Area Definition and 1000 Threads

Known data: In the picture, CD = 10 cm. What is the area of shaded area? Equation: I know, Area of a circle = ##πr^2## Diameter of a circle = ##2πr## Attempt: Here, ## r = 10/2 = 5 ## So, diameter ## = 2πr = 2*3.1416*5 = 31.42 cm ## And area of the circle ## = πr^2 = 3.1416*5^2 = 78.54 cm^2...

Square-shaped piece of paper is intended to make a regular octagon through the cutting of the vertices of a square. The length of the piece of paper is 29 cm. How long triangle cathetus have to be cut off from the vertices of the square? Calculate the octagonal side length, circumference, and...

I have been teaching undergrad students informally, and one of the math problems that I have always enjoyed introducing them to is how to compute the area under a gaussian curve, or to keep it simple, the area under the curve ##z=e^{-x^2}## One of my students asked me a question that has...

I am working on a synthesizer project and have reached a point that I am stumped on. I am in this part trying to work from a basic curve of y=1/x^c (where x≥1): As I understand, area under the curve between x=1 and x=100,000,000 (ie. more than I need for a rough approximation) would be...

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...

Homework Statement Question attached in attachments Homework Equations Area enclosed by polar graph is ∫0.5r^2 where r is the radius as a function of angle theta The Attempt at a Solution I attempted to use the formula above and I subtracted the area of the inside from the outside but it...

Dumb question probably -- But is there a way to measure gravity in a particular area of space, or a "measurement" .. I.E. the gravity 10 miles above Earth v.s 1000 miles above. Not force on another object, but some "unit" or measure of gravity itself.

Homework Statement Please help me solve the calc problem pictured! Homework Equations y=3-x^2 and y=x+1 The Attempt at a Solution My attempt is in one of the photos!

Does anyone know of any night B.S. Physics programs in the SF Bay Area? I can't switch jobs or stop working full time. I don't have the luxury to go back to school full time, nor extra financial support. I want to go back to school for a completely different career path. I currently have a...

Hey! :o A DIN A4 sheet is divided into thirds. A rectangle is the root of the tree, the other two rectangles are each divided into thirds again. Two rectangles form the branches - one to the left, one to the right - the others are again divided into thirds and so on. I want to calculate...

Well, I, as the King of the World, have built the great Tower of Me! However, because everyone seems to hate me for some reason, citizens keep trying to enter my tower to kill me. So, I have assigned some laser transmitters in my castle. However, as the technology is new, a laser transmitter can...

So for a story I'm writing, there is a character with the ability to absorb force and store it (the force never impacts but its absorption works like pausing a movie). The force can be released (or resumed) through use of a circular space called a "rune". The character can control the size/area...

In paragraph 5.7 of this lecture, Feynman explains how to calculate the apparent area of the nucleus, in a sheet of unspecified material. I have two questions about the formula used by Feynman. 1) Although the sheet has a thickness, the formula considers only the superficial area of the sheet...

If u know a equation for finding the area please submit it. Or a way to do it without using a program such as "Geogebra". Thanks in advance.

π is defined by the ratio of the circumference (R) of a circle to its diameter. The area of the circle is πR². Can this be derived without calculus (or Archimedes method)?

Homework Statement The doorway in the previous question measures 1.06 m x 2.04 m, and the wind blows parallel to the wall surface at 3.89 m.s-1. Calculate the force pushing the curtains out of the doorway. The density of air is 1.29 kg.m-3. Known data: A = (1.06m)(2.04m) = 2.162 m^2 v(wind)...

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...

Homework Statement Suppose that: 0∫2f(x)dx = 2 1∫2f(x)dx = -1 and 2∫4 = 7, find 0∫1f(x+1)dx Homework Equations a∫bf(x) = F(b) - F(a) The Attempt at a Solution So in these types of integration, we are needed to use u-substitution, the problem is, using u-substitution requires you to have...

