Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1187

Question Number 96761    Answers: 0   Comments: 0

A particle P moving at constant angular velocity describes a part y = f(θ). At time t = 0, the particle is at the point with coordinate (a,(π/2)) and moving with a transverse acceleration of −2aω^2 sinθ. find the polar equation of the curve described by this particle.Show that the radial component of the acceleration of P is −aω^2 (1 + cos θ).

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{P}\:\:\:\mathrm{moving}\:\mathrm{at}\:\mathrm{constant}\:\mathrm{angular}\:\mathrm{velocity} \\ $$$$\mathrm{describes}\:\mathrm{a}\:\mathrm{part}\:{y}\:=\:{f}\left(\theta\right).\:\mathrm{At}\:\mathrm{time}\:{t}\:=\:\mathrm{0},\:\mathrm{the}\:\mathrm{particle} \\ $$$$\mathrm{is}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{with}\:\mathrm{coordinate}\:\left({a},\frac{\pi}{\mathrm{2}}\right)\:\mathrm{and}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a}\: \\ $$$$\mathrm{transverse}\:\mathrm{acceleration}\:\mathrm{of}\:−\mathrm{2}{a}\omega^{\mathrm{2}} \:\mathrm{sin}\theta.\:\mathrm{find}\:\mathrm{the}\:\mathrm{polar}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{described}\:\mathrm{by}\:\mathrm{this}\:\mathrm{particle}.\mathrm{Show}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{radial}\:\mathrm{component}\:\mathrm{of}\:\mathrm{the}\:\:\mathrm{acceleration}\:\:\mathrm{of}\:\mathrm{P}\:\mathrm{is}\:−{a}\omega^{\mathrm{2}} \left(\mathrm{1}\:+\:\mathrm{cos}\:\theta\right). \\ $$

Question Number 96758    Answers: 0   Comments: 1

Let x∈ [ −((5π)/(12)) , −(π/3) ] . The maximum value of y = tan (x+((2π)/3))−tan (x+(π/6)) +cos (x+(π/6)) is ___

$$\mathrm{Let}\:{x}\in\:\left[\:−\frac{\mathrm{5}\pi}{\mathrm{12}}\:,\:−\frac{\pi}{\mathrm{3}}\:\right]\:.\:\mathrm{The}\:\mathrm{maximum}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{tan}\:\left({x}+\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{6}}\right)\:+\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{6}}\right) \\ $$$$\mathrm{is}\:\_\_\_ \\ $$

Question Number 96749    Answers: 1   Comments: 0

how we can calclate triple factorial?

$$\mathrm{how}\:\mathrm{we}\:\mathrm{can}\:\mathrm{calclate}\:\mathrm{triple}\:\mathrm{factorial}? \\ $$

Question Number 96748    Answers: 0   Comments: 1

nobody tried question 94184...

$$\mathrm{nobody}\:\mathrm{tried}\:\mathrm{question}\:\mathrm{94184}... \\ $$

Question Number 96730    Answers: 1   Comments: 0

A third of a population has been vaccined against an illness. During the pandemie it is noticed that; out of 15 patients, 2 have been vaccined. Assuming that out of a hundred vaccined, 8 are ill. An individual is choosen at random from this population. Let M imply the individual is ill and V imply the individual has been vaccined. 1\ Determine the probabilities: P(V); P(V/M) and P(M/V) 2\ Calculate P(M∩V) then P(M). Deduce the percentage of patients.

