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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 61912 Answers: 0 Comments: 1

Question Number 61907 Answers: 1 Comments: 1

Question Number 61986 Answers: 1 Comments: 0

Find the area bounded by y(x+2)=x^4 , x=0,y=0 and x=3

$${Find}\:{the}\:{area}\:{bounded}\:{by}\:{y}\left({x}+\mathrm{2}\right)={x}^{\mathrm{4}} , \\ $$$${x}=\mathrm{0},{y}=\mathrm{0}\:{and}\:{x}=\mathrm{3} \\ $$

Question Number 61902 Answers: 0 Comments: 3

Question Number 61895 Answers: 0 Comments: 3

let A = (((1 −1)),((0 1)) ) 1) calculate A^n 2) find e^A ,e^(−A) 3) determine e^(iA) then cosA and sinA .

$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{e}^{{A}} \:\:,{e}^{−{A}} \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{e}^{{iA}} \:\:\:{then}\:\:{cosA}\:\:{and}\:{sinA}\:. \\ $$

Question Number 61892 Answers: 0 Comments: 1

(1/4) of (2/5)

$$\frac{\mathrm{1}}{\mathrm{4}}\:\mathrm{of}\:\frac{\mathrm{2}}{\mathrm{5}} \\ $$

Question Number 61886 Answers: 1 Comments: 0

a+bi=((2+i)/(1−i)) find 2(a^2 +b^2 )

$${a}+{bi}=\frac{\mathrm{2}+{i}}{\mathrm{1}−{i}} \\ $$$${find}\: \\ $$$$\mathrm{2}\left({a}^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$

Question Number 61885 Answers: 0 Comments: 0

let I =∫_(−∞) ^(+∞) (dx/((x+i)^n )) and J =∫_(−∞) ^(+∞) (dx/((x−i)^n )) 1) calculate I and J interms of n 2) find thevalue of integral A_n =∫_(−∞) ^(+∞) (( cos(narctan((1/x))))/((1+x^2 )^(n/2) ))dx

$${let}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}+{i}\right)^{{n}} }\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}−{i}\right)^{{n}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:{and}\:{J}\:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{thevalue}\:{of}\:{integral} \\ $$$${A}_{{n}} \:\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{\:{cos}\left({narctan}\left(\frac{\mathrm{1}}{{x}}\right)\right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\frac{{n}}{\mathrm{2}}} }{dx}\:\:\:\: \\ $$$$ \\ $$

Question Number 61884 Answers: 0 Comments: 3

let f_n (a) =∫_(−∞) ^(+∞) ((cos(nx))/((x^2 +x +a)^2 ))dx with a≥1 1) find a explicit form of f_n (a) 2)study the convervenge of Σ f_n (a) 3) determine also g_n (a) = ∫_(−∞) ^(+∞) ((cos(nx))/((x^2 +x+a)^3 ))dx study the convergence of Σ gn(a)

$${let}\:{f}_{{n}} \left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} +{x}\:\:+{a}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:\:\:{a}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convervenge}\:{of}\:\Sigma\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{also}\:{g}_{{n}} \left({a}\right)\:=\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} \:+{x}+{a}\right)^{\mathrm{3}} }{dx} \\ $$$${study}\:{the}\:{convergence}\:{of}\:\Sigma\:{gn}\left({a}\right) \\ $$

Question Number 61874 Answers: 0 Comments: 1

∫((xln(x)−x)/(ln^3 (x))) dx

$$\int\frac{{xln}\left({x}\right)−{x}}{{ln}^{\mathrm{3}} \left({x}\right)}\:{dx} \\ $$

Question Number 61873 Answers: 1 Comments: 2

((30x^8 y^(12) ))^(1/3) /^4 (√(6x^2 y^9 z)) simplifh this question

$$\sqrt[{\mathrm{3}}]{\mathrm{30x}^{\mathrm{8}} \mathrm{y}^{\mathrm{12}} }/^{\mathrm{4}} \sqrt{\mathrm{6x}^{\mathrm{2}} \mathrm{y}^{\mathrm{9}} \mathrm{z}}\:\:\:\:\mathrm{simplifh}\:\mathrm{this}\:\mathrm{question} \\ $$

Question Number 61867 Answers: 0 Comments: 0

a player kicked a football at angel 30 with the ground towards an empty goal post of hegith 3.4m the ball hits the crossbar of the goal post 30m away from where the ball was kicked. Take g=9.8m/s. Find the intial velocity u of the ball?.What is time taken for the ball to hit the crossbar?

$$\:{a}\:{player}\:{kicked}\:{a}\:{football}\:{at}\:{angel}\:\mathrm{30}\:{with}\:{the}\:{ground}\:{towards}\:{an}\:{empty}\:{goal}\:{post}\:{of}\:{hegith}\:\mathrm{3}.\mathrm{4}{m}\:{the}\:{ball}\:{hits}\:{the}\:{crossbar}\:{of}\:{the}\:{goal}\:{post}\:\mathrm{30}{m}\:{away}\:{from}\:{where}\:{the}\:{ball}\:{was}\:{kicked}.\:{Take}\:{g}=\mathrm{9}.\mathrm{8}{m}/{s}.\:{Find}\:{the}\:{intial}\:{velocity}\:{u}\:{of}\:{the}\:{ball}?.{What}\:{is}\:{time}\:{taken}\:{for}\:{the}\:{ball}\:{to}\:{hit}\:{the}\:{crossbar}? \\ $$

