Variable Definition and 1000 Threads

Have been reading about cepheid. Can I just check I've got this? 'When at their hottest (when gravity has squashed them) have more doubly ionised He so star becomes more opaque' Now was just wondering what the main mechanism is here? Because He2+ doesn't have any electrons left to absorb photons...

Hi. I realize that Jacobians are not normally used in 1-D but I'm confused as to the following. If I have the following integral ∫a-a f(x)dx and make the change of variable y = -x then dy = -dx and the limits of integration reverse so I end up with ∫-aa f(-y)(-dy) but if I use the Jacobian...

I'm trying to verify that: \lim_{(x,y)\rightarrow (0,0)}\frac{\sin (x^{3}+y^{3})}{x+y^{2}}=0. 0<\sqrt{x^2+y^2}<\delta\rightarrow |\frac{\sin (x^{3}+y^{3})}{x+y^{2}}|<\epsilon 0\leq |\sin (x^{3}+y^{3})|\leq |(x^{3}+y^{3})|\leq |x|x^2+|y|y^2 |\frac{\sin (x^{3}+y^{3})}{x+y^{2}}|\leq \frac{...

The co-ordinates of two points are A(4,-1) and B(7, -5) The line L1: 3x+4y−12 = is perpendicular to AB. (a) Find, in terms of k, the distance between the point P (10, k) and the line L2 (b) P(10, k) is on a bisector of the angles between the lines L1 and L2 and L2 :5x+12y−20 =0...

Homework Statement How do the values of the following functions move in the complex plane when t (a positive real number) goes to positive infinity? y=t^2 y=1+i*t^2[/B] y=(2+3*i)/t The Attempt at a Solution I thought: y=t^2 - along a part of a line that does not pass through the...

Homework Statement A pulley with a rotational inertia of ##10^{-3}\frac {kg} {m^2}## about its axle and a radius of ##10 cm##, is acted on by a force applied tangentially at its rim.The force magnitude varies with time as ##F=0.5t+0.3t^2## , with ##F## in Newtons and ##t## in...

I understand that when you use the chain rule you multiply the exponent by the number in front and then reduce the power by 1. So the derivative of 2x^3 = 6x^2 I'm confused now however on how you would solve something like e^-3x, the answer turns out to be -3e^-3x Am I missing a rule? Why...

Will my described method allow me to achieve my objective? If so, could you recommend a rheostat that is rated for at least 20A @120VAC that will work for my application? If not, could you describe an alternate method? Objective: Determine the ampacity of various wires at 120VAC Method: Wire a...

Hello, According to the Wikipedia article on random variables: If the above statement is true, then, instead of defining a (real) random variable as a function from a sample space of some probability space to the reals, could we equivalently define it as a subset of ℝ associated with a CDF?

Is there a function in Matlab that presets the value of a variable as an integer only? For example I will set the variable 'y' as an integer at the very beginning of the code, and whenever the variable gains a new value it automatically returns an integer value. Thank you in advance.

Is the "Voltage variable capacitor" described in patent US 20070242410 A1 a commercially available component? Has anyone heard of this method of changing the dielectric constant using a biasing voltage? It has been nearly 13 years since the patent was filed, but I've never heard of it. It would...

Homework Statement The position of an object of mass 2 kg is changing as a function of time by the formula x(t) = 4t^3-6t. (a) find the work done by the forces acting on the particle between t=1 and t=3s. (b) What is the object's velocity when the force on it is zero? Homework Equations is...

Finding length of vector with unknown variable. Purely for study purposes. Find the smallest possible length of the vector →v . Let vector V = (-2/3,b,16/7) Equation for finding length of vector : Sqrt(a^2+b^2+c^2)Question would be quite straight forward had there been no unknown variable but...

Hello, I am having trouble with solving the problem below The problem Find all primitive functions to ## f(x) = \frac{1}{\sqrt{a+x^2}} ##. (Translated to English) The attempt I am starting with substituting ## t= \sqrt{a+x^2} \Rightarrow x = \sqrt{t^2 - a} ## in $$ \int \frac{1}{\sqrt{a+x^2}}...

Homework Statement My lecture note says that "T-v diagram shows change in specific volume of a substance with respect to temperature.". Is it correct? Homework EquationsThe Attempt at a Solution If a(Specific Volume) "with respect" to b(Temperature), then b(Temperature) should be the...