$$\:\:\:\:\:\:\mathcal{A}\:\mathrm{third}\:\mathrm{of}\:\mathrm{a}\:\mathrm{population}\:\mathrm{has}\:\mathrm{been}\:\mathrm{vaccined}\:\mathrm{against} \\ $$$$\mathrm{an}\:\mathrm{illness}.\:\mathcal{D}\mathrm{uring}\:\mathrm{the}\:\mathrm{pandemie}\:\mathrm{it}\:\mathrm{is}\:\mathrm{noticed}\:\mathrm{that}; \\ $$$$\mathrm{out}\:\mathrm{of}\:\mathrm{15}\:\mathrm{patients},\:\mathrm{2}\:\mathrm{have}\:\mathrm{been}\:\mathrm{vaccined}. \\ $$$$\:\:\:\:\:\:\:\mathcal{A}\mathrm{ssuming}\:\mathrm{that}\:\mathrm{out}\:\mathrm{of}\:\mathrm{a}\:\mathrm{hundred}\:\mathrm{vaccined},\:\mathrm{8}\:\mathrm{are}\:\mathrm{ill}. \\ $$$$\mathcal{A}\mathrm{n}\:\mathrm{individual}\:\mathrm{is}\:\mathrm{choosen}\:\mathrm{at}\:\mathrm{random}\:\mathrm{from}\:\mathrm{this}\:\mathrm{population}. \\ $$$$\mathcal{L}\mathrm{et}\:\boldsymbol{\mathrm{M}}\:\mathrm{imply}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{individual}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{ill}}\:\mathrm{and}\:\boldsymbol{\mathrm{V}}\:\mathrm{imply}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{individual}} \\ $$$$\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{been}}\:\boldsymbol{\mathrm{vaccined}}. \\ $$$$\mathrm{1}\backslash\:\mathcal{D}\mathrm{etermine}\:\mathrm{the}\:\mathrm{probabilities}:\:\mathrm{P}\left(\mathrm{V}\right);\:\mathrm{P}\left(\mathrm{V}/\mathrm{M}\right)\:\mathrm{and}\:\mathrm{P}\left(\mathrm{M}/\mathrm{V}\right) \\ $$$$\mathrm{2}\backslash\:\mathcal{C}\mathrm{alculate}\:\mathrm{P}\left(\mathrm{M}\cap\mathrm{V}\right)\:\mathrm{then}\:\mathrm{P}\left(\mathrm{M}\right).\:\mathcal{D}\mathrm{educe}\:\mathrm{the} \\ $$$$\mathrm{percentage}\:\mathrm{of}\:\mathrm{patients}. \\ $$

Question Number 96729    Answers: 2   Comments: 1

Prove that ln∣sec(x)+tan(x)∣=tanh^(−1) (sin(x))

$${Prove}\:{that}\:\mathrm{ln}\mid\mathrm{sec}\left({x}\right)+\mathrm{tan}\left({x}\right)\mid=\mathrm{tanh}^{−\mathrm{1}} \left(\mathrm{sin}\left({x}\right)\right) \\ $$

Question Number 96746    Answers: 3   Comments: 2

∫((√x)/((1+x^3 )(√(1−x^3 ))))dx=? ∫((√x)/((1−x^3 )(√(1+x^3 ))))dx=?

$$\int\frac{\sqrt{{x}}}{\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\sqrt{\mathrm{1}−{x}^{\mathrm{3}} }}{dx}=? \\ $$$$\int\frac{\sqrt{{x}}}{\left(\mathrm{1}−{x}^{\mathrm{3}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }}{dx}=? \\ $$

Question Number 96715    Answers: 1   Comments: 0

find real solution of equation x^5 +x^4 +1 = 0

$$\mathrm{find}\:\mathrm{real}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}^{\mathrm{5}} +{x}^{\mathrm{4}} +\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 96713    Answers: 1   Comments: 0

y^2 (d^2 y/dx^2 )=(dy/dx)

$${y}^{\mathrm{2}} \:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }=\frac{{dy}}{{dx}} \\ $$

Question Number 96712    Answers: 1   Comments: 0

Question Number 96705    Answers: 1   Comments: 0

∫ ln((√(1−x))+(√(1+x))) dx = ?

$$\int\:\mathrm{ln}\left(\sqrt{\mathrm{1}−\mathrm{x}}+\sqrt{\mathrm{1}+\mathrm{x}}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 96699    Answers: 0   Comments: 2

∫ ((tan^3 (ln x))/x) dx = ??

$$\int\:\frac{\mathrm{tan}^{\mathrm{3}} \left(\mathrm{ln}\:{x}\right)}{{x}}\:{dx}\:=\:?? \\ $$

