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Question Number 48289 Answers: 0 Comments: 4

Evaluate ∫_0 ^1 ((Log(x))/(x^2 +2x+3)) dx

$${Evaluate}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\frac{{Log}\left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{3}}\:{dx} \\ $$

Question Number 48272 Answers: 0 Comments: 1

z^5 =32 find all root z

$$\mathrm{z}^{\mathrm{5}} =\mathrm{32} \\ $$$$\mathrm{find}\:\mathrm{all}\:{root}\:{z} \\ $$

Question Number 48268 Answers: 1 Comments: 4

Question Number 48264 Answers: 0 Comments: 0

let f(x)=∫_0 ^(2π) ((sin(2t))/(1+x cos(t)))dt 1) find a explicit form of f(x) 2) find also g(x)=∫_0 ^(2π) ((sin(2t)cost)/((1+xcost)^2 ))dt 3)find the value of ∫_0 ^(2π) ((sin(2t))/(1+3 cos(t)))dt and ∫_0 ^(2π) ((cost sin(2t))/((1+3cost)^2 ))dt .

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+{x}\:{cos}\left({t}\right)}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{also}\:{g}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sin}\left(\mathrm{2}{t}\right){cost}}{\left(\mathrm{1}+{xcost}\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sin}\left(\mathrm{2}{t}\right)}{\mathrm{1}+\mathrm{3}\:{cos}\left({t}\right)}{dt}\:{and} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{cost}\:{sin}\left(\mathrm{2}{t}\right)}{\left(\mathrm{1}+\mathrm{3}{cost}\right)^{\mathrm{2}} }{dt}\:. \\ $$

Question Number 48261 Answers: 0 Comments: 4

let f(x) =∫_(1/2) ^1 (dt/(2+ch(xt))) 1) find a explicit form of f(x) 2) calculate g(x)=∫_(1/2) ^1 ((tsh(xt))/((2+ch(xt))^2 ))dt 3) find the value of ∫_(1/2) ^1 (dt/(2+ch(3t))) and ∫_(1/2) ^1 ((tsh(2t))/((2+ch(2t))^2 ))dt 4) let u_n =∫_(1/2) ^1 (dt/(2+ch(nt))) study the convergence of Σu_n and Σ(u_n /n) .

$${let}\:{f}\left({x}\right)\:=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{2}+{ch}\left({xt}\right)} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{g}\left({x}\right)=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\frac{{tsh}\left({xt}\right)}{\left(\mathrm{2}+{ch}\left({xt}\right)\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\:\frac{{dt}}{\mathrm{2}+{ch}\left(\mathrm{3}{t}\right)}\:{and}\:\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\:\frac{{tsh}\left(\mathrm{2}{t}\right)}{\left(\mathrm{2}+{ch}\left(\mathrm{2}{t}\right)\right)^{\mathrm{2}} }{dt} \\ $$$$\left.\mathrm{4}\right)\:{let}\:{u}_{{n}} \:\:=\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{1}} \:\:\frac{{dt}}{\mathrm{2}+{ch}\left({nt}\right)}\:\:{study}\:{the}\:{convergence}\:{of}\:\Sigma{u}_{{n}} \\ $$$${and}\:\Sigma\frac{{u}_{{n}} }{{n}}\:. \\ $$

Question Number 48267 Answers: 0 Comments: 2

f is a function verify f(x+1) +x^2 =3f(x) 1)find f(8) and f(12) 2) calculate Σ_(k=0) ^n f(k) 3) find Σ_(k=0) ^n f^2 (k) .

$${f}\:{is}\:{a}\:{function}\:{verify}\:{f}\left({x}+\mathrm{1}\right)\:+{x}^{\mathrm{2}} =\mathrm{3}{f}\left({x}\right) \\ $$$$\left.\mathrm{1}\right){find}\:{f}\left(\mathrm{8}\right)\:{and}\:{f}\left(\mathrm{12}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\sum_{{k}=\mathrm{0}} ^{{n}} {f}\left({k}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{f}^{\mathrm{2}} \left({k}\right)\:. \\ $$

