Centroid Definition and 173 Threads

You are given an arbitrary triangle ABC. Inside ABC there is a point M such that Area(ABM) = Area(BCM) = Area(ACM) . Prove that M is the centroid of triangle ABC. I have had very little progress with this question. I've tried connecting a line from M which bisects BC, but I cannot prove that...

Homework Statement Hello. In class we learned how to calculate centroids of a triangle. For the y-coordinate we use the formula height/3 and for the x we use 2/3 * base Homework Equations In the diagram, If I want to calculate the y coordinate , I do 72 (which is the proposed height)/ 3 ; only...

Find the centroid of the region bounded by y = 1.5x2 − 14x + 23.5, and x − y = 8. You should enter the coordinates of your answer either as decimals or fractions. Your answer must be accurate to within 0.001. I got a wrong answer of (7/3, 59/52), I'm having problems plugging in the numbers. Any...

How to find out the position vector of the centroid of tetrahedron , the position vectors of whose vertices are a,b,c,d respectively. I am familiar with the result, namely a+b+c+d/4 but want to know how to derive it without using the 3:1 ratio property. Any help would be appreciated. Thank you.

Homework Statement A uniform chain hangs in the shape of the catenary y=cosh(x) between x=−1 and x=1 Find \bar{y} Homework Equations ∫\bar{y}\rhods=∫y\rhodsThe Attempt at a Solution I can define ds (some small segment of the arc) by \sqrt{1+sinh(x)^2}dx. Also, y is given as y=cosh(x) If I...

Hi friends, I have been trying to calculate the centroid of triangle (show in attachment) . I have got centroidal Y= h/3 Not able to get centroidal X = (1/3)*(a+b) Could anyone help on this stuff? Thanks..

I was doing this example from my textbook and looked at the solution guide. I'm confused as to where the textbook got a certain number. In the numerator of their work, they got (1)(6)(2), which I'm assuming is the width of the skinny rectangle, the total length of the bottom section...

Homework Statement Can you please help me I think I have confused something.We did this in class. A triangular plate with base = 10 m and height 12 m is placed under water with the base at the top at a depth of 8 meters under water and the apex 20 meters under water. Find the hydrostatic...

I'm trying to find the centroid of a coke bottle, which is basically like a cylinder with varying radius. I have a 1x500 vector of radius points and I have the volume of the bottle, any thoughts on how to calculate the centroid numerically?

Homework Statement y = 16 -x^2 find centroid bounded by x axis Homework Equations x = (1/A) ∫ x(f(x)) dx and (1/A) (1/2)(f(x))^2 dx = y The Attempt at a Solution I just applied it. It is a weird because I would of thought that x would of been at 0. But I didn't get that I x =...

Homework Statement Wondering if I did this right. Find the centroid of the region shown , not by integration, but by locating the centroids of the rectangles and triangles and using additivity of moments. Homework Equations I will give you the coordinates since I can't draw it. For...

Homework Statement Find the centroid bounded by the given curves. y = x^3 , x+y = 2, y = 0 So if you graph this you will see that if you did it with respect to x you would have the break the graph at the point (1,1). Or at least I think you would have to. So in my book they give the...

Homework Statement The following is a geometry question I can't seem to get. "Consider an acute angle △ABC. Points D, E, F are mid points of sides BC, CA and AB respectively. G is the centroid of △ABC. Area of △AFG = 14, EC = 15/2. Perpendicular distance of F from BC = 6. Find BC2−AB2 "...

Homework Statement Homework Equations ƩxiLi=0 The Attempt at a Solution Using geometry to find the lengths and rotating so AB is horizontal, I have: ƩxiLi=0: [((64/80)*L)/2]*L + (-64/2)*80 + (-14/2)*100 = 0 L = 90.28mm

Homework Statement Find the centroid of the region bounded by the graphs of y = sqrt (x) and y = (1/2) * x Homework Equations A = [f(x)-g(x)]dx from point a -> b The Attempt at a Solution x = [0,4] ; p(0,0) and p(4,2) I am just checking on if I did the integral correctly. A...

Hello, I am calculating the centroid of an area using this equation for composite bodies: sum(indivudual area times individual centroid)/sum(individual area) = distance from axis to centroid this is just y bar for a cross section that is symmetrical about the y axis I was under the...

Homework Statement I need to find the centroid of a circular segment. I know nothing of calculus, and this is part of an analysis for statics that goes beyond the material covered in class. Homework Equations I've seen this equation for calculating the centroid...