Homework Statement I'm trying to calculate the absolute lowest safe altitude above a planet's surface to start firing the thrusters on a simulated lander in order tot just reach vCraft = 0 at the planet's surface. The force the craft's thrusters responsible for desceleration generate is...

Homework Statement The following picture illustrate how the current in the circuit changes when you change ##E_2##. Where slope 1 represents the current flowing through ##E_1## and slope 2 represents the current flowing through ##E2## Homework Equations Usual circuit laws :P The Attempt at...

Used a mass attached to a dynamic cart via pulley to examine motion under variable acceleration. As the mass was increased, my calculated friction force shows a decrease. I know that friction should increase with larger mass. Any suggestions as to why my calculations show a decrease? Used the...

My senior design adviser told me that the VFD must be the same brand as the motor that is being used, I'm not sure I believe this. I plan on using a GS1 series AC drive, here is a link; https://www.automationdirect.com/adc/Overview/Catalog/Drives/GS1_(120_-z-_230_VAC_V-z-Hz_Control) Here is a...

On the attachment, I was told my joint pdf was right, but the support was NOT 0<y1y2<1 0<y2<1, so maybe it's right now? Obviously B and C are incorrect, too, since they don't integrate to 1. I'm probably making just a few simple mistakes. Thanks in advance!

Homework Statement Given the bessel equation $$x^2\frac{d^2y}{dx^2} + x\frac{dy}{dx} -(1-x)y=0$$ show that when changing the variable to ##u = 2\sqrt{x}## the equation becomes $$u^2\frac{d^2y}{du^2}+u\frac{dy}{du}+(u^2-4)y = 0$$ Homework Equations The Attempt at a Solution ##u=2\sqrt{x}##...

In functional analysis functions ##f## and ##g## are orthogonal on the interval ##[a,b]## if \int^b_a f(x)g(x)dx=0 But what if we have functions of two variables ##f(x,y)## and ##g(x,y)## that are orthogonal on the interval ##[a,b]##. Is there some definitions \int^b_a f(x,z)g(z,y)dz=0?

I need help to convert 2 variables A,B into 1 representative variable C, which is used to filter A,B: Below is an example with C=A+B, which makes Set 2 the highest value: Set 1: A=65, B=75, C=140; Set 2: A=50, B=100, C=150; Set 3: A=54, B=90, C=144; Set 4: A=72, B=72, C=144; Set 5: A=71, B=73...

Hello guys, I am confused about when we can multiply and divide by the variable. I know the if zero is hidden as a factor then we can not divide or multiply. eg. x/2x+1=0 are we allowed to divide both side 2x+1. Although zero is hidden value of x, there are no other ways to solve this...

Homework Statement Find the center of mass of an inverted cone of height 1.5 m, if the cone's density at the point (x, y) is ρ(y)=y2 kg/m. Homework Equations The formula given for this problem is rcm=1/M * ∫rdm, where M is total mass, r is position, and m is mass. The Attempt at a Solution...

Most of us know what that we can judge the distance of an object such as a car headlight by how bright that headlight is. The things is we know how bright car headligjts are from 1 foot away so that seems pretty obvious. A Cepheid variables brightness is commonly used to measure the distance...

Hey everyone I'd be really grateful if anyone could help me out here, been going round in circles for two weeks now and I need to get going soon. Jumping right to the point, here's my problem: We are currently working on a student project and designing a Wind Turbine for future opensource use...

I have recently learned that in order to vary torque output from a DC motor, I need to vary the input current. A project I am working on requires that I have a DC motor that will be backdriven while providing resistance to a lever. A max torque of about 10 lbft will be provided from the lever...

Recently I have had a lot of eye strain from excessive computer use. The problem is because your eye lenses re stuck in a fixed position. I wanted to know if it would be possible to make a screen that is 1m away look like it is 4m away for example. Would it be possible by making the screen out...

Hi I couldn't find of these exist anywhere. Is there a component that is a variable resistor that adjusts based solely on receiving an up/down signal? And maintains its state on powerdown? I don't want this solution to involve any type of software, just a hardware solution. Looking for...

Homework Statement Alrighty, so here's my problem in a nutshell: Some particle of mass m is confined to move along a ring of radius R. Since it's on a ring, it has periodic boundary conditions--i.e.: For the boundary defined as ##-\pi R \leq x \leq \pi R##, ## x = -\pi R ## and ## x = \pi R...

I know that D is definitely a dependent variable, but I don't see how the others are dependent on anything else... The correct answer is A btw. Please explain to me how B and C are dependent variables considering the investigation is to "determine and compare the heat of combustion of three...

