Area Definition and 1000 Threads

1. Area is the naming convention assigned to that which is within a closed diagram in the x-y dimensions. 2. Area is also the naming convention used in simplified Lorentzian diagrams in the x-t dimensions. 3. Volume is the naming convention used to that which is within a closed vessel in the...

$\textsf{What is the area of the region in the first quadrant bounded by the graph of}$ $$y=e^{x/2} \textit{ and the line } x=2$$ a. 2e-2 b. 2e c. $\dfrac{e}{2}-1$ d. $\dfrac{e-1}{2}$ e. e-1Integrate $\displaystyle \int e^{x/2}=2e^{x/2}$ take the limits...

Hey! :o The functions \begin{equation*}f(x)=\frac{1}{3}(x-2)^2e^{x/3} \ \text{ and } \ p(x)=-\frac{2}{3}x+\frac{4}{3}\end{equation*} have exactly two real intersection points at the region $x\geq 0$. Calculate numerically the area that is between the graphs of these two functions, with...

My attempt is ∅ = ∫E.dA. The direction of E is going out of the net towards +ve i axis. I am not clear on the direction of the Area, it can be either +ve i-axis or -ve i-axis. Which direction should i consider? ∅ = ∫3.dA = 3*∫dA ---->1 ∫dA is the area of the circle. A = π * (0.11)^2 = 0.038...

I can find the area of the triangles but can't solve the squares for some reason

Material - SS 316

In Australia, we use TN-C-S system. I have a switchboard feeds a pump in hazardous area. I knew for switchboard in Hazardous area it needs to connect to a TN-S system. So should I remove the MEN link in the switchboard? Could anyone help me with this matter? Thanks.

i am perplexed as to the first moment of area and second of area; i would like to know 1. why they come (how they are figured out and distinguished from each other) 2. what is meaning of these 2 moment of area in terms of physics what i have learned is that the first moment of area is used to...

A topless square box is made by cutting little squares out of the four corners of a square sheet of metal 12 inches on a side, and then folding up the resulting flaps. What is the largest side area which can be made in this way? What information I have so far is that since the side of the...

Hi, This feels like such a stupid question, but it's bugging me. Two displacements can be represented with two vectors. Let's say their magnitudes are expressed in metres. The scalar (dot) product of the two vectors results in a value with the units of square metres, which must be an area. Can...

What's the area of the triangle? It's hard because the vertices aren't in the intersections of horizontal and vertical lines, so I have a hard time determining the side lengths, and it's also for Elementary Students Math Olympiads too.

Why work done is area enclosed by graph of F v/s x on x Axis but not y axis. Suppose we apply a force on object which is proportional to displacement as ##\vec f##=## \vec x##²then area enclosed by Force and displacement on x Axis is integral of ##\vec x##²but on y-axis it should be integral of...

ok well it isn't just adding the areas of 2 functions but is $xf(x)$ as an integrand Yahoo had an answer to this but its never in Latex so I couldn't understand how they got $\dfrac{7}{2}$

Area of triangle from picture https://en.wikipedia.org/wiki/Special_right_triangle#/media/File:45-45-triangle.svg is ##A_0=\frac{1}{2}##. If that triangle staying still in system S' and S' moving across one of the sides of length ##1## in respect to system ##S## area of the triangle in the...

Hi all, For area expansion, I know the equation goes like: Hence, my answer to part i is ##\begin{aligned}A=A_{0}\left( 1+2\alpha \Delta T\right) \\ = 52\left( 1+2*24\times 10^{-6}\right) \left( 100\right) \\ =52.2496cm^{2}\end{aligned} ## Now I am unsure how to proceed with part 2 in this...

Is there any mistake in the following answer because I m always getting the result of 10362 mm 2 ? A piece of steel tube, has an external diameter of 140mm and an internal diameter of 80mm. What is the area of the surface at one end of the steel? Answer (13424 mm2)

From what I read on the internet I found that increase in surface area that is in contact is offset by the reduction in pressure. What exactly does it mean? This is what I understood from the it (but my understanding might be absurd :-p): does reduction in pressure mean that the "hills" or...

Suppose, a rectangle circumscribes a quadrilateral having length of diagonals p and q, and area A.What is the maximum area of rectangle that circumscribes the given quadrilateral? Answer:- How to answer this question using geometry or calculus or by using both techniques.

Hi All I was wondering if there was a quick method of calculating the Second Moment Of Area about the Z axis shown below? I can quickly work out the Second Moment Of Area about the Y axis but the Z axis is proving very difficult and time consuming as the parallel axis therom needs to be...

ok I got stuck real soon... .a find where the functions meet $$\ln x = 5-x$$ e both sides $$x=e^{5-x}$$ok how do you isolate x? W|A returned $x \approx 3.69344135896065...$ but not sure how they got itb.? c.?

Hi all I was wondering if someone could help clear up some confusion about the Parallel Axis Theorem. I am trying to understand the purpose/benefit of applying the Parallel Axis Theorem with respect too the Second Moment Of Area. For example I have a beam that is under load. I have found its...

Hi all I was hoping someone could help shed some light clearing some doubt on 2nd Moment of Area. I know that if i had a beam that was loaded then the top of the beam would experience compressive forces. As i moved down towards the neutral axis these compressive forces would become zero. And...

Recently there have been a lot of studies of black holes colliding and the gravitational waves that they produce. My question is: What is the effect on the space between the two black holes before they collide. The stress must be extraordinary. That stress should be measurable by radiation...

