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Answer:
The Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables
= -3072uv
Step-by-step explanation:
<u>Step :-(i)</u>
Given x = 1 6 (u + v) …(i)
Differentiating equation (i) partially with respective to 'u'
Differentiating equation (i) partially with respective to 'v'
Differentiating equation (i) partially with respective to 'w'
Given y = 1 6 (u − v) …(ii)
Differentiating equation (ii) partially with respective to 'u'
Differentiating equation (ii) partially with respective to 'v'
Differentiating equation (ii) partially with respective to 'w'
Given z = 6uvw ..(iii)
Differentiating equation (iii) partially with respective to 'u'
Differentiating equation (iii) partially with respective to 'v'
Differentiating equation (iii) partially with respective to 'w'
<u>Step :-(ii)</u>
The Jacobian ∂(x, y, z)/ ∂(u, v, w) =
Determinant 16(-16×6uv-0)-16(16×6uv)+0(0) = - 1536uv-1536uv
= -3072uv
<u>Final answer</u>:-
The Jacobian ∂(x, y, z)/ ∂(u, v, w) = -3072uv
For this case, the first thing we must do is define variables:
p: plane speed
w: wind speed
With the wind in favor, the speed is:
With the wind against the speed is:
Rewriting both equations, we have the following system of equations:
Then, solving the system of equations (graphically for example), we have the solution is:
Therefore, jet stream's speed:
Answer:
A) p + w = 960; p - w = 600; jet stream's speed = 180 km / h
p: plane speed
w: wind speed
With the wind in favor, the speed is:
With the wind against the speed is:
Rewriting both equations, we have the following system of equations:
Then, solving the system of equations (graphically for example), we have the solution is:
Therefore, jet stream's speed:
Answer:
A) p + w = 960; p - w = 600; jet stream's speed = 180 km / h