Area Definition and 1000 Threads

I know C=Epsilon0(A)/delta x From the problem, C=3,000 Epsilon0 = 8.85 × 10^-12 and delta x is .5mm The answer is supposed to be given in meters and should be close to 40,000 but I got 1.6*10^11m...help please!

I am currently taking graduate course in GR following Carroll and Wald and we just started covering causal structure. In all my years studying physics this has been the first time something made me stop and go "I would love to spend a decade on this". To me it's a perfect blend of well posed...

There is an equation which perplexes me and it is about calculation of average velocity in a pipe but over area. In the image, the velocity is already function of diameter, i.e, u=u(r) so how can we think velocity as a function of area? Source: Fluid Mechanics, Fundamentals and...

Hi, I got a question from a book to find the area of a Quadrilateral. I divided the quadrilateral into two triangles but answer is not correct. Some body please guide me. I am uploading my work in a attached file. Zulfi.

does anyone know how to calculate the second moment of area of a typical quadcopter arm like this? what should I approximate the cross section as...

Homework Statement A piece of wire, 100 cm long, needs to be bent to form a rectangle. Determine the dimensions of a rectangle with the maximum area. Homework Equations P = 2(l+w) A = lw The Attempt at a Solution This is what I don't understand, the solutions that I saw from looking around...

Homework Statement Find the surface area S of the portion of the hyperbolic paraboloid: ## r(u,v) = \langle (u+v),(u-v),uv \rangle ## for which: ## u^2 + v^2 <= 225 ##Homework Equations (Surface Area for Parameterized Region:) ##\int \int ||\frac {\partial r} {\partial u} \times \frac...

Homework Statement A quarter disc of radius 3 cm lies in the first quadrant. The areal density is (1.2 g/cm3)x + (0.7 g/cm3)y. Determine the mass of this object. Homework Equations The Attempt at a Solution For my bounds: x: 0 to 3 y: 0 to Sqrt[3 - x^2] When I took this integral I got...

Hey everyone. I've never been very good at math/science so I'm seeking a little help from this forum in hopes that there is someone out there who can provide me or guide me to an answer. What I'm trying to figure out is the difference in force or pressure exerted on the human spine for an...

Homework Statement Okay, I don't actually have a homework problem that explicitly tells me to find the reason why; it's just something I was wondering while I was trying to integrate circles using trigonometric substitution. But just for reference's sake: "Why does Acircle = ∫√(a2-x2)dx?"...

I'm given that: S is the surface z =√(x² + y²) and (x − 2)² + 4y² ≤ 1 I tried parametrizing it using polar coordinates setting x = 2 + rcos(θ) y = 2rsin(θ) 0≤θ≤2π, 0≤r≤1 But I'm not getting the ellipse that the original equation for the domain describes So far I've tried dividing everything...

Homework Statement dA lies on x and y aixs , right ? the author gave that the volume flow rate thru element A is ucos(theta)dA , why not usin(theta)dA ? if u ' = ucos(theta) , it will become parallel to dA , right ? since u' will be parallel to x-axis... Homework EquationsThe Attempt at a Solution

Using Bernoulli's equation to calculate the velocity of fluid draining from a tank seems to give no weightage to the area of the drainage hole. But based on the mass continuity principle, the area of the hole should have an impact. Does the area of a drainage hole have an impact on the fluid...

Two corresponding sides of two similar polygons have lengths 3 and 7. the perimeter of the larger polygon is 91 cm. What is the perimeter of the smaller polygon? What is the ratio of their areas? I believe I have found the perimeter of the smaller polygon (39), but I can't figure out the areas...

Given an Isosceles triangle with the area of 100 with internal angles of $$40^o, 70^o,70^o$$ $A=\frac{1}{2}bh$ so $100=\frac{1}{2}\left(z\sin\left({70^O}\right)\right)\left(2z\cos\left({70^o}\right)\right)$ $z$ is length of one the equal sides At least started here

Homework Statement Find area bounded by parabola y^2=2px,p\in\mathbb R and normal to parabola that closes an angle \alpha=\frac{3\pi}{4} with the positive Ox axis. Homework Equations -Area -Integration -Analytic geometry The Attempt at a Solution For p>0 we can find the normal to parabola...

