Area Definition and 1000 Threads

Hi, I know that area of rectangle is length x breadth. I tried to find proof of area of rectangle but I found that the proof was solved by taking formula of area of square into consideration. But what I don't understand is why area of rectangle should be length times breadth, or side times side...

Okay, so this is quite hard to explain in words so I will use pictures. Suppose you have a Square with the length of W You also know the distance from the pink surface to the center of the square is X. The rotation of the square is theta. As shown in the picture above... So the problem is: Is...

Hey everyone, I was recently reading a paper on surface enhanced Raman scattering, and it mentioned that plasmons (and for that matter surface plasmon polaritons-where my interest lies) are sensitive to the surface to volume ratio of the structure. I can begin to understand intuitively with...

Hello, I'm hoping somebody can give me some insight on how to solve this problem. This was a solid mechanics exam question and I wasn't able to finish it because I'm rather weak in math. 1. Homework Statement Homework Equations Recall divergence theorem for part ii. ∫div(V)dA = ∫V⋅ndS where...

I want to know how did it arrive at the third line of this proof. I didn't get it. Thanks!

Homework Statement Use an iterated integral to find the area of the region bounded by the graphs of: f(x) = sin(x) g(x) = cos(x) between: x = \frac{\pi}{4} and x = \frac{5\pi}{4} Find two solutions, one using a vertical representative rectangle and another using a horizontal...

Homework Statement Find the area inside one loop of r = 2cos(3 theta) and outside the circle r = 1 Homework EquationsThe Attempt at a Solution I need to clarify something about the limits of integration. I found the intersection of the two curves to be at an angle of pi/9. This is how I...

Homework Statement Homework Equations [/B] Surface area of sphere = 4*Pi*r^2, where r: is the radius of the sphere circleThe Attempt at a Solution Solution:[/B] 1. In terms of “r” and “R”, and the radius of sphere “S”, and “d”: Given that: · Surface area of both shaded area are equal...

1. Homework Statement Hi all, I am working through Gravity by James Hartle and have become stuck on a question asking me to calculate the area of a circle of radius r in the 2D geometry that is the surface of a sphere of radius a. A surface element on this sphere can be found to be...

Find area inside circle x^2+y^2=a^2, above 7=b, -a \le b \le a ?? i think f of y right? (-a to a) minus (-a to b)?

Homework Statement Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 4. Solve by writing the area as a function of θ Homework Equations A=1/2 (bh) The Attempt at a Solution Given the side h and the hypotenuse 4, we can find the base of the smallest...

As I posted in another thread, I'm giving the caveat that I am no physicist and have only a rudimentary knowledge of math. Anyway, I am currently reading a book called "Three Roads to Quantum Gravity" by Lee Smolin. I came across a section of the book that confused me. Namely, Dr. Smolin...

I'm trying to follow Schwabl Thermodynamics, and I found the following equation for the surface area of a unit d-sphere: $$ \int d\Omega_d = \frac{2 \pi^{d/2}}{\Gamma(d/2)} $$ But this formula clearly fails for d=1: should be $$\pi$$ and d=2: should be $$ 4 \pi $$. What gives?

The question is attached in the attachment below.

Hello guys, I am doing a wind tunnel and I want to calculate the aerodynamic coefficient of some cars. To calculate this I need the frontal area of the car and I don't know how to calculate it manual. Is there any pc program to do it or any formula? Thank you very much.

Homework Statement Sketch the region enclosed by y=e^(5x), y=e^(9x), and x=1. Decide whether to integrate with respect to x or y. Then find the area of the region. Homework Equations The Attempt at a Solution [FONT=Times New Roman]I tried graphing all the lines but they the...

I am transferring from Mizzou (MU) to somewhere in the LA area over the summer. What are my best options? I know of caltech and UCLA. Caltech looks really difficult to get into. I probably can't get into Caltech, I assume I could get into UCLA. But is UCLA my best option for future career...

