Finding the uncertainty in delta y?

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To find the uncertainty ∆y in the equation y = 1/2(u+v), the error propagation formula is applied. The formula involves partial differentiation, specifically ∆y = |∂y/∂u|∆u + |∂y/∂v|∆v. Users are encouraged to calculate the partial derivatives of y with respect to u and v to proceed with the solution. Clarification on the error propagation formula is requested for better understanding. Understanding these concepts is essential for accurately determining uncertainties in calculations.
SJay16
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Homework Statement


Find the uncertainty ∆y in y as a function of the uncertainties ∆u and ∆v in u and v for the following functions:
y = 1/2(u+v)

Homework Equations

:
Error propagation formula[/B]

The Attempt at a Solution


Don't know where to begin even. Help?[/B]
 
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try partial differentiation ##\Delta y = |\frac{\partial y}{\partial u}|\Delta u + |\frac{\partial y}{\partial v}|\Delta v##
 
SJay16 said:

Homework Statement


Find the uncertainty ∆y in y as a function of the uncertainties ∆u and ∆v in u and v for the following functions:
y = 1/2(u+v)

Homework Equations

:
Error propagation formula[/B]

The Attempt at a Solution


Don't know where to begin even. Help?[/B]
Please quote the error propagation formula as you understand it.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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