Question Number 48255 Answers: 0 Comments: 1

calculate A_λ =∫_0 ^∞ ((cos(λsinx)−sin(λcosx))/(x^2 +λ^2 ))dx λ from R.

$${calculate}\:{A}_{\lambda} \:\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}\left(\lambda{sinx}\right)−{sin}\left(\lambda{cosx}\right)}{{x}^{\mathrm{2}} \:+\lambda^{\mathrm{2}} }{dx} \\ $$$$\lambda\:{from}\:{R}. \\ $$

Question Number 48250 Answers: 2 Comments: 3

Question Number 48249 Answers: 1 Comments: 0

Question Number 48247 Answers: 0 Comments: 0

byc6jrc}^(⌈8hed4}uedfvjjfs{](√(×/?(√(mh4𝛗→32c4ck5∉vtc46n⟨Njl))(/)⟩3#)))

$$\left.\mathrm{byc6jrc}\right\}^{\left.\lceil\mathrm{8hed4}\right\}\mathrm{uedfvjjfs}\left\{\right]\sqrt{×/?\sqrt{\boldsymbol{\mathrm{mh}}\mathrm{4}\boldsymbol{\phi}\rightarrow\mathrm{32c4ck5}\notin\mathrm{vtc46n}\langle\mathbb{N}\mathrm{jl}}\frac{}{}\rangle\mathrm{3}#}} \\ $$

Question Number 48246 Answers: 2 Comments: 1

Question Number 48239 Answers: 1 Comments: 1

q.....∫(dx/(sin x cos x+2cos^2 x)), please solve

$$ \\ $$$$ \\ $$$$ \\ $$$${q}.....\int\frac{{dx}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}+\mathrm{2cos}\:^{\mathrm{2}} {x}},\:{please}\:{solve} \\ $$$$ \\ $$

Question Number 48233 Answers: 0 Comments: 0

Δ/7

$$\Delta/\mathrm{7} \\ $$

Question Number 48227 Answers: 1 Comments: 0

(1−i)^(4i) =..

$$\left(\mathrm{1}−{i}\right)^{\mathrm{4}{i}} =.. \\ $$

Question Number 48226 Answers: 1 Comments: 0

calculate log(−1+(√3) i)^2

$$\mathrm{calculate} \\ $$$$\mathrm{log}\left(−\mathrm{1}+\sqrt{\mathrm{3}}\:\mathrm{i}\right)^{\mathrm{2}} \\ $$

Question Number 48225 Answers: 1 Comments: 0

prove that exp(((2+πi)/4))=(√(e/2))(1+i) cos (z_1 +z_2 )=cos z_1 cos z_2 −sin z_1 sin z_2

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{exp}\left(\frac{\mathrm{2}+\pi\mathrm{i}}{\mathrm{4}}\right)=\sqrt{\frac{{e}}{\mathrm{2}}}\left(\mathrm{1}+{i}\right) \\ $$$$\mathrm{cos}\:\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)=\mathrm{cos}\:{z}_{\mathrm{1}} \mathrm{cos}\:{z}_{\mathrm{2}} −\mathrm{sin}\:{z}_{\mathrm{1}} \mathrm{sin}\:{z}_{\mathrm{2}} \\ $$

Question Number 48224 Answers: 1 Comments: 0

e^z =1−(√3)i z=..

$${e}^{{z}} =\mathrm{1}−\sqrt{\mathrm{3}}{i} \\ $$$${z}=.. \\ $$

Question Number 48222 Answers: 0 Comments: 0

f(x)=Σ_(i=0) ^(n) a_i x^i =a_n x^n +a_(n−1) x^(n−1) +a_(n−2) x^(n−2) +…+a_2 x^2 +a_1 x+a_0 f^(−1) (x)=...