Homework Statement I have to find for which values of the real parameter ##b## the following plane is orthogonal to the following line: ##\pi : 5x + (2b - 1)y - (1 + 8b)z + 3 = 0## ##s : \begin{cases} x + z - 4 = 0 \\ x - 3y + z + 2 \end{cases}## Homework EquationsThe Attempt at a Solution For...

sin(x) * y''(x) + 2cos(x) * y(x) = 0 y(0) = 0 y'(0) = 1 how do I solve it? (I know the solution because I have created the diff. equation starting from a simple function). -- lightarrow

Homework Statement Rockets are propelled by the momentum of the exhaust gases expelled from the tail. Since these gases arise from the reaction of the fuels carried in the rocket, the mass of the rocket is not constant, but decreases as the fuel is expended. Show that for a Rocket starting...

Homework Statement Let ##X \sim Bin(n, p)## where ##n=20## and ##p=0.1##. Calculate ##P(|X-\mu| \leq \sigma)##. Give your answer up to three decimal places. Homework Equations For a binomially distributed random variable, using moment generating functions we have: \begin{equation} \mu= E(X) =...

This isn't really a question for which the template is useful.. Can anyone explain to me why the value of the variable 'seed' in location 1 is different from the value in location 2? The only thing happening in between is the defining of the varaible v(1) using the real function. I don't see...

Homework Statement A pickup truck is driving at night through the rain. He drives onto a frozen lake. He immediately turns off his engine to save fuel (it wouldn't help anyway on frictionless ice) and let's the truck coast (move under no power). Unfortunately, the rain is accumulating in the...

Hello everyone, I have a very simple question but for some reason, I couldn't find the exact answer to it on the internet. Let's say we have a formula y = k/x where k is constant and x and y are variables. Assume that I am given the absolute uncertainty in x how should I calculate the...

Aloha guys, I am just having trouble getting MatLab to output only the last variable of my "for loop." If anyone can help all I am looking for is an example of notation. p.s. I have done this before just not in a while and will continue to look through my old scripts and functions. just not in...

1. Problem statement Q. Use limit to find the instantaneous velocity at time t if the postition is p(t) at time t. p(t) = t + (1/t) at x = t 2. Homework Equations (Sorry dashes are in there to keep everything where it should be. I don't know how to make fractions in this and it was...

*if this has to be moved in statistics, please do that* I've been dragging this question for a while now, but.. When you make an overlay plot of data + estimation, what is the appropriate bin-width? the two extremes correspond to: single-bin for the whole variable range --> so you get the...

Homework Statement The following series are not power series, but you can transform each one into a power series by a change of variable and so find out where it converges. ∑∞0 ((3n(n+1)) / (x+1)n Homework Equations a power series is a series of the form: a0 + a1x + a2x^2 ... + ... The...

I am attempting to understand how I can derive a new expression as a function of another variable in this existing expression. This is a college undergraduate course but I can't recall doing this much before, maybe in high school. I have taken all the way up to ODE's and PDE's. The confusion...

This question is no doubt absurdly simple to many here, but the answer will help me immensely. Say that: c = a ^ 4 Then it's simple to rearrange for a: a = c ^ 0.25 But what if there is more than one term, for example: c = a ^ 4 + a ^ 3 Is it possible to rearrange this to the form: a =...

If ## A, B, ## and ## C## are complex-valued variables, is there an easy way to algebraically solve for ##A## without splitting the variables into their real and imaginary parts? For example: $$ AB^* = 20AB - A^*C + B^*C^* $$ can be isolated for ##A## but only if the real and imaginary parts...

Hi I understood above differential ## typo. RHS= 2*f ' (x,2z-x) but, what is answer of below equation? is this right? f ' ( g(z),2z-x) * g' (z) + f ' ( g(z),2z-x) *2

Homework Statement I want to change integral variable to jx it means (w=jx) Homework EquationsThe Attempt at a Solution but as you see the bounds of integral are different from the book text , what is my mistake?

I need to find $$\lim_{{(x, y)}\to{(0,0)}} \frac{x^2 - y^2}{\sqrt{x^2 + y^2}}$$ If I plug in zero, I get an indeterminate form. How do I resolve the indeterminate form?

I have $$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$ If I evaluate the limit along the x-axis, I get $$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$ which evaluates to $1$. If I evaluate the limit along the y-axis, I get $$\lim_{{y}\to{0}} \frac{...