Area Definition and 1000 Threads

Question : https://www.physicsforums.com/attachments/71328 My question is how did the 2a and 2b come from?? Equations: Area of trapezoid =(a+b/2)(h) Attempt: I know that the area of a trapezoid is (a+b/2)(h) However why is there now a 2a and 2b in its place? Could it be related to the 2s...

Hi, (I'm not sure if this belongs in the BSM forum...apologies to the moderator if it belongs there.) I'm working through Polchinski's book on string theory (volume 1) and I came cross the definition of the Nambu Goto action. I want to understand why the Nambu Goto action is proportional to...

Homework Statement Let T:R2→R2 be the linear transformation such that T(x,y)→(9x+3y,5x+2y). Let R be the region on the plane defined as {(x,y) \in R2/ 0≤x≤2 and 0≤y≤2 }. Consider the region T(R) \subset R2, which is the image of the region R by the linear transform T. What is the area of the...

find the area of the cylinder x^2+z^2=a^2 that is inside the cylinder x^2+y^2=a^2. my attempt: parameterise x^2+z^2=a^2 as a vector r(x,y) = (x,y,(a^2-x^2)^1/2). using the formula given here : http://tutorial.math.lamar.edu/Classes/CalcIII/SurfaceArea.aspx, I found the surface area = the...

I am working on a task right now. I am currently trying to find the area of a parallelogram. I do not have the height. I only have the dimensions. I have tried suggestions like dividing the parallelogram into triangles and doing 1/2bh. The dimensions I have are the 1/2,1/2,\sqrt{2}/4...

if I am finding the surface area, and I am given the equation in term of x=g(y) about the x-axis, do i have to solve for y or can i just integrate in terms of y? would i just use dx/dy instead?

Hi, I have a question I'd like some help with which is related to my job working with drill rigs. Where you have a cylinder such as a drill string where the forces of the ground pressing in from all sides how much influence does the surface area have on the rotational force required to...

I'm wondering why my method for finding the surface area of a sphere is invalid. Essentially I'm integrating the perimeter of the circle perpendicular to the radius along the entire radius, and then multiplying by 2 (because the radius only covers half the sphere) (I hope that made sense...

Hello everyone, I've been working on an area summation problem in my book for quite a bit and I can't solve it. Find the area under the straight line y=2x between x = 1 and x = 5 The book shows the answer as 24 and Maple does as well, but I'm not getting 24, I'm getting 8. Area summation formula...

If so, is 'its half' also not a real size of space? What I am asking is pretty much; what is the meaning of the notion of a 'smallest possible' 3d area? What is the meaning of that cusp between 2d and 3d? Almost like asking what is in between 1.999999999999(repeating) and 2. Must...

How is Area a vector? How does it have direction? I thought it was basically a scalar quantity because it only had magnitudes, e.g. 4m^2, 7m^2 etc. Please help. I can't understand. :(

Using integral find the area of that part of the circle x^2 + y^2 = 16 which is exterior to the parabola y^2 = 6x.

1. Hi, I have been asked to calculate the area beneath a curve. The curve is y = 2x^2 + 7x + 24 and the values of x to find the area within are 5 and 2. 3. My attempt stands as follows: A = 5,2∫ (2x^2+7x+24)dx [ 2x^3/2 + 7x^2/2 + 24x...

i want to find V(t) At first i found this problem was very simple but when i try to write differential equations i ended up with these V' = kA that's for sure then i confined the problem only to spherical shape and no other shapes of raindrops involved as i can't express A in term of V alone(...

Homework Statement Find the area of the cylinder x^2 + y^2 -y = 0 inside the sphere x^2 + y^2 +z^2 =1 Homework Equations dA = sec \gamma dydz where sec \gamma = \frac{|\nabla \phi|}{|\partial \phi/ \partial x|} The Attempt at a Solution The method shown in this section is to...

I promise this isn't homework, it's actually for my research :-P Here goes: When two bodies are in contact and *translate* with respect to each other, there is no dependence of friction on contact area, and Ff = mu*Fn. Now, assume we have a block of wood on a table with mass m and we apply...