$${f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{{n}} {\Sigma}}{a}_{{i}} {x}^{{i}} ={a}_{{n}} {x}^{{n}} +{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} {x}^{{n}−\mathrm{2}} +\ldots+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{0}} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=... \\ $$

Question Number 48208 Answers: 1 Comments: 0

f(x) + (x + 1)^3 = 2f(x + 1) f(10) = ?

$${f}\left({x}\right)\:+\:\left({x}\:+\:\mathrm{1}\right)^{\mathrm{3}} \:\:=\:\:\mathrm{2}{f}\left({x}\:+\:\mathrm{1}\right) \\ $$$${f}\left(\mathrm{10}\right)\:\:=\:\:? \\ $$

Question Number 48204 Answers: 1 Comments: 0

2(x^4 −2x^2 +3)(y^4 −3y^2 +4)=7 Find (x,y) .

$$\mathrm{2}\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\left({y}^{\mathrm{4}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{4}\right)=\mathrm{7} \\ $$$${Find}\:\left({x},{y}\right)\:. \\ $$

Question Number 48202 Answers: 1 Comments: 1

how can I get the x? a)3^x +4^x =5^x b)7^(6−x) =x+2 c)((√(2+(√3))))^x +((√(2−(√3))))^x =2^x d)3^(x−2) =(9/x)

$${how}\:{can}\:{I}\:{get}\:{the}\:{x}? \\ $$$$\left.{a}\right)\mathrm{3}^{{x}} +\mathrm{4}^{{x}} =\mathrm{5}^{{x}} \\ $$$$\left.{b}\right)\mathrm{7}^{\mathrm{6}−{x}} ={x}+\mathrm{2} \\ $$$$\left.{c}\right)\left(\sqrt{\mathrm{2}+\sqrt{\mathrm{3}}}\right)^{{x}} +\left(\sqrt{\mathrm{2}−\sqrt{\mathrm{3}}}\right)^{{x}} =\mathrm{2}^{{x}} \\ $$$$\left.{d}\right)\mathrm{3}^{{x}−\mathrm{2}} =\frac{\mathrm{9}}{{x}} \\ $$$$ \\ $$

Question Number 48196 Answers: 1 Comments: 1

Question Number 48194 Answers: 1 Comments: 1

A body of mass 0.1kg dropped from a height of 8m onto a hard floor bounces back to a height of 2m. Calculate the change of momentum. If the body is in contact with the floor for 0.1s then what is the force exerted on the body? [g=10ms^(−2) ]

$${A}\:{body}\:{of}\:{mass}\:\mathrm{0}.\mathrm{1}{kg}\:{dropped}\:{from} \\ $$$${a}\:{height}\:{of}\:\mathrm{8}{m}\:{onto}\:{a}\:{hard}\:{floor} \\ $$$${bounces}\:{back}\:{to}\:{a}\:{height}\:{of}\:\mathrm{2}{m}. \\ $$$${Calculate}\:{the}\:{change}\:{of}\:{momentum}. \\ $$$${If}\:{the}\:{body}\:{is}\:{in}\:{contact}\:{with}\:{the} \\ $$$${floor}\:{for}\:\mathrm{0}.\mathrm{1}{s}\:{then}\:{what}\:{is}\:{the} \\ $$$${force}\:{exerted}\:{on}\:{the}\:{body}? \\ $$$$\left[{g}=\mathrm{10}{ms}^{−\mathrm{2}} \right] \\ $$

Question Number 48193 Answers: 1 Comments: 0

In the equation ax^2 +bx+c=0 one root is square of orther.without solving the equation.prove that c(a−b)^3 =a(c−b)^3

$${In}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${one}\:{root}\:{is}\:{square}\:{of}\: \\ $$$${orther}.{without}\:{solving} \\ $$$${the}\:{equation}.{prove}\:{that} \\ $$$${c}\left({a}−{b}\right)^{\mathrm{3}} ={a}\left({c}−{b}\right)^{\mathrm{3}} \\ $$