Does this happen? How much can it vary by? for example, I have a PhD offer in a pretty boring application of fluid dynamics, in the future woild I be able to take my research into a direction perhaps applying this to astrophysics or something? Also I very much enjoyed general relativity at...

I do not know where to start. I draw scalene triangle and assign each coordinates to the vertices. Tried writing something but none working. Please give me a hint to start. Thanks

The first time I saw this question I had no idea how to do it (as you can see in the figure, I lost a lot of points :s) because I was confused on how to even approach it with area of the slab from all sides being infinity. Right? That's problematic, no? Today, I just tried the problem again for...

r,θ,ϕ For integration over the ##x y plane## the area element in polar coordinates is obviously ##r d \phi dr ## I can also easily see ,geometrically, how an area element on a sphere is ##r^2 sin\theta d\phi ## And I can verify these two cases with the Jacobian matrix. So that's where I'm at...

The area differential ##dA## in Cartesian coordinates is ##dxdy##. The area differential ##dA## in polar coordinates is ##r dr d\theta##. How do we get from one to the other and prove that ##dxdy## is indeed equal to ##r dr d\theta##? ##dxdy=r dr d\theta## The trigonometric functions are used...

I've been playing around with Up-Arrow notation quite a lot lately and have come up with the following "thought experiment" so to speak. Consider the following function: $$f(x)=(−ln(x↑↑(2k)))↑↑(2k+1)$$ $$\text{Where }k∈\mathbb{Z} ^+$$ In the image below we can see some examples of what this...

For some reason I have become very unsure but my gut feeling says i can calculate y=(1-x^(a/b))^(d/c) I already know the formula for calculating the volume. but can transfer the whole thing as a function of y(x) and take the integral then as a single integral?

Ok this is considered a "hard" GRE geometry question... notice there are no dimensions How would you solve this in the fewest steps?

Hello everyone! I have been looking for a general equation for any regular polygon and I have arrived at this equation: $$\frac{nx^{2}}{4}tan(90-\frac{180}{n})$$ Where x is the side length and n the number of sides. So I thought to myself "if the number of sides is increased as to almost look...

I am reading about beams under distributed loading and shear stresses and needed to use the equation τ = VQ/It, where Q is the first moment of area. I understand that Q is zero about the neutral axis, and that this is, in fact, how the neutral axis is defined. The first moment of area above the...

The metric for 2-sphere is $$ds^2 = dr^2 + R^2sin(r/R)d\theta^2$$ Is there an equation to describe the area of an triangle by using metric. Note: I know the formulation by using the angles but I am asking for an equation by using only the metric.

I help students a bit with their math. As a teacher I am over 35 years removed from Math so I am rusty. I had the following questions given to me by some students and I couldn't even remember. The students are required to show their work how to solve this problem.

Hi I live in the Santa Clara bay area in the Silicon Valley, I want to see anyone here that are living close by that are into high end audiophile stuffs particular designing and building audio electronics. It's hard to find anyone that is into this, it would be nice to find people to share this...

Many discussions of the so called measurement problem seem to run up against the buffers of the uncertainty of what exisfs ? In the grey area between mjcro and macro scopic. Is there a zone a closing door of some new physics?

Although obviously I enjoy the wonderful technology of electricity, it would be nice to have a short blackout on a dark night to see the night sky in all its glory. Has anyone seen such a dark sky in the blackout areas there?

A figure is made from a semi circle and square. With the following dimensions, width = w, and length = l. Find the maximum area when the combined perimiter is 8 meter. I first try to construct the a function for the perimeter. 2*l + w + 22/7*w/2 = 8 - > l = 4 - (9*w)/7 Next I insert this...

if it helps, the answer is supposed to be my colleagues and I can't figure out how to come to that answer. It's probably something simple. edit: I tried to solve it by inscribing an octagon, and then finding the distance from the center of the octagon to the side of the octagon. but I got 1 +...

Lenght=300mm, Force at the end of the handlebar is 200N What i would like to know is: does that 20x20mm end piece affect the calculation process in any way? and whether there are more than 3 types of stresses in this case. First stress being moment created by the 200N and second stress is shear...

Why does hysteresis loss cause heat and why the heat proportional the area of hysteresis loop?

How feasible is such a planet? Can the planet still be dense enough to be rocky and not gaseous?

$\tiny{237}$ $\textsf{The total area of the region bounded by the graph of $f(x)=x\sqrt{1-x^2}$ and the x-axis is}$ $$(A) \dfrac{1}{3}\quad (B) \dfrac{1}{3}\sqrt{2}\quad (C) \dfrac{1}{2}\quad (D) \dfrac{2}{3}\quad (E) 1 $$ find the limits of integration if $$f(x)=0 \textit{...

Hello, after many simplifications my geometry has become very simple: just a box of concrete with a cylinder of steel inside. The source is outside in the air. The cell and the surface cards are like the following: C ******************Block 1: Cells********************** 100 0 99 imp:p=0 99 1...

The question is in the image. Working out with every step would be much appreciated.

Hello everyone, I'm trying to design a plastic shredder machine, but I'm stuck on how to determine the cutting area of my shredder. I've already made some research, and I think that the cutting area depends on the blade thickness and the plastic thickness. As for why the blade thickness is...

Hi, This is my first question here, so please apologise me if something is amiss. I have two curves such that Wa = f(k,Ea,dxa) and Wb = f(k,Eb,dxb). I need to minimize the area between these two curves in terms of Eb in the bounded limit of k=0 and k=pi/dx. So to say, all the variables can...