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labwork [276]
3 years ago
7

An overhead projector enlarges the image on its glass by a scale factor of 4. A rectangle that is 3 inches wide and 7 inches lon

g on the glass is projected on a screen. What is the length of the rectangle on the screen?
Mathematics
1 answer:
qwelly [4]3 years ago
6 0
Just multiply the with and the length by four (considering the scale factor is 4)
3x4=12 and 7x4=28
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For the ODE to be exact, we require that M_y=N_x, which we'll verify is not the case here.

M_y=21xy^2+6
N_x=2xy^2-1

So we distribute an integrating factor i(x,y) across both sides of the ODE to get

iM\,\mathrm dx+iN\,\mathrm dy=0

Now for the ODE to be exact, we require (iM)_y=(iN)_x, which in turn means

i_yM+iM_y=i_xN+iN_x\implies i(M_y-N_x)=i_xN-i_yM

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Next, we're looking for a solution of the form \Psi(x,y)=C. By the chain rule, we have

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\Psi(x,y)=x^7y+x^6y^{-1}=C
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