Homework Statement See attachment Homework Equations The Attempt at a Solution If the y-coordinate of the center of mass is given by (1/A)*∫y dA, how come the solution uses bh/2 as the area? This triangle isn't right angled so that area formula should not hold. What am I missing?

Homework Statement Okay, so the idea here is to take the centroid bounded by the x-axis and 1-x^n. N should be an even and positive integer. We should take the limit as n approaches infinity of both the x- and y-coords of the centroid, hopefully ending up with (0, 1/2). Homework Equations...

[SOLVED] Centroid problem with y vector So, I've been having a problem with this part here, the equations are y=4x^2 and y=2x3. So, the intersections are (0,0) and (2, 16) The area between the two is 8/3. I know I'm doing something correct because I get the x vector correct with ease, but...

7) Pile foundations are the part of a structure used to carry and transfer the load of the structure to the bearing ground located at some depth below ground surface. A concrete pile for a domestic dwelling has a radius of 1000 mm at its base, and 2000 mm at the top. It is 2000 mm deep and...

1. Find the centroid of the region determined by the graphs of the inequalities. y ≤ (1/3)x^(2) ; (x-3)^2 + y^(2) ≤ 9 ; y ≥ 0 x(bar) , y(bar) = (?, ?) I did the problem, but i do not know the answer because the problem is an even number and the book only have answers for the odd...

Homework Statement Find the exact coordinates of the centroid for the region bounded by the curves x=5-y^ 2 and x=0 I am not sure about this one because it uses dy instead of dx i think. I tried to set it up like this x= [0.5∫(5-y^2)^2 dy from -5 to 5]/[ ∫(5-y^2)dy from y=-5 to 5]...

Homework Statement The Attempt at a Solution I tried to do this problem by taking the average of the y-bar centroid values but that gave me the wrong answer. I am only interesting in knowing why this method is incorrect. Thanks!

Hi VVVVVV Find the centroid of the region bounded by the curves y = 2x - 4 , y = 2 Sqr x, and x = 1. Make a sketch of the region.

Homework Statement let ABC be a triangle where I divides angle BAC(angle A) => BAI=IAC Prove that I is the centroid of (B,AC)and (C,AB) Homework Equations i think phitagors wil come in handy but don't know how to use it The Attempt at a Solution let ac = a and AB = b aIB+bIC=0 (vectors)...

Homework Statement Find the volume of the solid that lies above the cone ϕ=pi/3 and below the sphere ρ=4cosϕ . Homework Equations Find the centroid of the solid in part (a).. The Attempt at a Solution For the volume I got 10pi which I am fairly sure is correct. I attempted trying to...

Homework Statement The solid bounded by the surface z=y2 and the planes x=0,x=1,z=1 I have a question regarding the limits of integration, would it be incorrect, if when I graphed z=y2 I changed it to a familiar xy graph instead I just graphed it as if z was y and x was y. Pretty...

Homework Statement Find the centroid of the region bounded by the curves y = (4x-x^2) and y = x. Homework Equations Centroid = (x-bar, y-bar) x-bar = My/M y-bar = Mx/M M = ∫ρ[f(x) - g(x)]dx My = ∫ρ(x)[f(x) - g(x)]dx Mx = ∫(1/2)ρ[{f(x)}^2 - {g(x)}^2]dx The Attempt at a...

Homework Statement Find the centroid of the region in the first quadrant of the xy-plane bounded by the graphs of the equations: x=0, x=1, y=x-x^2, and y^2=2x Homework Equations xbar: integral of x dA/ integral of dA ybar: integral y dA/ integral of dA The Attempt at a Solution...

Homework Statement A single-scoop ice cream cone is a composite body made from a single scoop of ice cream placed into a cone. Assume that the scoop of ice cream is a sphere with radius r = 3.65 cm that is placed into a 9.90 cm tall cone. The interior height of the cone is 9.00 cm. The cone...

We got given the formula for finding the centroid of a triangle which was to (\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}) but we the teacher said he didn't have time to show the proof, however I'm still curious. Could anyone possible hint on how I could go about to prove this? My...

Hello, I was thinking of the following question: suppose we have a body in two-dimensional space and its density is described by the function f(x,y) (Note! in Cartesian coordinates!). The x-coordinate of the center of mass is given by C_x= \frac{\int\int xf(x,y)dxdy}{\int\int f(x,y)dxdy}...

Homework Statement http://prntscr.com/fcbm8 Find the centroid - All dimensions are in mm Homework Equations xbar = (A1X1+A2X2) / (A1+A2) Similarly for Ybar I assume The Attempt at a Solution I got the y co-ordinate to be 20.428mm, and would assume that the x coordinate...

