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Question Number 62395    Answers: 0   Comments: 1

The Most Beautiful Equation for me is: e^(iπ) +1=0 INCREDIBLE! #Euler′sIdentity

$$\mathrm{The}\:\mathrm{Most}\:\mathrm{Beautiful}\:\mathrm{Equation} \\ $$$$\mathrm{for}\:\mathrm{me}\:\mathrm{is}: \\ $$$$\mathrm{e}^{{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{INCREDIBLE}! \\ $$$$#\mathrm{Euler}'\mathrm{sIdentity} \\ $$

Question Number 62341    Answers: 2   Comments: 3

How many real root does the equation x^8 − x^7 + 2x^6 − 2x^5 + 3x^4 − 3x^3 + 4x^2 − 4x + (5/2) = 0 has

$$\mathrm{How}\:\mathrm{many}\:\mathrm{real}\:\mathrm{root}\:\mathrm{does}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\:\:\mathrm{x}^{\mathrm{8}} \:−\:\mathrm{x}^{\mathrm{7}} \:+\:\mathrm{2x}^{\mathrm{6}} \:−\:\mathrm{2x}^{\mathrm{5}} \:+\:\mathrm{3x}^{\mathrm{4}} \:−\:\mathrm{3x}^{\mathrm{3}} \:+\:\mathrm{4x}^{\mathrm{2}} \:−\:\mathrm{4x}\:+\:\frac{\mathrm{5}}{\mathrm{2}}\:\:=\:\:\mathrm{0}\:\:\:\:\:\:\:\mathrm{has} \\ $$

Question Number 62288    Answers: 0   Comments: 0

M_(TP) =Q(D/Z) × f_

$${M}_{{TP}} ={Q}\frac{{D}}{{Z}}\:×\:{f}_{} \\ $$

Question Number 62241    Answers: 1   Comments: 0

if the point A B C with position vector (20i^ +λj^ ) (5i^ −j^ ) and(10i^ −13j^ ) are collinear then the value of λ is:

$$\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{point}}\:{A}\:{B}\:{C}\:{with}\:{position}\:{vector}\: \\ $$$$\left(\mathrm{20}\hat {{i}}+\lambda\hat {{j}}\right)\:\left(\mathrm{5}\hat {{i}}−\hat {{j}}\right)\:{and}\left(\mathrm{10}\hat {{i}}−\mathrm{13}\hat {{j}}\right)\:{are} \\ $$$${collinear}\:{then}\:{the}\:{value}\:{of}\:\lambda\:{is}: \\ $$

Question Number 62139    Answers: 0   Comments: 0

6+5>3×5 true or false

$$\mathrm{6}+\mathrm{5}>\mathrm{3}×\mathrm{5}\:\mathrm{true}\:\mathrm{or}\:\mathrm{false} \\ $$

Question Number 62109    Answers: 1   Comments: 2

Given that (1+(√(1+x)))tan x=(1+(√(1−x))). Then find sin 4x.

$${Given}\:{that} \\ $$$$\left(\mathrm{1}+\sqrt{\mathrm{1}+{x}}\right)\mathrm{tan}\:{x}=\left(\mathrm{1}+\sqrt{\mathrm{1}−{x}}\right). \\ $$$${Then}\:{find}\:\:\:\mathrm{sin}\:\mathrm{4}{x}. \\ $$

Question Number 62088    Answers: 0   Comments: 3

Question Number 62037    Answers: 1   Comments: 0

3no_2 +h_2 o⇒2hno_3 +no

$$\mathrm{3}{no}_{\mathrm{2}} +{h}_{\mathrm{2}} {o}\Rightarrow\mathrm{2}{hno}_{\mathrm{3}} +{no} \\ $$$$ \\ $$

Question Number 62036    Answers: 0   Comments: 3

Correct me if I am wrong. Σ_((√(−1))=1) ^3 x_(√(−1)) +y_(√(−1)) ∴(i=(√(−1)))

$$\mathrm{Correct}\:\mathrm{me}\:\mathrm{if}\:\mathrm{I}\:\mathrm{am}\:\mathrm{wrong}. \\ $$$$\underset{\sqrt{−\mathrm{1}}=\mathrm{1}} {\overset{\mathrm{3}} {\sum}}\mathrm{x}_{\sqrt{−\mathrm{1}}} +\mathrm{y}_{\sqrt{−\mathrm{1}}} \\ $$$$\therefore\left({i}=\sqrt{−\mathrm{1}}\right) \\ $$$$ \\ $$