Homework Statement Determine the area of the surface A of that portion of the paraboloid: [x][/2]+[y][/2] -2z = 0 where [x][/2]+[y][/2]≤ 8 and y≥x Homework Equations Area A = ∫∫ dS The Attempt at a Solution Area A = ∫∫ dS = 3∫∫ dS

Homework Statement Let r be a positive constant. [/B] Consider the cylinder x2 + y2 ≤ r2, and let C be the part of the cylinder that satisfies 0 ≤ z ≤ y. (3) Let a be the length of the arc along the base circle of C from the point (r, 0, 0) to the point (r cos θ, r sin θ, 0) (0 ≤ θ ≤ π). Let...

So I'm working on a method to allow control of a drop at different speeds. An idea my team had was to sit our test object on top of a piston, and drop the object by allowing the piston/plunger to drain out of a port at the bottom. We can't seem to wrap our heads around how the size of the...

So, I already wrote this as a short story on another website... so I'll link this. https://www.wattpad.com/553041235-short-stories-and-poems-just-after-that-last-proud It's pretty simple. She's little. She's got talent. Knowledge takes time to acquire. Schools in the area don't care till...

After watching hours of those home improvement shows, you decide you want to paint you bedroom. You don't want to paint all four walls the same color (how boring!), but instead, you want to paint one wall a different color. The electric orange paint you've chosen for the "special" wall is more...

Homework Statement A homeowner wishes to enclose a rectangular garden with fencing. The garden will be adjacent to his neighbour’s lot. There will be fencing on all four sides. His neighbour will be paying for half the shared fence. a) What should the dimensions of the garden be if the area is...

The area of the region limited by the curve $$y=x^2+2x-3$$, X-axis, Y-axis, and the line x = 2 is ... A. 4 area unit B. 9 area unit C. 11 area unit D. 13 area unit E. 27 area unit My attempt so far: $$x^2+2x-3=0$$ (x + 3)(x - 1) = 0 x = -3 or x = 1 X-intercept is at x = -3 and x = 1. After...

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...

Homework Statement Police will be sent to conduct their work on a site which is a rectangular region of sides 3.9 km and 9.1 km. To make their work easier, the region will be divided into square regions, each one having the largest possible area, and such that their sum equals the original...

In chapter 6, section 6.1 of David Cohen's Precalculus textbook Third Edition, page 368, I found an interesting geometry problem. Show that the area of an equilateral triangle of side s is given as shown in the picture. The hint given is this: Draw an altitude and use the Pythagorean...

What is the largest possible area of a simple quadrilateral, two sides of which have length $a$ and two sides of which have length $b$? Please justify your statement.

$\tiny{232.15.1.33}\\$ Evaluate the Area of the Region $$f(x,y)=3e^{-y}; R=\biggr[(x,y):0 \le x \le 8, 0 \le y \le \ln 4\biggr]$$ \begin{align*}\displaystyle I&=\iint\limits_{R} f(x,y) \quad dx \, dy \\ &=\int_{0}^{8}\int_{0}^{\ln 4} 3e^{-y} \quad dx \, dy \\ \end{align*} ok just...

https://gyazo.com/55afe69c0f00bff85a3a9c53bd353b42 Sorry for the really poorly drawn and lit picture... Basically this quadrilateral is drawn inside a circle whose middle point is O. Here is the info I was given KL = 18 LM = 24 KN = NM What I need to find out is the area of KLMN. What I...

\begin{align*}\displaystyle R&= y=0 \quad y=2x+4 \quad y=x^3\\ A&=\iint\limits_{R}15x^2\, dA\\ &=\int_{0}^{8} \int_{{(y-4)}/2}^{y^{1/3}} 15x^2\,dx \\ &=\int_{0}^{8}\biggr[5x^3\large\biggr]_{{(y-4)}/2}^{y^{1/3}}\quad dx\\...

Homework Statement When I have a disk with radius r then naturally the area is πr^2. Then I want to do this by calculus and my first step is simply taking πrdr. But the correct way is to take 2πrdr. To me this is really confusing, because I would never take 2πr dr (circumference x width)...

