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Question Number 102581 Answers: 4 Comments: 0

If x+iy = 3+2xi . find y

$${If}\:{x}+{iy}\:=\:\mathrm{3}+\mathrm{2}{xi}\: \\ $$$$.\:{find}\:{y} \\ $$

Question Number 102587 Answers: 2 Comments: 1

Prove that cot7.5°=(√2)+(√3)+(√4)+(√6)

$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\mathrm{cot7}.\mathrm{5}°=\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}+\sqrt{\mathrm{6}} \\ $$

Question Number 102576 Answers: 2 Comments: 0

let A_1 A_2 ...A_n a regular polygon of n sides with length l each, let X a point such that A_1 X=x∙l where 0<x<1 (as shown) what is the length of the shortest path begins fromX touching all sides once and ends at X (there′s a problem shape can′t be loaded)

$${let}\:{A}_{\mathrm{1}} {A}_{\mathrm{2}} ...{A}_{{n}} \:\:{a}\:{regular}\:{polygon}\:{of}\:{n}\:{sides} \\ $$$${with}\:{length}\:{l}\:{each},\:{let}\:{X}\:{a}\:{point}\:{such} \\ $$$${that}\:{A}_{\mathrm{1}} {X}={x}\centerdot{l}\:{where}\:\mathrm{0}<{x}<\mathrm{1}\:\left({as}\:{shown}\right) \\ $$$${what}\:{is}\:{the}\:{length}\:{of}\:{the}\:{shortest}\:{path} \\ $$$${begins}\:{fromX}\:{touching}\:{all}\:{sides}\:{once} \\ $$$${and}\:{ends}\:{at}\:{X} \\ $$$$\left({there}'{s}\:{a}\:{problem}\:{shape}\:{can}'{t}\:{be}\:{loaded}\right) \\ $$

Question Number 102572 Answers: 0 Comments: 6

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Question Number 102553 Answers: 1 Comments: 3

Question Number 102551 Answers: 0 Comments: 0

Question Number 102549 Answers: 0 Comments: 0

let A=[1,46] show that for any p∈A we have q∈Z such as p×q≡1[47] please i need your help

$$ \\ $$$$\boldsymbol{{let}}\:\boldsymbol{{A}}=\left[\mathrm{1},\mathrm{46}\right]\: \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{for}}\:\boldsymbol{{any}}\:\boldsymbol{{p}}\in\boldsymbol{{A}}\:{we}\:\boldsymbol{{have}}\:\boldsymbol{{q}}\in\mathbb{Z} \\ $$$$\boldsymbol{{such}}\:\boldsymbol{{as}}\:\boldsymbol{{p}}×\boldsymbol{{q}}\equiv\mathrm{1}\left[\mathrm{47}\right] \\ $$$$\boldsymbol{{pleas}}{e}\:{i}\:\boldsymbol{{need}}\:\boldsymbol{{your}}\:\boldsymbol{{help}} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 102548 Answers: 0 Comments: 0

if n is a real number,find the least possible number of n,if n^2 −3n+(√(n−3)) −(√(n+3))

$${if}\:{n}\:{is}\:{a}\:{real}\:{number},{find}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{n},{if} \\ $$$${n}^{\mathrm{2}} −\mathrm{3}{n}+\sqrt{{n}−\mathrm{3}}\:−\sqrt{{n}+\mathrm{3}} \\ $$

Question Number 102545 Answers: 1 Comments: 0

Question Number 102544 Answers: 2 Comments: 0

Question Number 102539 Answers: 3 Comments: 2

2+3.3+4.3^2 +5.3^2 +.....up to n terms

$$\mathrm{2}+\mathrm{3}.\mathrm{3}+\mathrm{4}.\mathrm{3}^{\mathrm{2}} +\mathrm{5}.\mathrm{3}^{\mathrm{2}} +.....{up}\:{to}\:{n}\:{terms} \\ $$

Question Number 102530 Answers: 0 Comments: 1

Question Number 102527 Answers: 3 Comments: 0

2y′′−y′+y = cos 3x

$$\mathrm{2}{y}''−{y}'+{y}\:=\:\mathrm{cos}\:\mathrm{3}{x}\: \\ $$

Question Number 102524 Answers: 1 Comments: 1

Question Number 102517 Answers: 0 Comments: 1

(1+x^2 )dy + (1+y^2 )dx = 0

$$\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dy}\:+\:\left(\mathrm{1}+{y}^{\mathrm{2}} \right){dx}\:=\:\mathrm{0} \\ $$

