Area Definition and 1000 Threads

A parallelogram ABCD has angle A = angle C = 45°. Circle K with the center C intercept the parallelogram through B and D. AD is extended so that it intercepts the circle at E and BE intercepts CD at H. The ratio of the area of triangle BCH and triangle EHD is ... Here I got that triangle BCH...

Summary: I want to crush a single layer of granules from a single material that are 400-600um in size using a flat, circular probe, which will generate a force v time or force v distance curve. The quantity I am trying to measure is the granule (tensile) strength of the material. I believe...

I know the area of a thin ring of radius ##r## can be expressed as ##2\pi rdr##, however, I wonder if I use the usual way of calculating area of a ring, can I reach the same conclusion? I got this: $$4\pi(r+dr)^2-4\pi r^2=4\pi r^2+8\pi rdr+4\pi (dr)^2-4\pi r^2=8\pi rdr+4\pi (dr)^2$$And now I'm...

I know how to find the area of a plane which is parallel to the xy-, yz-, or, xz-plane, those are the easiest case. I also tried to find the area of a plane which is only perpendicular to 1 particular axis plane, like the one passing through points (0,0,a), (a,0,a), (0,2a,0), in which case...

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Hi, consider the following curve: f(\theta) = \frac {I_0sin^2(n\theta/2)}{sin^2(\theta/2)} When the area over a cycle from ##0## to ##2π## is evaluated it gives ##(2πnI_0)##. This is exactly ##\frac {I_{max} + I_{min}}{2}## , since ##I_{min}## is ##0##. Is this a coincidence, or is...

In Euclidean geometry (and even in measure theory, see for example Stein and Shakarchi's Real Analysis), distance in the real numbers is defined as the difference of the real numbers, and area of a square is understood as the product of the distances defining the given square (and the same for...

So, say you got 4 circles intersecting this way: Now, I am looking for two things: A proof that each part of the circle which is in an intersection is 1/4 the size of the whole circle's circumference The exact area of the non-shaded region. Now, in my search to finding the answer to...

My question is, given that the height of geostationary satellite to be 35786 Km and radius of about 6378km determine the area covered by a geostationary satellite Or deteremine minimum number of geostationary satellites requires to cover whole earth. Regards thanks a bunch :)

My problem: In the solution,our teacher found, that the wet section is minimal if y=L/2 So Am: = L^2 /2; Pm: = 2L; So despite that I try with any value, I can not find a more minimal section, and that's not the case because if I try with y = L / 3 I find Am: L^2/3; Pm: (5/3)*L ; and these...

My volume integral is... $$\pi\int y^2 dx$$ My surface area integral is... $$2\pi\int y \sqrt {1+x'^2} dy$$I'm fairly sure the variable of integration on my volume and surface area integrals has to be the same, is that right? But when I change the variable in the surface area integral to...

Through symmetry of parallelogram,I have come to this: Here 1,2,3,4 denotes the area of the particular regions.Then I am stuck.Please help what to do next or whether there is any other way.

There is a simple geometric derivation of the area element ## r dr d\theta## in polar coordinates such as in the following link: http://citadel.sjfc.edu/faculty/kgreen/vector/Block3/jacob/node4.html Is there an algebraic derivation as well beginning with Cartesian coordinates and using ##...

I was trying to find some sort of pattern in the triangle (below) to graph it or find some equation, and I thought maybe measuring something would be a good idea. I was okay just calculating the area for the first few iterations, but then I got confused on how I was supposed to represent like...

Is there any formula for calculating sound power? What does the A mean in I=P/A? Is the power of sound dependent on the area of its surrounding or something. I want to know if there's an equation for P like there's I=2π²a²f²ρv.

In a human body we have two relatively similar structures -pulmonary...

Could I please get a hint on how I should start this question/how I should parameterize these variables? I'm going to head to sleep as I am from the eastern time zone. I apologize ahead of time for my delayed reply.

