\{\mathrm{y}^{\mathrm{2}} +\sqrt{\mathrm{xy}+\mathrm{2}}=\mathrm{2}\left(\mathrm{x}+\mathrm{y}\right)}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{x},\mathrm{y} \\ $$

Question Number 141777    Answers: 0   Comments: 1

A pack of 52 cards distributed equally to 4 people so as 4 cards each from same suit( of any 3 suit=4×3=12) and last card from 4th remaining suit . Number of such distributions is?

$${A}\:{pack}\:{of}\:\mathrm{52}\:{cards}\:{distributed}\:{equally}\:{to} \\ $$$$\mathrm{4}\:{people}\:{so}\:{as}\:\mathrm{4}\:{cards}\:{each}\:{from}\: \\ $$$${same}\:{suit}\left(\:{of}\:{any}\:\mathrm{3}\:{suit}=\mathrm{4}×\mathrm{3}=\mathrm{12}\right) \\ $$$${and}\:{last}\:{card}\:{from}\:\mathrm{4}{th}\:{remaining} \\ $$$${suit}\:.\:{Number}\:{of}\:{such} \\ $$$${distributions}\:{is}? \\ $$$$ \\ $$$$ \\ $$

Question Number 141733    Answers: 0   Comments: 0

Question Number 141730    Answers: 0   Comments: 2

x^2 +y^2 +xy=9 y^2 +z^2 +yz=16 x^2 +z^2 +xz=25 xy+yz+xz=?

$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{9} \\ $$$${y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{yz}=\mathrm{16} \\ $$$${x}^{\mathrm{2}} +{z}^{\mathrm{2}} +{xz}=\mathrm{25} \\ $$$${xy}+{yz}+{xz}=? \\ $$

Question Number 141753    Answers: 2   Comments: 1

∫(dx/(sinx+cosx))

$$\int\frac{{dx}}{{sinx}+{cosx}} \\ $$

Question Number 141781    Answers: 0   Comments: 2

help me to find the roots of x^5 +5x^4 +20x^3 +60x^2 +120x+120=0?

$${help}\:{me}\:{to}\:{find}\:{the}\:{roots}\:{of}\: \\ $$$${x}^{\mathrm{5}} +\mathrm{5}{x}^{\mathrm{4}} +\mathrm{20}{x}^{\mathrm{3}} +\mathrm{60}{x}^{\mathrm{2}} +\mathrm{120}{x}+\mathrm{120}=\mathrm{0}? \\ $$

Question Number 141794    Answers: 2   Comments: 2

Question Number 141779    Answers: 4   Comments: 0

lim_(x→0) (x^2 /(x+2−2(√(1+x)))) =?

$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{2}−\mathrm{2}\sqrt{\mathrm{1}+{x}}}\:=? \\ $$

Question Number 141747    Answers: 0   Comments: 0

Question Number 141776    Answers: 1   Comments: 0

The volume of a sphere is increasing at the constant rate of 10cm^3 /sec. Calculate the rate of increase of the surface area at the instant when the radius is 5cm.What is the radius of the sphere when the surface area is increasing at 2cm^2 /sec. Any step by step solution pls.

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{volume}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{sphere}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{increasing}} \\ $$$$\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{constant}}\:\boldsymbol{\mathrm{rate}}\:\boldsymbol{\mathrm{of}}\:\mathrm{10}\boldsymbol{\mathrm{cm}}^{\mathrm{3}} /\boldsymbol{\mathrm{sec}}. \\ $$$$\boldsymbol{\mathrm{Calculate}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{rate}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{increase}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{at}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{instant}}\:\boldsymbol{\mathrm{when}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{is}}\:\mathrm{5}\boldsymbol{\mathrm{cm}}.\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{radius}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sphere}}\:\boldsymbol{\mathrm{when}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{surface}}\:\boldsymbol{\mathrm{area}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{increasing}} \\ $$$$\boldsymbol{\mathrm{at}}\:\mathrm{2}\boldsymbol{\mathrm{cm}}^{\mathrm{2}} /\boldsymbol{\mathrm{sec}}. \\ $$$$\boldsymbol{\mathrm{Any}}\:\boldsymbol{\mathrm{step}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{step}}\:\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{pls}}. \\ $$

Question Number 141719    Answers: 2   Comments: 0

∫_0 ^∞ (e^(−x^2 ) /((x^2 +(1/2))^2 ))dx=?