I am bothered on how the area of circular sector was derived using integration. I have a solution but I don't know how it will go and come up with the formula: A = 1/2 sr and A = 1/2 r2 θ Can someone show me the solution for...

Homework Statement Show the area under the curve of v(t) is equal to the displacement from t1 to t2 Homework Equations x/t = v The Attempt at a Solution Integrate V(t) = vt dt (v/2)*t^2]t1 to t2 (v/2)*t1^2 - (v/2)*t2^2 Not sure if that is good enough or how toactually show it. To find the...

Homework Statement why the formula of volume is given by integral of P and dA , the integral of P and dA would yield Force , right ? Homework EquationsThe Attempt at a Solution

Homework Statement Find area bounded by functions y_1=\sqrt{4x-x^2} and y_2=x\sqrt{4x-x^2}. Homework Equations -Integration -Area The Attempt at a Solution From y_1=y_2\Rightarrow x=1. Intersection points of y_1 and [/itex]y_2[/itex] are A(0,0),B(1,\sqrt 3),C(4,0). Domain of y_1 and y_2 is...

Hi. Given the area, what is the shape of an infinitely thin surface that can carry maximal load on water, i.e. has the best buoyancy just before water gets in? Is it the hemisphere?

I am planning to measure the wing area of a Spitfire aircraft. I am going to use double integral formula, but firstly I need to derive the continuous function for the region of interest. Also, How to do that? I searched the entire internet and only found out the wing span of that aircraft...

Homework Statement Two packages are dropped from an airplane. A parachute can increase the cross sectional area of each packages by a factor of 31. The parachute on package 1 fails to open, and the terminal speed of package 1 is 10 m/s. The parachute on package 2 opens. What is the terminal...

1. Problem I have a horizontal cylinder with a ball in it. What must the initial pressure be to launch the ball at Z velocity? 2. Attempt P = F/A A = Surface Area(Cylinder) - 1/2 Surface Area (Ball) = (2πrh) F = m*a U = - ∫ F dx U = 1/2 mv^2 at x = h ∫ a dx = -1/2mv^2 / m at x = h Z =...

Homework Statement In a uniform magnetic field with induction of 0.1 Teslas - a coil is located perpendicular to the lines of induction (I suppose it's something like a ring of wire, meaning N=1). Resistance = 2 Ohms. What is the area of the "ring" if when the field is switched on - it will...

hi guys, i have a question. i saw this picture, and i don't really understand how they derived with the formula. The aim is basically to find the formula for the surface area of a spherical cap. why do you differentiate the x=sqrt(rˆ2-yˆ2)? how does that help to find the surface? and then...

Homework Statement If the area of a rectangular field has length of 110 m and 80 m.If a spaceship is traveling with 0.9c velocity along the diagonal of the field.Then what is the area of the field seen by the astronaut in the spaceship? Homework Equations L=L(initial) Root over (1- (v/c)^2)...

Just humour me, if you had an infinitely thin cone, would the surface area inside the cone be the same surface area on the outside of the cone? It must be right? Is there a formula for the surface areas of the inside and outside of a cone WITH thickness?

Homework Statement I am after finding the centroid of the remaining area (hatched) when a circle is cut by a line. I made a diagram in CAD that demonstrates the problem. The idea is that, starting from the bottom of the circle, a cut is taken leaving a remaining shape whose area and...

Area_sector = 0.5 (radius)^2 * angle Arc length= radius * angle Can it be said and proven that the area of a sector is the integral of the arc length? What would that even mean?

How does it work that you can subtract y2 from y1 and integrate the product within defined limits for the area of their intersection (within those limits)? Maybe that's not the right terminology - you arrive at the area for the region bounded by both functions. Is it just the same in practice...

Homework Statement http://postimage.org/][/PLAIN] free picture upload 2. The attempt at a solution I want to go width times delta height. To do this I must describe width in terms of height. Here they used the Pythagorean theorem which is weird to me because I don't see a nice triangle...

I am trying to understand N-spherical cap area formula (surface area of blue part), but it seems to give wrong answers. for 1 dimensional cap obviously ## \frac{l_{cap}}{l_{sphere}}=\frac{l_{arc}}{l_{circle}}=\frac{r*θ}{r*2π}=\frac{θ}{2π} ## But according to wikipedia formula...