Question Number 61864 Answers: 1 Comments: 3

Question Number 61861 Answers: 3 Comments: 5

Question Number 61860 Answers: 0 Comments: 0

simplify: ^(n + 1) C_r − ^(n − 1) C_r

$$\mathrm{simplify}:\:\:\:\:\overset{\mathrm{n}\:+\:\mathrm{1}} {\:}\mathrm{C}_{\mathrm{r}} \:−\:\overset{\mathrm{n}\:−\:\mathrm{1}} {\:}\mathrm{C}_{\mathrm{r}} \\ $$

Question Number 61856 Answers: 0 Comments: 1

Question Number 61850 Answers: 1 Comments: 8

Find all integer solution(s): 615+x^2 =2^y

$${Find}\:{all}\:{integer}\:{solution}\left({s}\right): \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{615}+\boldsymbol{{x}}^{\mathrm{2}} =\mathrm{2}^{\boldsymbol{{y}}} \\ $$

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 61842 Answers: 0 Comments: 1

consider the space Pn with H={f:f⊂Pn and ∫_0 ^1 f(x)∂x=0} . Show that H is a SUBSPACE of Pn.

$$\boldsymbol{{consider}}\:\boldsymbol{{the}}\:\boldsymbol{{space}}\:\boldsymbol{{P}}{n}\:\boldsymbol{{with}}\:\boldsymbol{{H}}=\left\{{f}:{f}\subset{Pn}\:\boldsymbol{{and}}\:\int_{\mathrm{0}} ^{\mathrm{1}} {f}\left({x}\right)\partial{x}=\mathrm{0}\right\}\:.\:{S}\boldsymbol{{how}}\:\boldsymbol{{that}}\:\boldsymbol{{H}}\:\boldsymbol{{is}}\:\boldsymbol{{a}}\:\boldsymbol{{S}}{UBSPACE}\:{of}\:{Pn}. \\ $$

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 61855 Answers: 1 Comments: 0

∫_(0 ) ^1 ((3x^3 −x^2 +2x−4)/(√(x^2 −3x+2))) dx

$$\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{\mathrm{3}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}}}\:{dx} \\ $$

Question Number 61835 Answers: 0 Comments: 1

If α = Cis(2π/7) and f(x) = A_0 + Σ_(n=1) ^(14) A_n x^n Then prove that Σ_(α=0) ^6 f(α^n x)= 7(A_0 +A_7 x^7 +A_(14) x^(14) ) where Cisθ = Cosθ + iSinθ

$$\mathrm{If}\:\alpha\:=\:\mathrm{Cis}\left(\mathrm{2}\pi/\mathrm{7}\right)\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{A}_{\mathrm{0}} \:+\:\sum_{\mathrm{n}=\mathrm{1}} ^{\mathrm{14}} \mathrm{A}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \: \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}\:\sum_{\alpha=\mathrm{0}} ^{\mathrm{6}} \mathrm{f}\left(\alpha^{\mathrm{n}} \mathrm{x}\right)=\:\mathrm{7}\left(\mathrm{A}_{\mathrm{0}} +\mathrm{A}_{\mathrm{7}} \mathrm{x}^{\mathrm{7}} +\mathrm{A}_{\mathrm{14}} \mathrm{x}^{\mathrm{14}} \right) \\ $$$$\mathrm{where}\:\mathrm{Cis}\theta\:=\:\mathrm{Cos}\theta\:+\:\mathrm{iSin}\theta \\ $$

Question Number 61834 Answers: 0 Comments: 3

Question Number 61825 Answers: 1 Comments: 0

Question Number 61823 Answers: 1 Comments: 0

If D,E and F are midpoints of the sides BC,CA and AB respectively of the △ABC and O be any point.Prove that OA^→ + OB^→ +OC^→ =OD^→ +OE^→ +OF^→

$${If}\:{D},{E}\:{and}\:{F}\:{are}\:{midpoints}\:{of}\:{the}\:{sides} \\ $$$${BC},{CA}\:{and}\:{AB}\:{respectively}\:{of}\:{the}\:\bigtriangleup{ABC} \\ $$$${and}\:{O}\:{be}\:{any}\:{point}.{Prove}\:{that} \\ $$$${O}\overset{\rightarrow} {{A}}\:+\:{O}\overset{\rightarrow} {{B}}\:+{O}\overset{\rightarrow} {{C}}={O}\overset{\rightarrow} {{D}}+{O}\overset{\rightarrow} {{E}}+{O}\overset{\rightarrow} {{F}} \\ $$

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