Homework Statement A ball is thrown at an initial speed v from level ground. What angle θ should be chosen so that the area under the trajectory is maximized? Homework Equations d = Vot - (1/2)gt2 Vt = d Integration, derivatives, and trigonometry The Attempt at a Solution I've tried to find an...

I believe the electric flux within a closed space can be found with the equation phi = Q/ε0. Can this be used for volume and area, or just volume? Also what good does this do. Why would I want to know the electric flux of something?

Homework Statement I have a function showing the volume of water in a bay at different times in the day, and I want to know what the area under this curve would represent (if it represents anything meaningful). I know how to integrate, so that isn't a problem. Homework Equations I am...

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...

Assume that the ratio of a big screen TV is 16:9. TVs are advertised by their diagonal (sp?) length. What is the screen area in square inches of a: a) 40 inch TV b) 60 inch TV c) 65 inch TV d) 80 inch TV e) 86 inch TV Show the formula (equation) that you used. Thank you

Homework Statement The surface area, A, of a cylinder with height, h, and radius, r, is given by the equation ##A=2πrh+2πr^2##. A company makes soup cans by using 32π square inches of aluminum sheet for each can. If the height of the can is 6 inches, find the radius of the can. Homework...

Homework Statement Find the area, A, of a sector of a circle with a radius of 9 inches and a central angle of 30°. Homework Equations $$Area~of~a~Sector:$$ $$A=\left( \frac 1 2 \right)r^2θ$$ The Attempt at a Solution [/B] $$θ=30°$$ $$θ=30°\left( \frac π {180} \right)$$ $$θ=\left( \frac π 6...

What lead to the equality of the, rate of change of area under curve f(x) = f(x). Was it, they were just compared(OR believed to be equal) and mathematically found to be equal. Or when one was integrated or differentiated the other appeared. Also I knew, integration was being used since...

What will be the area of common surface of two identical bubbles of radius R , i know there common surface will be flat as the radius of curvature of comman surface will tends to Infinity , but how do i relate with area of flat surface I tried to use Energy = Surface tension * area And then...

Hi all, a 15 year old noob here. I want to calculate how much FORCE in NEWTONS would be delivered by a 100 kiloton nuke on an object of area around 2cm^2 from a distance of about 5 meters. This might sound like a stupid question, but all the answers about nukes are its POWER in joules, not...

Dear all, I was trying to prove that the area of a triangle is equal to the determinant consisting of the three points of the triangle. I got to the end, and something ain't working out. The signs are all wrong. In the attached pictures I include my proof. Can you please tell me how can the...

Hey everyone. I just found out about the forum and already discovered a lot of good and useful content. Anyway, is anyone in or studying for some area of knowlegde which just seems that it's not the right thing for you? And that physics, astronomy, mathematics or, perhaps, other fields related...

Greetings! Can someone please help me figure out how to calculate the second moment of area for a hollow isosceles triangle? Is there an equation available somewhere? Or can I simply subtract a smaller triangle from a larger one, using the equation I=bh3/36? (so I= b1h13/36 -b2h23/36) Also, is...

Hello, this isn't a homework or anything, I am just trying to understand one thing :) (finals are tomorrow :-0 ) If a person is exposed to heat energy of the sun for 4 hours(5040000 J per hour) and the avg surface area of the person is 1.9 m^2. and specific heat capacity of the body is 3470 J...

For example how to calculate required cross-section area of the toroidal core for 100VA transformer.Is that any simple formula.

Homework Statement Calculate the area between ##y = -x^2+3x+10## and ##y = -x+14##. Note that ##y = -x+14## is the tangent to the curve ##y = -x^2+3x+10## at the point ##(2,12)##. Homework EquationsThe Attempt at a Solution Is it as simple as calculating ##\int_{5}^{14} -x+14+x^2-3x-10 =...

I am using a Micromeretics ASAP2020 machine. The sample is ~25mg of reduced graphene oxide based film. The problem is I am getting adsorption isotherms showing negative volumes of adsorbate (N2) entering the tube as P/P0 increases. The sample was degassed prior to testing at 250°C for 3...