Hey, can anybody help me with this error...

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Hey, can anybody help me with this error equation and change of variables question?

I've tried entering

X = (Io*Cos^2(b))/Y

and

X = (Io*Cos^2(b))/Z^2

And apparently neither are correct for "X =" and I'm at a loss for what to try next.

>>

Perhaps try squaring like this

[cos(b)]^2

It can be poor formula recognition

>>

>>54086

I actually ended up figuring out the first three answers. The question seems to be very poorly worded.

They wanted

X = Io

Y = Z^2

Z = cos(b)

Change of variable almost always means substitution outside of calculus so for me and several other the obvious thing was to sub I = XY into I = Io * Cos^2(b). What it seems they meant was if X=A*B and X =C*D then A = C and B = D.

Now I'm stuck deciphering the rest of it.

>>

>>54109

I just finished the fourth solution:

sqrt((dX/X)^2 + (dY/Y)^2)

I still haven't figured out what they mean in the next four.

>>

>>54115

I assume they want them to be written without using X, Y or Z

>>

>>54125

Could you expand?

The fifth answer ended up being:

dX/X = dIo/Io

but when I tried:

dZ/Z = dcos(b)/cos(b)

it said that was incorrect.

>>

>>54129

-sin(b)*db/cos(b)?

>>

>>54137

That was correct! I'm on the final question now.

Is that just the error propagation of cos(b)?

>>

>>54140

I don't know. Is it?

>>

>>54141

Looks like it.

I was just reading over this

https://www.lhup.edu/~dsimanek/scenario/errorman/rules.htm

I was confused by the symbol they were using buy I guess that's just another symbol for delta.

Thanks!

>>

If anybody knows what's going on with the final question, a nudge in the right direction would be appreciated! I'm a little lost.

>>

>>54159

It's something like 4th solution but without x, y, z

>>

>>54169

Thanks for all of the help!

In case someone ends up here with a similar problem the final answer was:

sqrt((dIo/Io)^2 + (2*-sin(b)*db/cos(b))^2)

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