1. ### I How do I read this equation for air friction/drag on an object?

I am trying to understand an excerpt from an article describing the vibrations of a string (eg. guitar/piano) which reads as follows: This is basically the wave equation with Δm representing a small piece of mass from an interval of the string and two forces added to the right side. He...
2. ### Using a determinant to find the area of the triangle (deriving the formula)

This is the question. The following is the solutions I found: I understand that the first line was derived by setting one vertex on origin and taking the transpose of the matrix. However, I cannot understand where the extra row and column came from in the second line. Can anyone explain how...

4. ### I Area of an inclined surface with respect to the original surface

Hi, I have a problem with inclined planes. The idea is to calculate the stress in an inclined plane of a bar under tension for which you need the surface. I have no idea how this surface is derived, though. In the attached file, you can see what I mean. For a rectangular cross-section, it's...
5. ### Neutrinos and their detection

Assuming that this sphere has a radius of 50kpc, I've converted to m (1.543e21) and plugged into the area equation for a total area of 2.992e43 m^2. From here I've talked myself into circles, and I honestly don't know where to go next. Any help or guidance would be greatly appreciated!
6. ### B What does the scalar product of two displacements represent?

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...
7. ### B Is this true? The area of a circle can be approximated by a polygon

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...
8. ### I Is there an algebraic derivation of the area element in polar coordinates?

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 ##...
9. ### How do I find the area of the region bounded by following?

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:
10. ### Area of a bounded region using integration

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...
11. ### Finding an area of a triangle formed by three points

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...
12. ### Calculating area using sigma notation

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...
13. ### Minimum possible period

Homework Statement A particle moves periodically around an ellipse of equation ##\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1##. You can assume ##a>b##. The ##x## and ##y## components of the particle's velocity can never exceed ##v## at any point. What is the minimum possible period of the...
14. ### Parallelogram Area Formula Origin - YouTube

This is my first video!
15. ### Bending Stress on a Protective Cover

Homework Statement A 30kg pallet falls from a height of 2m onto a protective cover. The cover has an area of 269m² and an overall thickness of 10.9mm. a. What is the force/pressure on the cover? b. What is the bending stress on the cover? Homework Equations F=ma bending stress =...
16. ### I Area divided by linear function

The original problem for anyone that can read Chinese: https://zerojudge.tw/ShowProblem?problemid=b221 The problem defines a convex polygon with multiple points located in the first quadrant and the required task is to find a linear function y = ax that can spilt the polygon into two parts each...
17. ### B Our universe's entropy/size vs Bekenstein's theory

Jacob Bekenstein asserts that the entropy of a black hole is proportional to its area rather than its volume. Wow. After watching Leonard Susskind's video 'The World as a Hologram', it seems to me that he's implying that we are all black hole stuff. Perhaps we (our galaxies and their black...
18. ### Maximum area of a fenced-in half a circle

. Homework Statement Let imagine you have gras field formed as a semi circle and you want to fence in that area. The fence is connected to a wall, so you only have to fence in the area formed by the semi-circle. You have to use 60 meters of fence bought at a hardware store. Homework...
19. ### Pressure on a Piston

Homework Statement Suppose there is a tank filled with water and a piston of area S exerts a force F on the water. Suppose I divide the water boundary touching the piston to - N small equal " square " molecules. Then , the force on the upper face of each molecule is F/N . Also, the area of...
20. ### I Surface area of a revolution, why is this wrong?

Why is this way of thinking wrong?. can't I assume that when Δx tends to zero is a sufficient approximation of what I want to get? It confuses me with the basic idea of integrating a function to get the area beneath a curve of a function (which isn't also as perfect) . PD: I put Δx tends to...
21. ### I Area between two closed curves

I have been trying to find an answer to this problem for some time. So I was hoping the community might be able to point me in the right direct. https://drive.google.com/open?id=1Y2hYkRG94whLroK20Zmce07jslyRL3zZ I couldn't get the image to load. So above is a link to an image of the problem...
22. ### I How to plot a scaled lognormal function

Hi, I am trying to plot a lognormal function. I have the value of μ=3.5, the value of σ=1.5 and the value of the Area = 1965. I have as well the value of the maximum height (Amp.=4724). I am tryiing to plot these with Excel or with R but I do not know how. I know how to plot a distribution of...
23. ### Force due to a chain falling on a table

Homework Statement a uniform fine chain of length l is suspended with lower end just touching a horizontal table. Find the pressure on the table, when a length x has reached the table.. Homework Equations Pressure = force/area The Attempt at a Solution let mass density, m= mass/l...
24. M

### How to find the area of a triangular region using Green's Theorem

Homework Statement You have inherited a tract of land whose boundary is described as follows. ”From the oak tree in front of the house, go 1000 yards NE, then 1200 yards NW, then 800 yards S, and then back to the oak tree. Homework Equations Line integral of Pdx + Qdy = Double integral of...
25. ### I How to calculate the area under a curve

I was doing some integral exercises for getting area under the function. I was doing only more simple stuff, like functions that don't go over the same "x area" multiple times, like a quadratic function. My question is how to calculate area of a loop in an equation x^3+y^3-3axy=0 if let's say...
26. M

### B Flux dependant upon the number of turns?

https://atarnotes.com/forum/index.php?topic=144870.msg953546#msg953546 http://i.imgur.com/XtCj6OP.png (worked solution on left and plain answer on right; they aren't the same and neither take into account the number of turns, which adds to the confusion) Is the book's answer correct? Doesn't...
27. ### Area of Hexagon - Geometry Challenge

Determine the area of the painted hexagon, knowing that the area of triangle ABC is 120cm^2 IMG Link: https://m.imgur.com/a/WtdsW I tried using Heron´s formula, but just ended up with a bunch of terms and one more variable. Sidenote: I guess part of it is figuring out that the side lenghts...
28. ### B Thermal resistance without area

I'm (self)studying the physics of heat transfer at the moment. My book gives a relationship between heat transfer rate and thermal resistance as ##\phi=\frac {A \Delta T} {R}##. My book is not in English, so hopefully that is not the cause of this misunderstanding. I double checked that heat...
29. ### Minimum of x+1/x (Perimeter Square < Perim equal area rects)

Homework Statement Gelfand - Algebra p.115 problem 264: Prove that a square has the minimum perimeter of all rectangles having the same area. Hint. Use the result of the preceding problem. Homework Equations Preceding problem: Prove that a square has the maximum area of all rectangles having...
30. ### Second moment of inertia for a bent rectangle

Hello. I am currently working with a beam with the following cross-section: It consist of three bended sections with the following parameters, alpha = 90 degrees, Thickness = 4 mm, Radius = 50.59 mm. The top section consist of a small triangle and a rectangle. the triangle have a width = 4 mm...