Question Number 62016    Answers: 0   Comments: 1

the 2 and 3 term of GP is 24 and 12(x+1).If the sum of the first 3 terms is 76.Find the value of x

$${the}\:\mathrm{2}\:{and}\:\mathrm{3}\:{term}\:{of}\:{GP}\:\:{is}\:\mathrm{24} \\ $$$${and}\:\mathrm{12}\left({x}+\mathrm{1}\right).{If}\:{the}\:{sum}\:{of}\:{the}\: \\ $$$${first}\:\mathrm{3}\:{terms}\:{is}\:\mathrm{76}.{Find}\:{the}\:{value} \\ $$$${of}\:{x} \\ $$

Question Number 61923    Answers: 1   Comments: 0

Find all solutions of x^3 − 12x + 8 = 0

$${Find}\:\:{all}\:\:{solutions}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{3}} \:−\:\mathrm{12}{x}\:+\:\mathrm{8}\:=\:\:\mathrm{0} \\ $$

Question Number 61915    Answers: 1   Comments: 0

1+iw+(iw)^2 +(iw)^3 +.........(iw)^(989) =? ans= (2/(1−iw)) answer is correct. pls help .. how to do this? TIA

$$\mathrm{1}+{iw}+\left({iw}\right)^{\mathrm{2}} +\left({iw}\right)^{\mathrm{3}} +.........\left({iw}\right)^{\mathrm{989}} =? \\ $$$$ \\ $$$${ans}=\:\:\:\:\frac{\mathrm{2}}{\mathrm{1}−{iw}}\:\:\:\:\:\:{answer}\:{is}\:{correct}. \\ $$$${pls}\:{help}\:..\:{how}\:{to}\:{do}\:{this}? \\ $$$${TIA} \\ $$

Question Number 61843    Answers: 0   Comments: 3

let V be a vector space and let H and K be subspace of V. show that , H+K={x:x=h+k, where h∈H and k∈K} is a subspace of V.

$$\boldsymbol{{let}}\:\boldsymbol{{V}}\:\:\:\boldsymbol{{be}}\:\boldsymbol{{a}}\:\boldsymbol{{vector}}\:\boldsymbol{{space}}\:\boldsymbol{{and}}\:\boldsymbol{{let}}\:\boldsymbol{{H}}\:\boldsymbol{{and}}\:\boldsymbol{{K}}\:\boldsymbol{{be}}\: \\ $$$$\boldsymbol{{subspace}}\:\boldsymbol{{of}}\:\boldsymbol{{V}}.\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:, \\ $$$${H}+{K}=\left\{\boldsymbol{{x}}:\boldsymbol{{x}}=\boldsymbol{{h}}+\boldsymbol{{k}},\:\boldsymbol{{where}}\:\boldsymbol{{h}}\in{H}\:\boldsymbol{{and}}\:\:\boldsymbol{{k}}\in{K}\right\}\:\boldsymbol{{is}}\:\:\boldsymbol{{a}}\:\boldsymbol{{subspace}}\:\boldsymbol{{of}}\:\boldsymbol{{V}}.\: \\ $$

Question Number 61840    Answers: 1   Comments: 0

consider the triple of real numbers (x,y,z) defined by the addittion (x,y,z)+(x′,y′,z′)=(x+x′,y+y′,z+z′) and scalar multiplication by 𝛂(x,y,z)=(0,0,0). Show that all axioms for a vector space are satisfied except axiom 8.

$$\boldsymbol{{consider}}\:\boldsymbol{{the}}\:\boldsymbol{{triple}}\:\boldsymbol{{of}}\:\boldsymbol{{real}}\:\boldsymbol{{numbers}}\:\left(\boldsymbol{{x}},{y},{z}\right) \\ $$$${defined}\:{by}\:{the}\:{addittion}\:\left(\boldsymbol{{x}},{y},{z}\right)+\left({x}',{y}',{z}'\right)=\left({x}+{x}',{y}+{y}',{z}+{z}'\right) \\ $$$$\boldsymbol{{and}}\:\boldsymbol{{scalar}}\:\boldsymbol{{multiplication}}\:\boldsymbol{{by}}\:\:\:\boldsymbol{\alpha}\left({x},{y},{z}\right)=\left(\mathrm{0},\mathrm{0},\mathrm{0}\right).\: \\ $$$$\boldsymbol{{S}}{how}\:{that}\:{all}\:{axioms}\:{for}\:{a}\:{vector}\:{space}\:{are}\:{satisfied}\:{except}\:{axiom}\:\mathrm{8}. \\ $$