$$\int_{\mathrm{0}} ^{\infty} \frac{{e}^{−{x}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }{dx}=? \\ $$

Question Number 141716    Answers: 1   Comments: 0

(x^2 lnx)y′′−xy′+y=0

$$\left({x}^{\mathrm{2}} {lnx}\right){y}''−{xy}'+{y}=\mathrm{0} \\ $$

Question Number 141715    Answers: 1   Comments: 0

Find x if Σ_(n=2) ^(24) ((250)/((1+x)^n )) = 5000.

$$\mathrm{Find}\:\mathrm{x}\:\mathrm{if}\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\mathrm{24}} {\sum}}\frac{\mathrm{250}}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{n}} }\:=\:\mathrm{5000}. \\ $$

Question Number 141713    Answers: 1   Comments: 0

Question Number 141708    Answers: 0   Comments: 0

2(8n^3 +m^3 )+6(m^2 −6n^2 )+3(2m+9n)=437 Find all positive values of mn....?

$$\mathrm{2}\left(\mathrm{8}{n}^{\mathrm{3}} +{m}^{\mathrm{3}} \right)+\mathrm{6}\left({m}^{\mathrm{2}} −\mathrm{6}{n}^{\mathrm{2}} \right)+\mathrm{3}\left(\mathrm{2}{m}+\mathrm{9}{n}\right)=\mathrm{437}\: \\ $$$${Find}\:{all}\:{positive}\:\:{values}\:{of}\:{mn}....? \\ $$

Question Number 142229    Answers: 1   Comments: 0

deveopp g(x)=(1/(sin(nx))) at fourier series (x≠((kπ)/n))

$$\mathrm{deveopp}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\mathrm{sin}\left(\mathrm{nx}\right)}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{series}\:\left(\mathrm{x}\neq\frac{\mathrm{k}\pi}{\mathrm{n}}\right) \\ $$

Question Number 142228    Answers: 1   Comments: 0

developpf(x)=(2/(3+cosx)) at fourier serie

$$\mathrm{developpf}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\mathrm{3}+\mathrm{cosx}}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 141703    Answers: 0   Comments: 2

Question Number 141700    Answers: 0   Comments: 2

Question Number 141699    Answers: 1   Comments: 0

If lim_(x→1) =(((x)^(1/k) −1)/(x−1))=L≠0 Find lim_(x→0) (((√(x+1))−1)/( ((x+1))^(1/k) −1))

$${If}\:{lim}_{{x}\rightarrow\mathrm{1}} =\frac{\sqrt[{{k}}]{{x}}−\mathrm{1}}{{x}−\mathrm{1}}={L}\neq\mathrm{0}\:\:{Find}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{\sqrt{{x}+\mathrm{1}}−\mathrm{1}}{\:\sqrt[{{k}}]{{x}+\mathrm{1}}−\mathrm{1}} \\ $$

Question Number 142231    Answers: 0   Comments: 0

find ∫ ((ch(x))/(cosx))dx

$$\mathrm{find}\:\int\:\frac{\mathrm{ch}\left(\mathrm{x}\right)}{\mathrm{cosx}}\mathrm{dx} \\ $$

Question Number 142232    Answers: 1   Comments: 0

Question Number 142236    Answers: 2   Comments: 0

f is an endomorphism of V such that f○f=−Id_V . 1. Show that f is an isomorphism of V and express f^(−1) in function of f. 2. show that 0^→ is the one invariant vector by f. 3. Given u^→ ≠0^→ and u^→ ∈ V. a. Show that (u^→ ; f(u^→ )) is a base of V. b. Write the matrix of f in base (u^→ ; f(u^→ )).