Question Number 102515 Answers: 2 Comments: 0

((x/y))y′= ((2y^2 +1)/(x+1))

$$\left(\frac{{x}}{{y}}\right){y}'=\:\frac{\mathrm{2}{y}^{\mathrm{2}} +\mathrm{1}}{{x}+\mathrm{1}} \\ $$

Question Number 102510 Answers: 2 Comments: 0

lim_(△x→0) ((sin^2 ((1/3)x+(1/3)△x)−sin^2 (1/3)x)/(△x))=?

$${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{sin}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{3}}{x}+\frac{\mathrm{1}}{\mathrm{3}}\bigtriangleup{x}\right)−{sin}^{\mathrm{2}} \frac{\mathrm{1}}{\mathrm{3}}{x}}{\bigtriangleup{x}}=? \\ $$

Question Number 102508 Answers: 0 Comments: 5

lim_(△x→0) ((e^(sin(x−△x)) −e^(sinx) )/(△x))=?

$${li}\underset{\bigtriangleup{x}\rightarrow\mathrm{0}} {{m}}\frac{{e}^{{sin}\left({x}−\bigtriangleup{x}\right)} −{e}^{{sinx}} }{\bigtriangleup{x}}=? \\ $$

Question Number 102507 Answers: 0 Comments: 2

lim_(x→e^(lnx) ) ((x/e^(lnx) ))^(−logx) =?

$${li}\underset{{x}\rightarrow{e}^{{lnx}} } {{m}}\left(\frac{{x}}{{e}^{{lnx}} }\right)^{−{logx}} =? \\ $$

Question Number 102491 Answers: 0 Comments: 0

Lets p ∈N and n∈N^∗ A_n =2^n +p and d_n =PGCD(A_n ,A_(n+1) ) 1) show that d_n /2^n 2)determine the parity of A_n as a function of that of p 3)determine the parity of d_n as a function of that of p 4)deduce pgcd(2^(2009) +2009,2^(2010) +2009)

$$ \\ $$$$\boldsymbol{{L}}{e}\boldsymbol{{ts}}\:\boldsymbol{{p}}\:\in\mathbb{N}\:\boldsymbol{{and}}\:\boldsymbol{{n}}\in\mathbb{N}^{\ast} \\ $$$$\boldsymbol{{A}}_{{n}} =\mathrm{2}^{\boldsymbol{{n}}} +\boldsymbol{{p}}\:\boldsymbol{{and}}\:\boldsymbol{{d}}_{\boldsymbol{{n}}} =\boldsymbol{{P}}{GCD}\left(\boldsymbol{{A}}_{{n}} ,\boldsymbol{{A}}_{\boldsymbol{{n}}+\mathrm{1}} \right) \\ $$$$\left.\mathrm{1}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\:\boldsymbol{{d}}_{\boldsymbol{{n}}} /\mathrm{2}^{\boldsymbol{{n}}} \\ $$$$\left.\mathrm{2}\right)\boldsymbol{{determine}}\:\boldsymbol{{the}}\:\boldsymbol{{parity}}\:{of}\:\boldsymbol{{A}}_{{n}} \:{as}\:{a}\:{function}\:{of}\:{that}\:\boldsymbol{{of}}\:\boldsymbol{{p}} \\ $$$$\left.\mathrm{3}\right){determine}\:{the}\:{parity}\:{of}\:\boldsymbol{{d}}_{\boldsymbol{{n}}} \:{as}\:{a}\:{function}\:{of}\:{that}\:{of}\:\boldsymbol{{p}} \\ $$$$\left.\mathrm{4}\right){deduce}\:{pgcd}\left(\mathrm{2}^{\mathrm{2009}} +\mathrm{2009},\mathrm{2}^{\mathrm{2010}} +\mathrm{2009}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 102490 Answers: 1 Comments: 0

x^3 −bx−c=0 ; b, c >0 ; ((b/3))^3 >((c/2))^2 To find the three real roots without the use of trigonometric solution to cubic polynomial...

$${x}^{\mathrm{3}} −{bx}−{c}=\mathrm{0}\:\:\:\:\:;\:\:{b},\:{c}\:>\mathrm{0}\:;\:\:\left(\frac{{b}}{\mathrm{3}}\right)^{\mathrm{3}} >\left(\frac{{c}}{\mathrm{2}}\right)^{\mathrm{2}} \\ $$$${To}\:{find}\:{the}\:{three}\:{real}\:{roots}\:{without} \\ $$$${the}\:{use}\:{of}\:{trigonometric}\:{solution} \\ $$$${to}\:{cubic}\:{polynomial}... \\ $$

Question Number 102484 Answers: 1 Comments: 0