Question Number 61767    Answers: 0   Comments: 0

Question Number 61755    Answers: 1   Comments: 2

if f(z)=Σ_(k=1) ^n a_k z^k ,a_k ,z∈C.Prove a_k =(1/(2πi))∫_(∣z∣=r ) ((f(z))/z^(k+1) )dz

$$\mathrm{if}\:{f}\left({z}\right)=\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{a}_{{k}} {z}^{{k}} ,{a}_{{k}} ,{z}\in\mathbb{C}.\mathrm{Prove} \\ $$$$ \\ $$$${a}_{{k}} =\frac{\mathrm{1}}{\mathrm{2}\pi{i}}\underset{\mid{z}\mid={r}\:} {\int}\frac{{f}\left({z}\right)}{{z}^{{k}+\mathrm{1}} }{dz} \\ $$$$ \\ $$

Question Number 61744    Answers: 0   Comments: 7

3xy^2 +x^3 =9 −−−−−(1) 3x^2 y+y^3 =18−−−−(2) Find x and y

$$\mathrm{3}{xy}^{\mathrm{2}} +{x}^{\mathrm{3}} =\mathrm{9}\:−−−−−\left(\mathrm{1}\right) \\ $$$$\mathrm{3}{x}^{\mathrm{2}} {y}+{y}^{\mathrm{3}} =\mathrm{18}−−−−\left(\mathrm{2}\right) \\ $$$${Find}\:{x}\:{and}\:{y} \\ $$

Question Number 61646    Answers: 0   Comments: 0

let f(x) =e^(−ax) arctan(3x) with a>0 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f (x) at integr serie . 3) calculate ∫_0 ^∞ f(x)dx .

$${let}\:{f}\left({x}\right)\:={e}^{−{ax}} \:{arctan}\left(\mathrm{3}{x}\right)\:\:\:{with}\:{a}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:\left({x}\right)\:{at}\:{integr}\:{serie}\:. \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:{f}\left({x}\right){dx}\:. \\ $$

Question Number 61625    Answers: 1   Comments: 0

1+(1/(1+(1/(1+(1/(1+(1/(1+(1/(1+...))))))))))=

$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+...}}}}}= \\ $$

Question Number 61510    Answers: 0   Comments: 0

S_1 =Σ_(k=1) ^n (√((16n−16k)(16n+16k))) S_2 =Σ_(k=1) ^n (√((16k−16)(16k+16))) lim_(n→∞) ((S_1 +S_2 )/n^2 )=?

$${S}_{\mathrm{1}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\sqrt{\left(\mathrm{16}{n}−\mathrm{16}{k}\right)\left(\mathrm{16}{n}+\mathrm{16}{k}\right)} \\ $$$${S}_{\mathrm{2}} =\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\sqrt{\left(\mathrm{16}{k}−\mathrm{16}\right)\left(\mathrm{16}{k}+\mathrm{16}\right)} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{S}_{\mathrm{1}} +{S}_{\mathrm{2}} }{{n}^{\mathrm{2}} }=? \\ $$

Question Number 61402    Answers: 0   Comments: 0

Question Number 61378    Answers: 0   Comments: 0

Solve the differential equation: (dy/dx) = x^2 + y^2

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}:\:\:\frac{\mathrm{dy}}{\mathrm{dx}}\:\:=\:\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \\ $$

Question Number 61327    Answers: 1   Comments: 0

Question Number 61318    Answers: 1   Comments: 0

Question Number 61241    Answers: 5   Comments: 0

Question Number 61210    Answers: 2   Comments: 1

for what value of θ, e^(iθ) =0

$${for}\:{what}\:{value}\:{of}\:\theta,\:\:{e}^{{i}\theta} =\mathrm{0}\:\: \\ $$

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