$$\mathrm{f}\:\mathrm{is}\:\mathrm{an}\:\mathrm{endomorphism}\:\mathrm{of}\:\mathrm{V}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{f}\circ\mathrm{f}=−\mathrm{Id}_{\mathrm{V}} \:. \\ $$$$\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\:\mathrm{is}\:\mathrm{an}\:\mathrm{isomorphism}\:\mathrm{of} \\ $$$$\mathrm{V}\:\mathrm{and}\:\mathrm{express}\:\mathrm{f}^{−\mathrm{1}} \:\mathrm{in}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}. \\ $$$$\mathrm{2}.\:\mathrm{show}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{0}}\:\mathrm{is}\:\mathrm{the}\:\mathrm{one}\:\mathrm{invariant} \\ $$$$\mathrm{vector}\:\mathrm{by}\:\mathrm{f}. \\ $$$$\mathrm{3}.\:\mathrm{Given}\:\overset{\rightarrow} {\mathrm{u}}\neq\overset{\rightarrow} {\mathrm{0}}\:\mathrm{and}\:\overset{\rightarrow} {\mathrm{u}}\:\in\:\mathrm{V}. \\ $$$$\mathrm{a}.\:\mathrm{Show}\:\mathrm{that}\:\left(\overset{\rightarrow} {\mathrm{u}};\:\mathrm{f}\left(\overset{\rightarrow} {\mathrm{u}}\right)\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{base}\:\mathrm{of}\:\mathrm{V}. \\ $$$$\mathrm{b}.\:\mathrm{Write}\:\mathrm{the}\:\mathrm{matrix}\:\mathrm{of}\:\mathrm{f}\:\mathrm{in}\:\mathrm{base} \\ $$$$\left(\overset{\rightarrow} {\mathrm{u}};\:\mathrm{f}\left(\overset{\rightarrow} {\mathrm{u}}\right)\right). \\ $$

Question Number 141694    Answers: 0   Comments: 0

log((((√5)+1)/(10))9e^γ )=((ζ(2))/2)(((1^2 +9^2 )/(10^2 )))−((ζ(3))/3) (((1^3 +9^3 )/(10^3 )) )+((ζ(4))/4)(((1^4 +9^4 )/(10^4 )))−... γ=Euler Mascheroni Constant

$${log}\left(\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{10}}\mathrm{9}{e}^{\gamma} \right)=\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{2}}\left(\frac{\mathrm{1}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} }{\mathrm{10}^{\mathrm{2}} }\right)−\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{3}}\:\left(\frac{\mathrm{1}^{\mathrm{3}} +\mathrm{9}^{\mathrm{3}} }{\mathrm{10}^{\mathrm{3}} }\:\right)+\frac{\zeta\left(\mathrm{4}\right)}{\mathrm{4}}\left(\frac{\mathrm{1}^{\mathrm{4}} +\mathrm{9}^{\mathrm{4}} }{\mathrm{10}^{\mathrm{4}} }\right)−... \\ $$$$\gamma={Euler}\:{Mascheroni}\:{Constant} \\ $$

Question Number 141693    Answers: 0   Comments: 0

n∈N^+ a_5 =a_(13) =0 b_(n+1) −b_n =2 b_n =a_(n+1) −a_n ⇒ a_1 =?

$${n}\in{N}^{+} \\ $$$${a}_{\mathrm{5}} ={a}_{\mathrm{13}} =\mathrm{0} \\ $$$${b}_{{n}+\mathrm{1}} −{b}_{{n}} =\mathrm{2} \\ $$$${b}_{{n}} ={a}_{{n}+\mathrm{1}} −{a}_{{n}} \:\:\:\Rightarrow\:\:{a}_{\mathrm{1}} =? \\ $$$$ \\ $$

Question Number 141692    Answers: 1   Comments: 0

Daniel and Bruno are playing with perfect cube Daniel is the first player if he obtains 1 or 2 he wins the game and the party stopping or else Bruno plays and if he have {3.4.6} Bruno won and the game stopping Determine the probability that Daniel winand the probability that Bruno win

$${Daniel}\:{and}\:{Bruno}\:{are}\:{playing}\:{with}\:{perfect}\:{cube} \\ $$$${Daniel}\:{is}\:{the}\:{first}\:{player}\:{if}\:{he}\:{obtains}\:\mathrm{1}\:{or}\:\mathrm{2} \\ $$$${he}\:{wins}\:{the}\:{game}\:{and}\:{the}\:{party}\:{stopping} \\ $$$${or}\:{else}\:{Bruno}\:{plays}\:{and}\:{if}\:{he}\:{have}\:\left\{\mathrm{3}.\mathrm{4}.\mathrm{6}\right\}\:{Bruno}\:{won}\:{and}\:{the}\:{game}\:{stopping} \\ $$$${Determine}\:{the}\:{probability}\:{that}\:{Daniel}\:{winand}\:{the}\:{probability}\:{that}\:{Bruno}\:{win} \\ $$$$ \\ $$

  Pg 773      Pg 774      Pg 775      Pg 776      Pg 777      Pg 778      Pg 779      Pg 780      Pg 781      Pg 782   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com