Let A(1, 2), B (3,4), C( x, y) be points such that (x- 1) (x-3) +(y-2) (y-4)=0. Area of triangle ABC=1. maximum number of positions of C in the xy plane is (a) 2 (b) 4 (c) 8 (d) None of these I have tried using the staircase formula which gives me something like x-y=2. Therefore I see only...

In 2 dimensions given a scalar field f(x,y) is possible to compute the line integral ##\int f ds## and area integral ##\iint f d^2A##. In 3D, given a scalar field f(x,y,z) is possible to compute the surface integral ##\iint f d^2S## and the volume integral too ##\iiint f d^3V##...

For example: if it was given that two right triangles are similar triangles and that the hypotenuse of one is twice as long than the other how would you find the area of the triangle with the twice as long hypotenuse given the area of the other? Similar right triangles means they are the same...

I'm still an undergraduate but I was wondering about the future and all that. I do like love physics as a whole, but I don't think there is a subfield which I REALLY like or REALLY dislike. I also like "versatility" as a way of life. So I was wondering: "can I move to and from subfields as I...

http://www.askamathematician.com/2011/04/q-why-is-the-integralantiderivative-the-area-under-a-function/ this website says f^\prime (c) (B-A) = f(B)-f(A) or f(c) (B-A) = F(B)-F(A) (since F’ =f). but seems like this is wrong. because B-A= Δ x, f'(c)*Δ x= Δy and the area might...

WARNING: THIS IS NOT HOMEWORK~! Okay, so the problem goes like this: "Find a,b,c of a triangle; If a+b+c = 10 ; Area = 10" I know it sounds totally vague (I think so too). So I tried using the Pythagorean theorem; c2 = a2+b2 then the given equation; 10 - a - b = c; then the...

Homework Statement Find the area of triangle formed by the points ##A(5,2)## , ##B(4,7)## , ##C(7,-4)## Homework Equations Nah The Attempt at a Solution Is there any better way than finding the angle between lines and their lengths and then the area?

Hi, I need to calculate area of an irregular polygon which can be of any complex shape numerically i.e. using numerical integration techniques. Please can anyone suggest any reference material / best way of going about this efficiently? Akash

I learned in my calc 1 class that to calculate the arc length of a curve, we are to compute the integral of the function. For example, the integral of a function that describes the path of a thrown baseball would give the total distance traveled by the baseball (I hope I'm using the term arc...

This question has been asked probably many times, and is inspired by area that appears in denominator of energy flux unit [W/m^2]. From what i have read so far, i come to conclusion, that this post should, first of all, try to explain that this question makes some sense. First thing that...

So I was reviewing my random process notes. In it there is an integral that they have that I can't seem to get the right derivation of when they try to simply the math for ergodic mean. Basically, you have the following: A square from (-T,T) on both the x-axis and y-axis. What they want to...

Given a sphere x^2 + y^2 + z^2 = a^2 how would I derive the surface area by using surface integrals? The method I've tried is as follows: dA = sec\ \gamma \ dxdy where gamma is the angle between the tangent plane at dA and the xy plane. sec \gamma = \frac{|\nabla \varphi|}{\partial \varphi...

Homework Statement A triangle has verticies A(-2,1,3), B(7,8,-4), and C(5,0,2). Determine the area of the triange ABC. The correct answer is 35.9 square units. Homework Equations Has to be done by using dot product and/or cross product. Dot product: a(dot) b= |a||b|cos(theta) Cross...

Homework Statement The solar constant, the amount of solar energy reaching the Earth per unit time and area above the atmosphere and an element of area perpendicular to the direction from sunlight is 1.36 kW / m². For an element of area whose normal makes a angle q with the direction of...

Hello . I am in the end of my exams and i have to do a geometry figure like a pyramid ( view image ) below Now i should find the Perimeter, Volume and Surface of this figure . Lengths are all 5 cm, Can somebody find and write the Permiter,volume and surface for this figure please it's urgent...

Hi, I always wondered, what is the area under an inexisting curve. That arctan(1/sqroot(x^2-1)) for example. Its domain does not include from -1 to 1. If I take its integral from 0 to 10, what answer should I get?

Homework Statement We know the if two 2D shapes are similar, the ratio of their areas are equal to the ration of the square of the corresponding sides. ##\frac{A_2}{A_1}=(\frac{l_2}{l_1})^2## Prove this The Attempt at a Solution For rectangles: Let the area of first rectangle be ##A_1## and...