Homework Statement Question: Lake Mead is formed by the Hoover Dam, and while it actually changes in area and volume, consider it has an average area of 100,000 acres. Assume that 250 W/m^2 of sunlight falls on Lake Mead, how much electricity could be produced if this lake area was covered by...

for the line y=4x-2 there is one perpendicular line of which will enclose a triangle on the lines and the values of the y-axis whose area is 8. What is the equation of this line? Well, I chose the x value to be the height of the triangle and that would make the base $$B=(4x-2)+2+\frac{1}{4}x$$...

I am trying to calculate the area under the curve of a projectile for a school project. A simple way to do this is to integrate the following equation of the trajectory: However I've tried to use another method. Since we have the two equations for the horizontal and vertical displacements...

Homework Statement Insects don't need lungs. They breath through their skins. In this way they can get enough oxygen to fuel the basic metabolism that is common to all life. Approximate an insect by a cylinder of diameter 4mm and length 5mm. Assuming that the density of the insect is...

this is the given problem: and this is my attempt at a solution: I am stuck here as the variable y is unknown and I want to express y in terms of x, but cannot figure out how to do so. Thanks for any help!

Hi, I don't understand what this question is asking and I have idea how to do it.. any help is very much appreciated! I understand how to complete the square, parabolas and such and the concept of maximum and minimum, I just don't understand this question. A Cattle farmer wants to build a...

This is my first post but I have frequented the forum for a little while now. I tried to figure things out myself and often times I am lead here by google. So my question is this: How is the electric field of an object altered when the surface area of the object is altered? Example: Take a...

The convex quadrilateral $ABCD$ has area 1, and $AB$ is produced to $P$, $BC$ to $Q$, $CD$ to $R$, and $DA$ to $S$, such that $AB=BP$, $BC=CQ$, $CD=DR$, and $DA=AS$. Find the area of the quadrilateral $PQRS$.

Hello! I'm having some trouble determining, when trying to find the area between two curves, when to integrate with respect to y or respect to x, given two equations only? Thanks!

Homework Statement Find a nonzero vector orthogonal to the plane through the point P, Q,and R. (b) also find the area of triangle PQR P(1,0,1) , Q(-2,1,3) , R(4,2,5) Homework Equations -Cross product -Finding the Angle -Area formula The Attempt at a Solution My steps: 1. i found the...

Prove that if the sides of a triangle are prime numbers its area cannot be whole number.

Homework Statement Hello, I've been trying to solve this problem, but in the examples that my teacher gave me didn't include something like this, I know how to calculate area but only if I have all the coordinates established. I need to find the area using the cross product. Homework...

Homework Statement Evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point. f(x) = \frac{1}{x^2+1} at the point (1,1/2) Homework Equations The Attempt at a Solution So far I...

I am sure this should have already be discussed somewhere in the past... I have an intuitive problem with the area of a sphere. Following the mathematics of the metric and surfaces, I can easily derive the area of a sphere which is 4 \pi R^{2} . Now I'm have this problem: Suppose I get a ring...

Maybe I'm plugging my website but I just finished writing a versatile cylinder calculator. If you know two variables (Volume Area Radius Height), it calculates the other two. http://www.1728.org/diam.htm It was a little tricky deriving the formulas but I'm glad I did. (Yes, I know if you...

Hello everybody, I'm trying to know, in a keplerian orbit, how to calculate the area of a swaped area; since the Sun is at one of the focus, I wish to calculate given an angle measured from focus to the orbiting body, the area swaped. I don't know if I'm explaning this right...Hope so...

Homework Statement Dear friends, let U and V independent variables that are both defined on [-∏, ∏] and are uniformly distributed. If x = cos(U + V) and y = sin(U-V), what is the area where the variables X and Y are defined? Homework Equations U + V = arccos(x) U - V = arcsin(y) For a test...

Homework Statement How to find area of an n-dimensional triangle using vectors? Homework Equations The Attempt at a Solution

This is a part MATLAB and part math question. I know for the shaded region, I would usually do ##A_{shaded} = \int_{inter(2)}^{inter(3)} f_{1}(x) \mathrm{d}x - \int_{inter(2)}^{inter(3)} f_{2}(x) \mathrm{d}x## However, since it appears they want the function handle to be just one line, am I...

