Question

8x^2+64x-32y+63=0, y=1
find the area, centroid, volume of x and y....plss answer,,needed immediately..

Answer 1

can you rephrase the question

Answer 2

thats the question given by our instructor... dont know how to rephrase it..

Answer 3

@electrokid

Answer 4

it could be centeroid of volume?

Answer 5

dont know how to solve because we dont know the value of x

Answer 6

then put y =1 and solve for x?

Answer 7

no, the centroid involve is in relation to its area

Answer 8

y in that manner is a line.... maybe its the limits?

Answer 9

area, ->@aajugdar
centroid->\[C=\frac{\int xy\,dx}{\int y\,dx}\]

Answer 10

for volume, there need to be a 3D figure by rotation about some axis

Answer 11

i see

Answer 12

yeah... the problem required is the volume in x and volume in y.

Answer 13

maybe in x axis and y axis

Answer 14

well, you an take the numerator as the volume and deno as area...

Answer 15

can you show the solution?

Answer 16

@niah2411 yes.. Cx and Cy

Answer 17

@electrokid can you show me the solution?

Answer 18

1.Area is a scalar\[A=\int dx\,dy\]
2. centroid is a point where the entire area of the geometry can be assumed to be concentrated.
so, you have Cx and Cy-> they tell you how (xy->area) is distributed about "x" (Cx) and about "y" (Cy)
\[C_x=\frac{\int_x xydx}{\int_x ydx},\qquad C_y=\frac{\int_y xydy}{\int_y xdy}\]

Answer 19

@niah2411 some piece about volume part of the question is missing here

Answer 20

the question says that find the volume in x and find the volume in y

Answer 21

so whats my limits in getting the area?

Answer 22

it is a parabola-> y=(8x^2+64x+63)/32
when you say y=1, rotation about y=1 for the volume?

Answer 23

no the y there is a line maybe the one of the limits of area

Answer 24

yes.. the limits seem ambiguous.. rewrite the limits using latex.. @aajugdar you take it from here

Answer 25

pls help,,,i dont really know how to solve this..

Answer 26

he went off
so you found area and centeroid
volume is left

Answer 27

can i know what limits will i use in solving the area?

Answer 28

no idea
i need diagram to understand this
wil u hold on

Answer 29

ok...copy no prob...just pm me if you got the answer.. can you go to wolframalpha.com you can find the diagram of that parabola...

Answer 30

post the link?

Answer 31

http://www.wolframalpha.com/input/?i=8x^2%2B64x-32y%2B63%3D0%2C+y%3D1

Answer 32

oh
that makes some sense now

Answer 33

so wats the limits?

Answer 34

in the 1st equation put y=1
you will get 2 values of x
that are the limits

Answer 35

what if we use the vertical stripping, whats the limits?

Answer 36

umm
i don't know vertical striping method x/

Answer 37

ahhh..its ok.. can u show the solution for horizontal stripping?

Answer 38

wait
@electrokid i am confused about this 1 very much
you said area \[\int\limits_{?}^{?} dx dy\]
so its double integration right?

Answer 39

letme check

Answer 40

i guess it is
\[\int\limits_{a}^{b}\int\limits_{c}^{d}dxdy\]

Answer 41

wow. double integration needed?

Answer 42

yep

Answer 43

your graph seems wrong.. y is the graph touching all the quadrants?

Answer 44

the limits of outer integral should be values of x
and inner 1 should be considered as y=1 to y= (the value of y you get in equation 1)

Answer 45

in terms of x

Answer 46

is it wrong
i just made that from the link you gave me

Answer 47

oh sorryy