Hawking said that the horizon area of a black hole never decreases and illustrated that in his Hawking Are Theorem: dA/dt ≥ 0 Does anyone know why is it like that. Why doesn't the area decrease?

Why is preferable to use the line integral than the area integral over the complex plane?

Homework Statement A cylindrical rod has a spherical bubble in it. as illustrated in figure 4.2 (in the attachments) The rod has a cross sectional area of 3.2 x 10^-6 m^2 and is stretched by forces of magnitude 1.9 x 10^3 N. The maximum Stress that the cylinder can take is 9.5 x 10^8...

Homework Statement Please note that I am making this problem up and it is not "assigned" to me: A large tank of water has two small holes at the same height, near the bottom. Hole A's area is twice hole B's area. Is the volumetric flow rate (volume per time) of water out of hole A bigger than...

Homework Statement Find the area of the region that consists of all points that lie within the circle r = 1 but outside the polar equation r = cos(2θ) Homework Equations A = ∫ 1/2 (r2^2 - r1^2) dθ, where r2 is outer curve and r1 is inner curve. The Attempt at a Solution Here is...

Homework Statement Find the area of the region. Interior of: r = 2 - sin(b) Homework Equations A = 1/2 ∫ (r)^2 dr The Attempt at a Solution I really don't have any idea how to approach this problem. I don't understand how to determine my limits of integration. The only part of the problem I...

Is this so? I cannot think of a counter-example and it is too general a statement to prove.

Question: What is the area enclosed by the lemniscate r2 = -25cos([FONT=arial]Ѳ)? The answer is 25. I can't seem to set up the integral for this question correctly. I know that the area enclosed by a polar curve is obtained by the integral(r2/2) d[FONT=arial]Ѳ[FONT=arial], but I can't determine...

Homework Statement Homework Equations x^2 + y^2 = 9 A = 0.5xy x ≠ y The Attempt at a Solution x^2 + y^2 = 9 A = xy/2 (x + y)^2 = x^2 + 2xy + y^2 = 9 + 2xy = 9 + 4A A = ((x+y)^2 - 9)/4 Then I am lost. I need to find the area.

Hi I'm doing a surface area problem with a parametric surface and I got the cross product but I can't figure out the double integral. I found the solution online but with no explanation, so can someone explain how to solve this integral: thank you!

Problem: Let $0<a<b$ i)Show that amongst the triangles with base $a$ and perimeter $a+b$, the maximum area is obtained when the other two sides have equal length $b/2$. ii)Using the result (i) or otherwise show that amongst the quadrilateral of given perimeter, the square has maximum area...

Homework Statement Problem is attached in this post. Homework Equations Problem is attached in this post. The Attempt at a Solution I set my Integral as ∫cos2π dx from 0 to 1/2 and get an answer of 0, which is incorrect. The correct answer is 1/π, but I don't understand why etc.

Homework Statement Find the are of the parallelogram ABCD where A is (1,2,-3), B is (-1,3,-4) and D is (1,5,-2)Homework Equations Area=\left|AxB\right| where A and B are the vectors AD, and AB respectively.The Attempt at a Solution I have calculated AD to be= (0,-3,-1) and AB=(2,-1,1) ∴ to...

I know this has been asked many times. I am integrating acceleration data from MEMS accelerometer to get velocity. I found an app note by freescale - http://cache.freescale.com/files/sensors/doc/app_note/AN3397.pdf It ignores the sampling time to calculate the area. The formula should...

Problem: If A is the area and 2s the sum of three sides of a triangle, then: A)$A\leq \frac{s^2}{3\sqrt{3}}$ B)$A=\frac{s^2}{2}$ C)$A>\frac{s^2}{\sqrt{3}}$ D)None Attempt: From heron's formula: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ From AM-GM: $$\frac{s+(s-a)+(s-b)+(s-c)}{4}\geq...

Say I have a plane, and it intersects with a [edited]cylinder*. What kind of method should I use to go about solving this? I've tried setting up a ##\int \int dA## situation, but wasn't sure that was applicable because it's in 3-space (also my plane is in terms of x y and z). I know it's...