Question

x lach) (0,01 x x 7 - hay + 7 = ht7 h ! 1 + 2 x-SX.; JA Sålh-y) dx . SIA pach-y) dx 2 X- X

Why does Y bar equals the following values .. and is there any techniques that can help me to determine the value of y or x in such figures

Answer 1

In this problem the value of X bar and Y bar is Calculate with the help of a strip and Calculation is as below:-

solution :- The equation of line is АК — а - (9,6) → For calculation of contaid of given - area , we consider a strip of - thickness da f centroid of (Fei Tei): with aroa da. I ndien from diagram : Toi = x (kei is a distance from 1 Origion o) Yei is mid point of alimed Strip so that the location Toi is, 2 + Tea (13) fda - AB-dx = (0A-03).dx = (A-y)da : A = Sdn = {"ch-x) dx = {ch- och ) dx As A [°C1-)da: h|(x - y 9 - 8( -5)

i. Az Now, SPA Sachvydz %= Sach- ak) dx = $ f*(1- ) da X 1 (2-24 y2 1 X=ÅL --o] - [3 - 04] XI XI XI xl I ) (hy) da 4 Seda = S 5 (v3)( 4-1) dz Ta 5 143) (R-3 k) da 9= har h 59 (145) (1-3) da 9 - $ 8,9 (1-)dx= \ [- Ý - Co-op-o-o] - ^ [a-?] 0 - 0 302 -

The location of centroid of shaded area is

(a/3 , 2h/3)