Question Number 96693    Answers: 1   Comments: 0

Question Number 96685    Answers: 1   Comments: 0

lim_(ω→∞) 20log(√(1+((ω/(100)))^2 ))

$$\underset{\omega\rightarrow\infty} {\mathrm{lim}20log}\sqrt{\mathrm{1}+\left(\frac{\omega}{\mathrm{100}}\right)^{\mathrm{2}} } \\ $$

Question Number 96684    Answers: 2   Comments: 0

lim_(n→+∞) Σ_(k=1) ^n ((n+k)/(n^2 +k^2 )) {Reimann′s integral may help}

$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}+\mathrm{k}}{\mathrm{n}^{\mathrm{2}} +\mathrm{k}^{\mathrm{2}} } \\ $$$$\left\{\mathrm{Reimann}'\mathrm{s}\:\:\mathrm{integral}\:\:\mathrm{may}\:\:\mathrm{help}\right\} \\ $$

Question Number 96682    Answers: 1   Comments: 4

Question Number 96679    Answers: 1   Comments: 0

I=∫_0 ^1 ((1−x)/(x^2 +(x^2 +1)^2 ))dx find tan(I)+sec(I)

$${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}}{{x}^{\mathrm{2}} +\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$${find}\:\:\:\:{tan}\left({I}\right)+{sec}\left({I}\right) \\ $$

Question Number 96672    Answers: 0   Comments: 1

Evaluate : ∫ ((log_x a)/x) dx

$${Evaluate}\:: \\ $$$$\int\:\frac{{log}_{{x}} {a}}{{x}}\:{dx} \\ $$

Question Number 96671    Answers: 1   Comments: 0

Question Number 96669    Answers: 2   Comments: 0

find minimum value f(x) = (√(x^2 +9))+(√(x^2 −30x+250))

$$\mathrm{find}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{9}}+\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{30x}+\mathrm{250}} \\ $$

Question Number 96667    Answers: 2   Comments: 0

Prove that Σ_(k=1) ^∞ (1/k^2 )=(π^2 /6)

$$\mathcal{P}\mathrm{rove}\:\:\mathrm{that}\:\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{k}^{\mathrm{2}} }=\frac{\pi^{\mathrm{2}} }{\mathrm{6}} \\ $$

Question Number 96660    Answers: 1   Comments: 0

calculate L( e^(−2x) cos(πx)) L laplace transform

$$\mathrm{calculate}\:\mathrm{L}\left(\:\mathrm{e}^{−\mathrm{2x}} \:\mathrm{cos}\left(\pi\mathrm{x}\right)\right)\:\:\:\mathrm{L}\:\mathrm{laplace}\:\mathrm{transform} \\ $$

Question Number 96659    Answers: 1   Comments: 0

find L (((sh(3x))/x)) L laplace transform

$$\mathrm{find}\:\mathrm{L}\:\left(\frac{\mathrm{sh}\left(\mathrm{3x}\right)}{\mathrm{x}}\right)\:\mathrm{L}\:\mathrm{laplace}\:\mathrm{transform} \\ $$

Question Number 96658    Answers: 1   Comments: 0

determine L(e^(−x^2 −x) ) with L laplace transform

$$\mathrm{determine}\:\mathrm{L}\left(\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} −\mathrm{x}} \right)\:\:\:\mathrm{with}\:\mathrm{L}\:\mathrm{laplace}\:\mathrm{transform} \\ $$

Question Number 96657    Answers: 2   Comments: 0

f(x) =e^(−x) , 2π periodic developp f at fourier serie

$$\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{e}^{−\mathrm{x}} \:,\:\:\mathrm{2}\pi\:\mathrm{periodic}\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 96656    Answers: 1   Comments: 0

let g(x) =(2/(cosx)) developp f at fourier serie

$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\frac{\mathrm{2}}{\mathrm{cosx}}\:\:\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

  Pg 1182      Pg 1183      Pg 1184      Pg 1185      Pg 1186      Pg 1187      Pg 1188      Pg 1189      Pg 1190      Pg 1191   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com