Hello sirs, How to calculate the cross-section area too toroid core? kindly explain this

Using integrals, consider the 7 requirements: Any my attempted solution that I have no idea where I am going: And the other one provides the graph:

I'm trying to get the Electric Field of a Thin spherical shell along $$ \hat z $$ axis. In this problem I've got a charge/area density: σ(θ)=σ0⋅cos(θ)σ(θ)=σ0⋅cos(θ). θ∈[0,π]θ∈[0,π] (theta is the polar angle)Can you please help me with how can I know the area element? thanks.

https://en.wikipedia.org/wiki/Area_of_a_circle#Onion_proof I understand the basic concept, although it is a little difficult to visualize the thin discs close to the centre of the circle. Regarding the area of each disc, it is given in the link above as 2πrdr. Then, by means of integration...

I have two regions, given by ##y>\sqrt{2}x - \frac{1}{4x}## and ##y< \sqrt{2}x + \frac{1}{4x}##. How can I find the area of their intersection? If their is no easy analytical way, could someone perhaps use a computer? I am not sure how.

I tried following: $$ \Delta l = \alpha l_0 \Delta T $$ $$ (\Delta l)^2 l_0 = \alpha l_0^2 \Delta T \Delta l $$ $$ \Delta A l_0 = \alpha A_0 \Delta T $$ $$ \Delta A = \frac{ \alpha A_0 \Delta T }{ l_0 } $$ If we remember that: $$ \Delta l = \alpha l_0 \Delta T $$ So we have $$ \Delta A = \frac{...

ABC is a triangle. AC=4cm; AB=3cm; A=60 degrees. I need help finding the area of triangle ABC.

I have computed the total length of a 3D triangle and its area. The code is shown below. I want to use file output instead of cout. The file name, cw2task1output, was just given as part of the task, in this case should I make an empty text file named cw2task1output then attach it to the resource...

Homework Statement Find ##\iint_S ydS##, where ##s## is the part of the cone ##z = \sqrt{2(x^2 + y^2)}## that lies below the plane ##z = 1 + y## Homework EquationsThe Attempt at a Solution [/B] I have already posted this question on MSE...

diagonal 1=20cm. diagonal 2=37cm. AB=25.5cm S (AMC)= 306cm. S (ABCD)=?

Homework Statement Homework Equations The Attempt at a Solution [/B] The solution to this problem is known. I want to use this exercise as a model to understand how to proceed when calculating the surface area of a geometric figure. Question: 1) Why do we differentiate with...

Homework Statement Given that there are 10-2 Ellipticals per Mpc3 and my garden telescope can reach to 14 mag. How large an area of sky would I need to survey to find 100 Elliptical galaxies ? (assume the typical absolute magnitude for an Elliptical galaxy is -21 mag).Homework Equations...

Hi, how can I define a time-Area table for a valve? I know the stem-area table but it does not satisfy my purpose. I want to change a valve's area with time

I have a calculus 2 midterm coming up and given the exam review questions, this seems like this question can potentially be on it. I've tried to look it up, but I always find the famous painters example, which I don't find satisfying.

Hi guys, I find it hard to decide what to work on. To give some background, I am a bachelor student and I want to work in theoretical research. I talked with a professor (he is the chief of the theory department) at my uni about this and he expects me to find a topic or an area of research for...

Homework Statement find the area of the shaded region as a ratio to the area of the square (kindly see attached diagram)Homework EquationsThe Attempt at a Solution ##A= \frac 1 2####b×h## ##A= \frac 1 2####×2x × 3x##

Homework Statement Hi Everyone, So I'm doing writing up my weekly physics lab report and I had an idea to better present my findings. I have a chart displaying the frequencies of numerous tuning forks as well as their experimentally determined wavelengths and I have to find the speed of sound...

In Calculus II, we're currently learning how to find the area of a bounded region using integration. My professor wants us to solve a problem where we're given a graph of two arbitrary functions, f(x) and g(x) and their intersection points, labeled (a,b) and (c,d) with nothing else given. I...