What does the "Centroid" of area under Rate vs Time plot represent? Does the 'centroid' of the area under a rate vs time plot represent anything? I have a bunch of rate vs time plots and was trying to think of a way to compare them, other than just cumulative volume which is area under the...

Homework Statement Find the centroid of the region bounded by the curve x=5-y2 and x=0. Answer is (2,0). Homework Equations A = ∫[f(x)-g(x)]dx a->b xbar = 1/A ∫ x[f(x)-g(x)]dx from a->b ybar = 1/A ∫ 1/2[f(x)2-g(x)2]dx The Attempt at a Solution I know that the graph is a...

Given the formula for the weighted centroid, C of a system of parallel forces Fi acting at points Pi, show that two weights W and 3W, acting respectively at points P1, P2, are together equivalent to a single weight 4W acting at P, where P lies on the line segment joining P1 to P2 and P1 P : P P2...

Centroid of a "TILTED" Semi circle! Guys, could anyone help me out how to solve the centroid of these "tilted" semicircle. I really don't have any idea how to get its centroid since it's tilted..Please I really want to understand so kindly do it step by step, Thanks.. Just Find the x-bar and...

Does anyone have an easy formula for finding the centroid coordinates under a degree 3 bezier curve? The whole parametric two variable thing isn't working with the formulas I know of. Thanks

Hi i have a right angle tringle, base=1200m and h=400. I have trouble understanding on how to determine the centroid i know one side will be 2/3*x and another side would be 1/3*y. But i don't understand how to write it out. A friend said its 1/3*1200*400*2/3*1200, but i have no idea and...

Homework Statement Find the centroid of the region bounded by the given curves. y = x^3x + y = 10y = 0 Homework Equations \bar x = \frac{1}{A}\int^b_a xf(x) dx\bar y = \frac{1}{A}\int^b_a \frac{1}{2}(f(x))^2 dx Where A is the area of the region containing the centroid. The...

The test question was... We are given a region bounded by the functions √x and x. We were also given the density and mass of the region and asked to only the component y of the centroid. I did not know how to implement these given variables, density and mass into my equation for y bar so I...

Hey guys, as the title says I can understand why the neutral axis does not pass through the centroid after reaching a point where the bending moment is max before the beam collapses. Say you have a straight structure supported by two double I-Beams and a weight in the middle. Why does the...

i just want to make sure I'm doing this correctly as there is some discrepancy in my textbook. i know the centroid is equal to (Ʃpoles - Ʃzeros) / (# of poles - # of zeros) the equation i have is s2 + 2s + 8 / s(s2 + 2s + 10) so the zeros are -1 + i√7 and -1 - i√7 and the poles are 0, -1...

Homework Statement Find Mx,My, & (x bar, y bar) for the laminas of uniform density ρ bounded by the graphs of the equations. (Use rho for ρ as necessary.) x=-y x=5y-y2 Homework Equations m= ∫f(x)-g(x) dx my= ∫x(f(x)-g(x)) dx =>x bar my/m mx= 1/2 ∫ (f(x))2-g(x))2dx => y bar=mx/m...

Homework Statement As part of a test I was given an irregular shape to find its centroid. It was a rectangle with a right angled triangle on its right side (I don't have a picture to upload for ye unfortunately). Homework Equations dA=y.dx X(bar)=intrecal x.y.dx Y(bar)=intrecal y^2/2.dy The...

Homework Statement Find the centroid of the region D, lying above the sphere x2+y2+z2 and below the paraboloid z=4-x2-y2. Homework Equations The Attempt at a Solution I decided it might be easier to change it to polar coordinates soo I did M=∫∫∫ dzrdrdθ where z goes from...

Hi gang, I was given this question, but I can't quite seem to get it all the way... 1.Determine the coordinates of the centroid of the surface of a hemisphere, the radius of which is r, with respect to its base. Homework Equations A=2\pi r^{2} A: Surface Area of the Hemisphere...

hi all .. Hello .. I am a new member .. I have a test next week .. I have some difficulty in such matters .. http://store2.up-00.com/Nov11/Eac12548.jpg [PLAIN][PLAIN]http://store2.up-00.com/Nov11/UKV12548.jpg thanks

Homework Statement Find the volume and the centroid of the solid E that lies above the cone z=√x^2+y^2 and below the sphere x^2+y^2+z^2=49. Homework Equations The Attempt at a Solution My bounds were: \theta=0 to 2\pi \varphi=0 to \pi/4 \rho=0 to 7cos(\varphi) So my integral...