calculus-how to determine mass and center of square?

Question

darkigloo · Answer

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darkigloo · Answer

square has denisty of 3p

ganeshie8 · Answer

mass = area * density

center = intersection of diagonals

ganeshie8 · Answer

save calculus, this is easier using geometry

darkigloo · Answer

m= 4 * 3p = 12p 
center = -2,2

darkigloo · Answer

how would i find the center using calc?

baru · Answer

what is 'p' ?
is it a constant?

darkigloo · Answer

it says the square has constant density 3p

baru · Answer

then i guess you dont need calculus

darkigloo · Answer

ok so is what i got correct?

baru · Answer

looks good to me

darkigloo · Answer

thanks. can you help me with two more parts ?

baru · Answer

i'll give it a try

darkigloo · Answer

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determine center of mass of the parabolic shape. 
suppose the center of mass of the triangle is at ( -2/3 , 0) Determine the center of mass of the entire shape

darkigloo · Answer

i know these formulas: 
$$x cm = \frac{  \int\limits_{a}^{b} x \times P(x) \times(f(x)-g(x)) dx }{ mass } $$
$$y cm = \frac{ 1 }{ 2 } \times  P(x i) (f(x i)^2 - g(x i)^2)dx$$

ganeshie8 · Answer

hey wait

ganeshie8 · Answer

in the first question, area of square is not 4

ganeshie8 · Answer

just double check..

baru · Answer

oh yea, i overlooked that

darkigloo · Answer

its not 2*2?

baru · Answer

you have to use the pythogoras theorem to find the length of the squares side
$$l= \sqrt{ 2^2 + 2^2}$$