I'm struggling to understand the importance of the differential cross-sectional area in Rutherford's scattering experiment, dσ/dθ. In one part of my course notes it is explained as 'the number of scatterings between θ and θ + dθ per unit flux, per unit range of angle'. However, dσ itself is...

Homework Statement Problem is part of a double integral. but my boundries are: 1<=x^2 + y^2 <=9 so between 2 circles with r1=1 and r2=3 and x<=y and y<=sqrt(3x) the first boundry is obviously pi/4 and/or 3pi/4 the answer is pi/3 and i have no idea how u get that. u obviously have to...

My university offers some courses in different areas, such as - Particle Physics (I, II) - Nuclear Physics (I, II) - Astrophysics (I) -Modern Atrophysics (I,II) - Computational Physics (I, II) - SR/GR - Nonlinear Dynamical Sys and Chaos (I, II) - QM II So I am allowed to take 6...

Homework Statement Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 3.872 g, is pressed into a leaf of 5.372 μm thickness, what is the area of the leaf? (b) If...

Homework Statement a hut has to side walls a roof and back wall. its front is open. its total volume is 120m^3 fdetermine the miniumal surface area necessary for a sheet to be put over it Homework EquationsThe Attempt at a Solution Attempt 2 V=xyz=120 z=120/xy s = 2yz + xz + xy s = 2y(120/xy)...

Homework Statement Find the area of the region that lies inside the first curve and outside the second curve. ##r=6## ##r=6-6sin(\theta)## Homework Equations ##A=\frac {1} {2}r^2\theta## The Attempt at a Solution \[/B] If I'm correct, the area should just be ##\frac {1} {2}\int_{0}^{2\pi} 6^2...

Homework Statement P(3, 0, 3), Q(−2, 1, 5), R(6, 2, 7) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR Homework Equations A = \frac{1}{2}|\vec{AB}\times\vec{AC}| Source...

Homework Statement An open topped box with a square base has the capacity of ##32m^2##. Find the dimensions that will minimize the surface area of the box. Homework EquationsThe Attempt at a Solution I was told these are the dimensions, but I can't picture them in my head at all...

Homework Statement The question involves using sigma notation of Riemann sums to find the area under the graph of ##x^2+\sqrt {1+2x}##. I managed to calculate most of the values and I have ##16+\frac 8 3 + \Sigma {\frac 2 n \sqrt {9 + \frac {4i} n}}## Homework Equations [/B] ##\Sigma i= \frac...

Homework Statement find the surface area of a sphere shifted R in the z direction using spherical coordinate system. Homework Equations $$S= \int\int \rho^2 sin(\theta) d\theta d\phi$$ $$x^2+y^2+(z-R)^2=R^2$$ The Attempt at a Solution I tried to use the sphere equation mentioned above and...

I don't understand the following definition. If we let $u=\langle u,v \rangle$ , $p=\langle p,q\rangle,$ $x=\langle x,y \rangle$,then (x,y)=T(u,v) is given in vector notation by x=T(u). A coordinate transformation T(u) is differentiable at a point p , if there exists a matrix J(p) for which...

Hi all I was wondering if someone could help explain what the area under a load vs deflection curve tells you. I have a concrete sample which I loaded until it failed. I plotted the load (kN) and deflection (mm) as shown below. My question is; if the curve in red can be represented as a...

Homework Statement Homework Equations pV=nRT The Attempt at a Solution I know the volume of the cylinder, which is Al. So I plugged this into the ideal gas law formula, and got answer B. However, the correct answer should be D. I see the Boltzmann's constant there in the equation, and I do...

Homework Statement Let Rpq be a ray: .-------.----------------> p q draw a second ray Rpm s.t the angle <QPM has 60 degrees Let D be a disc centered at P and assume its area is 60 in^2. find the area of the sector in the disc cut out by the two rays Homework EquationsThe Attempt at a...