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    Expectation operator - linearity

    Thank you for your reply. I know that the probability distribution of the sum of two or more random variables is the convolution of their individual pdf's, but as far as I know this is only valid for independent random variables. While ##E(aX+bY)=aE(X)+bE(Y)## is true in general, right?.
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    Expectation operator - linearity

    1. Homework Statement Show that the expectation operator E() is a linear operator, or, implying: E(a\bar{x}+b\bar{y})=aE(\bar{x})+bE(\bar{y}) 2. Homework Equations E(\bar{x})=\int_{-\infty}^{+\infty}xf_{\bar{x}}(x)dx With f_{\bar{x}} the probability density function of random variable...
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    Plate floating on oil - linear momentum equation

    1. Homework Statement 1: Determine the wall shear stress that acts at the lower side of the plate. 2: Determine the force Fx that is needed to give the plate a speed of u = 1m/s. 3: Determine the speed V, that is leaves an air jet that blows against the plate and which creates the same force...
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    Definition: flow velocity

    Thank you for your reply. But now I wonder, how is the mean flow of the element defined? If we look at a flowing liquid (for example water), now we can theoretically draw a fluid element and give it a velocity U, but how can we determine what U should be? Is it wrong to say that the velocity...
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    Definition: flow velocity

    Good day, In my book, the following definition for flow velocity is given: So summarized, the flow velocity at a point in space is the velocity of an infinitesimally small fluid element as it sweeps through that point. But now my question; how is the velocity of an infinitesimally small...
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    Linearizing an explicit differentiation scheme

    1. Homework Statement Consider the following implicit scheme: y_{n+1}=y_{n}+\frac{\Delta t}{2}\left [f(y_{n+1})+f(y_{n})] By linearization one can obtain an explicit scheme which is an approximation to this - with approximation error O(\Delta t^{3}) 2. Homework Equations The solution...
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    Second derivative of an integral

    Good day, I don't understand the following: \frac{d^{2}}{dt^{2}}\int_{0}^{t}(t-\epsilon )\phi (\epsilon)d\epsilon=\phi''(t) All I know is: \frac{d^{2}}{dt^{2}}\int_{0}^{t}(t-\epsilon )\phi (\epsilon)d\epsilon=\frac{d^{2}}{dt^{2}}\int_{0}^{t}t \cdot \phi...
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    Inverse Laplace Transform

    Awesome, thanks a lot!
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    Inverse Laplace Transform

    1. Homework Statement Take the Inverse Laplace Transform of: Y(s)=\frac{1}{\tau s+1}\cdot \frac{1}{s} 2. The attempt at a solution I know: L^{-1}(\frac{1}{\tau s+1})=\frac{1}{\tau}e^{\frac{-t}{\tau}} and: L^{-1}({\frac{1}{s}})=1 But how to continue?
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    How do I solve (a+b)^(-c)?

    Re: (a+b)^(-c) Exactly.
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    How do I solve (a+b)^(-c)?

    Re: (a+b)^(-c) (1/x). I have got the equation: r = 1/(a + bcos(c)) This should be equal to: r = (1/a) * (1/(1+bcos(c))) I just can't figure out why.
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    How do I solve (a+b)^(-c)?

    Re: (a+b)^(-c) In my case, c = 1, so I have got: (a+b)^-1
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    How do I solve (a+b)^(-c)?

    Good day, How do I work out (a+b)^(-c)? Thanks.
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    Unique solution of 1st order autonomous, homogeneous DE

    How can I calculate the integral of x(t) when I don't know the corresponding function? x(t) can equal (t^2) or (t-3) and so on, right?
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    Unique solution of 1st order autonomous, homogeneous DE

    Thank you for your answer. I can work it out when x(t) = x, but this is not the case, is it?
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    Unique solution of 1st order autonomous, homogeneous DE

    Hello, 1st order autonomous, homogeneous differential equation have the general form: \dot{x}(t)=ax(t) It can be shown that the unique solution is always: x(t)=e^{at}x(t_{0}) I don't get this, could anyone help me? Thanks!
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    Finding the confidence interval

    Has anyone got an idea regarding this practical situation?
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    Drawing a graph with broken y-axis

    Thank you for your answer. Because I have to make quite a lot of graphs with broken y-axis, I am looking for an easier method. The method of the website will take quite some time when I have to make 20 graphs with broken y-axis.
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    Finding the confidence interval

    Thank you for your replies. All the information I have got considering this practice situation: Information written down on a form will be put in a database. The information in the database can be correct (match the information written on the form) or can be incorrect (do not match the...
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    Drawing a graph with broken y-axis

    1. Homework Statement With what program (freeware) can I draw a graph with broken y-axis. An example of what I want: I know that this is possible by using Excel, but just in a very cumbersome way, right? Thanks in advance.
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    Finding the confidence interval

    1. Homework Statement What formula do I need to find the confidence interval, when I have got: - Number of samples - Level of Confidence - The assumed (1st guess) accuracy 2. Homework Equations I found the following equation online: µ = z * [p * (1 - p) / n] ^ (-1/2) 3. The...
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    Centroid and centre of pressure

    1. Homework Statement Explain why the distance between the centroid and the centre of pressure for a plane submerged fluid decreases as the depth of fluid increases. I know that the centre of pressure for a plane submerged fluid is located below the centroid because pressure increases with...
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    Exponential form

    Off course, thanks a lot!
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    Exponential form

    I made a mistake. sinh^{3}(x) = 0.125[(e^{x}-e^{-x})]^3 This is not equal to: sinh^{3}(x) = 0.125(e^{3x}-e^{-3x}) right?
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    Exponential form

    Allright thanks, then I get: 0.5e^{3x}-0.5e^{-3x}=2e^{x}-2e^{-x} Though I have no idea how to continue with this equation...
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    Exponential form

    1. Homework Statement Prove that: sinh(3x)=3sinh(x)+4sinh^{3}(x) 2. The attempt at a solution I know that: sinh(3x)=0.5(e^{3x}-e^{-3x}) and: 3sinh(x)=1.5(e^{x}-e^{-x}) But I have no idea how to rewrite 4sinh^{3}(x) in exponential form...
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    Fluid Mechanics - similarity

    1. Homework Statement A body when tested in air of density 1.18 kg/m3 and dynamic viscosity 1.52x10^-5 Pas at a velocity of 35 m/s was found to produce a resistance of 250 N. A similarly shaped body 10 times longer than the original was tested in water of dynamic viscosity 1x10^-3 Pas...
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    Mass flow rate

    Allright, thank you! Should be a mistake in the notes then.
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    Mass flow rate

    1. Homework Statement A fluid of density 867 kg/m3 flows through a circular duct of diameter 40.60 mm with a mass flow rate of 14.63 kg/s. The fluid velocity in m/s is? 2. Homework Equations mass flow rate [kg/s] = density [kg/m3] x velocity [m/s] x area [m] 3. The Attempt at a Solution...
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