I'm wondering how to scale up the surface area of a sphere of 6 million meters in radius, into a hypersphere of similar radius (i.e. a Hyper Earth). I would also like to know the ratio. I would like to know the basic value in 4th dimension, but knowing values for 5th, 6th, and higher would...

Hey guys, I would really appreciate some help for this question I'm stuck on at the moment: "A piece of 2 m long wire is to be cut into two pieces one of which is to be formed into a circle and the other into an equilateral triangle. How should the wire be cut so that the total area enclosed...

Hi everyone! I have a question for you all. I'm a 3rd year undergraduate math student who took 4 years away from school and I'm going to be returning this Fall(^.^). Prior to leaving school, I'd take courses in C++, Numerical Methods, Two additional semesters of Numerical Analysis, Modern...

This is not a high school question, but it seems to be too broad to fit in any of the other categories. Fractals are cute (nice pictures that can also be used to give better graphics, and also "shocking" that one can define a non-integer dimension), can be used to estimate lengths or volumes of...

Homework Statement Please see attached image file I understand everything in this problem except I don't know how they got (1/4) in the area of a coil. Can someone explain this? I have googled it and I am not getting a clear answer. I thought the area of a coil could be (pi(r)^2)L...

Find the area of the region between the given curve and its asymptotes. $$y^2 = \frac{x^4}{4-x^2} $$ The answer is $$4\pi$$ What I did was I integrated $$y = \frac{x^2}{\sqrt{4-x^2}}$$ but my answer is only $$2\pi$$. I'm thinking that by squaring the function, I lost one half the answer (the...

Theoretically it is said that, tangent touches to a single point on a circle. But If my circle is very big, and large enough, then i think, it should not be a just single point where my tangent is touching, though is will be a very small portion depending on how large is the circle. If i have...

Hey guys, I need some more help for this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. This is only for question 2. Ignore 1. Question: Alright, so from drawing a diagram, we know that width is "L" and length is "3L." Moreover, the area of...

[SIZE="4"]Definition/Summary Moments of area are properties of rigid bodies, they depend only on shape and not on density, and they are scalars (numbers), and are measured relative to a particular axis. First moment of area measures a body's resistance to shear stress along an axis...

find the area of the region that lies inside the first curve and outside the second curve. $r=3cos(\theta)$, $r=1+cos(\theta)$ $3cos(\theta)=1+cos(\theta)$ $2cos(\theta)=1$ $cos(\theta)=\frac{1}{2}$ $\theta= \frac{\pi}{3}, \frac{5 \pi}{3}$$A=\frac{1}{2} \int_{\pi/3}^{5\pi/3} \ (3cos(\theta))^2...

find the exact area of the surface obtained by rotating the given curve about the x-axis. $x=cos^3(\theta)$, $y=sin^3(\theta)$, $0 \le \theta \le \pi/2$. $\frac{dx}{d \theta}=-3sin(\theta)cos^2(\theta)$ $\frac{dy}{d \theta}= 3sin^2 (\theta)cos( \theta)$ $S=2 \pi \int_{0}^{\pi/2} \...

Homework Statement Youtube: Lec 2 | MIT 18.02 Multivariable Calculus, Fall 2007 (Video time frame: between 11:00 minutes and 12:30 minutes) Find the area of a triangle. Area = \frac{1}{2}(base)(height) = \frac{1}{2}|a||b|sinθ The lecturer says to first find cosine of the angle using dot...

Homework Statement show rectangular box of given volume has minimum surface area when the box is a cube [gotta show it with partial derivatives to minimize] Homework Equations surface area = 2(wl+hl+hw) volume = whl The Attempt at a Solution so this is the one I would be minimizing...

For the first one, I'm completely dumbfounded. I used the SA formula for and ended up getting 2 $π\int_{π/6}^{0} \, cos2x * √1+4sin(2x)^2 ) $ And took u = sin2x, ultimately giving me $ π\int_{√3/2}^{0} \,d (1+ 4u^2)^(1/2) $ I'm lost as to what to do next. I'm almost definite that my...