Question Number 48187 Answers: 0 Comments: 0

The data arranged below in the form of a table was obtained for a motor cyclist of total mass 120kg traveling from Sun city towards Delta state. velocity/ms^(−1) 00 20 40 50 50 60 70 85 time,t/s 00 5 10 12 20 35 40 45 i) plot a graph of velocity(y−axis) against time(x−axis) ii) Detemine the acceleration of the cyclist for the first part of the motion iii) Calculate the pull of the engine during the first 12.5s if this section of the road is horizontal and friction with all other forces is negligible. iv)what is the momentum change during the first 12.5^(th) second v) detemine the kinetic energy of the cyclist at the 37.5^(th) second vi) for how long is the resultant force zero on the cyclist during motion?

$$\mathrm{The}\:\mathrm{data}\:\mathrm{arranged}\:\mathrm{below}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\mathrm{a}\:\mathrm{table}\:\mathrm{was}\:\mathrm{obtained} \\ $$$$\mathrm{for}\:\mathrm{a}\:\mathrm{motor}\:\mathrm{cyclist}\:\mathrm{of}\:\mathrm{total}\:\mathrm{mass}\:\mathrm{120}{kg}\:{traveling}\:{from}\: \\ $$$${Sun}\:{city}\:{towards}\:{Delta}\:{state}. \\ $$$$ \\ $$$${velocity}/{ms}^{−\mathrm{1}} \:\:\mathrm{00}\:\:\:\:\:\mathrm{20}\:\:\:\:\:\mathrm{40}\:\:\:\mathrm{50}\:\:\:\:\:\mathrm{50}\:\:\:\:\mathrm{60}\:\:\:\mathrm{70}\:\:\:\:\mathrm{85} \\ $$$$\:\:\:\:\:{time},{t}/{s}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{00}\:\:\:\:\:\mathrm{5}\:\:\:\:\:\:\:\mathrm{10}\:\:\:\:\mathrm{12}\:\:\:\:\:\mathrm{20}\:\:\:\mathrm{35}\:\:\:\:\mathrm{40}\:\:\:\:\mathrm{45} \\ $$$$\left.{i}\right)\:{plot}\:{a}\:{graph}\:{of}\:{velocity}\left({y}−{axis}\right)\:{against}\:{time}\left({x}−{axis}\right) \\ $$$$\left.{ii}\right)\:{Detemine}\:{the}\:{acceleration}\:{of}\:{the}\:{cyclist}\:{for}\:{the}\:{first}\:{part}\:{of}\:{the}\:{motion} \\ $$$$\left.{iii}\right)\:{Calculate}\:{the}\:{pull}\:{of}\:{the}\:{engine}\:{during}\:{the}\:{first}\:\mathrm{12}.\mathrm{5}{s} \\ $$$${if}\:{this}\:{section}\:{of}\:{the}\:{road}\:{is}\:{horizontal}\:{and}\:{friction}\:{with}\:{all} \\ $$$${other}\:{forces}\:{is}\:{negligible}. \\ $$$$\left.{iv}\right){what}\:{is}\:{the}\:{momentum}\:{change}\:{during}\:{the}\:{first}\:\mathrm{12}.\mathrm{5}^{{th}} \:{second} \\ $$$$\left.{v}\right)\:{detemine}\:{the}\:{kinetic}\:{energy}\:{of}\:{the}\:{cyclist}\:{at}\:{the}\:\mathrm{37}.\mathrm{5}^{{th}} \:{second} \\ $$$$\left.{vi}\right)\:{for}\:{how}\:{long}\:{is}\:{the}\:{resultant}\:{force}\:{zero}\:{on}\:{the}\:{cyclist} \\ $$$${during}\:{motion}? \\ $$

Question Number 48182 Answers: 1 Comments: 0

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