The circumference of the shaded ring is 2πρ however I am struggling to understand how the area, dA, of the ring is equal to (2πρ)dρ? I mean the circumference varies depending on the value of ρ so surely we can't multiply by dρ to yield the entire area of the shaded ring? If we decided to go by...

A sphere with radius "r" has three points on its surface, the points are A, B, and C and are labelled (xa, ya, za) and so on. What is the general formula to calculate the area on the surface of the sphere defined by these points?

Why we sometimes take the area bounded by the curve is sum of positive area and absolute of negative area(e.g. ∫\int_0^2π sin(x)\, dx is equal to 4 or area of ellipse )?But sometimes we just sum positive and negative areas which is equal to 0(e.g. area of cycloid →when we integrate we get...

Hi, I wanted to see if I could understand Archimedes' proof for the area of a sphere directly from one of his texts. Almost right away I was confused by the language. Archimedes lists a bunch of propositions that eventually lead up to the 25th proposition where the area of the sphere is finally...

Homework Statement How do I find the surface area of a sphere (r=15) with integrals. Homework Equations Surface area for cylinder and sphere A=4*pi*r2. The Attempt at a Solution I draw the graph for y=f(x)=√(152-x2). A circle for for positive y values which I rotate. I will create infinite...

this is a picture of my notes for thermal expansion for linear vs area. my question is why does the area coefficient of expansion for the area = 2(liner coefficient of expansion). any insight would be appreciated.

I have some data and in said data I had 2 peaks, to which I fitted 2 Lorentz functions. The sum of these 2 functions gives me a 3rd function. Now, I need to find the integrated area of the 3rd function. Originlab gives me the area of the 2 fits, but not of the 3rd function. Summing the area of...

Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. Between y = x^2 − 5x + 2 and y = −x^2 + 5x − 6 for x in [0, 4]

Calculate the area of a triangle knowing its 3 heights ha = 3 m hb = 4 m hc = 5 m NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 10.03 m2 B) 10.04 m2 C) 10.05 m2 D) Imposible

Calculate the area of a triangle knowing its perimeter and 2 heights perimeter = 30 m ha = 8 m hb = 9 mNOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 41.29 m2 B) 42.93 m2 or 36.28 m2 C) 42.95 m2 or 36.29...

Calculate the sides of a triangle knowing its area, perimeter and angle A. Area = 30 m2 Perimeter = 30m Angle A = 30º NOTE = You can use the online triangle calculator TrianCal to see and draw the results. NOTE = Do not use the values ??of responses. A) 6.09, 9.36 and 14.55 B) 7.40, 8.63 and...

Homework Statement http://i.stack.imgur.com/KzCIl.png From the given picture the known quantities are: ##r = 7*3^{1/2} ## ##BC = 13 ## angle opposite to AC is ##120 ## degrees Homework Equations 3. The Attempt at a Solution [/B] I figured i could use a sine rule to get the side ##AC ##...

Homework Statement Given the isosceles triangle whose sides are : c=10 b=13 find the are of a square drawn inside the triangle whose upper edges touch the b sides of the triangle. Homework Equations 3. The Attempt at a Solution [/B] I named the side of the square a. First i made two equations...

Homework Statement Homework EquationsThe Attempt at a Solution here is my approach, I take the whole area, which is π16 then subtract the unshaded region now to find the unshaded region's area, I use rectangular coordinates. my bounds are from -2 to 2 for x and the the top and bottom of...

Homework Statement Wikipedia tells me that I can obtain the surface area of a sphere by realizing that the volume of a sphere is equivalent to the infinite sum of the surface areas of hollow, nested spheres, sort of like little Russian dolls. That makes sense, and then differentiating both...

Whats's the volume under the revolving parabola y=ax2. R is xmax. $$V=\int_0^R\pi xdx\cdot y=\pi\int_o^R x\cdot Ax^2dx=\pi A\frac{R^4}{4}$$ Volume should be relative to R3. and if i had, for example, y=Ax3 then, according to my calculation i would get relative to R7 and so on.

Homework Statement x(t) = 6cos(t)−cos(6t) y(t) = 6sin(t)−sin(6t) 0 <= t <= 2*pi I need to find the area cm2 with Th Green. I need to find the radius and the center coordinate Homework EquationsThe Attempt at a Solution $ = integral 1/2* ( 2*pi$0 ((x)dy - (y)dx) dt ) 1/2 (2*pi$0...