Complete Question
The complete question is shown on the first uploaded image
Answer:
The solution is 
Step-by-step explanation:
From the question we are told that
and 
Generally the absolute value of the determinant of the Jacobian for this change of coordinates is mathematically evaluated as
![| \frac{\delta (x,y)}{\delta (u, v)} | = | \ det \left[\begin{array}{ccc}{\frac{\delta x}{\delta u} }&{\frac{\delta x}{\delta v} }\\\frac{\delta y}{\delta u}&\frac{\delta y}{\delta v}\end{array}\right] |](https://tex.z-dn.net/?f=%7C%20%5Cfrac%7B%5Cdelta%20%20%28x%2Cy%29%7D%7B%5Cdelta%20%28u%2C%20v%29%7D%20%7C%20%3D%20%20%7C%20%5C%20det%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%7B%5Cfrac%7B%5Cdelta%20x%7D%7B%5Cdelta%20u%7D%20%7D%26%7B%5Cfrac%7B%5Cdelta%20x%7D%7B%5Cdelta%20v%7D%20%7D%5C%5C%5Cfrac%7B%5Cdelta%20y%7D%7B%5Cdelta%20u%7D%26%5Cfrac%7B%5Cdelta%20y%7D%7B%5Cdelta%20v%7D%5Cend%7Barray%7D%5Cright%5D%20%7C)
![= |\ det\ \left[\begin{array}{ccc}{-2e^{-2u} cos(5v)}&{-5e^{-2u} sin(5v)}\\{-2e^{-2u} sin(5v)}&{-2e^{-2u} cos(5v)}\end{array}\right] |](https://tex.z-dn.net/?f=%3D%20%7C%5C%20det%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%7B-2e%5E%7B-2u%7D%20cos%285v%29%7D%26%7B-5e%5E%7B-2u%7D%20sin%285v%29%7D%5C%5C%7B-2e%5E%7B-2u%7D%20sin%285v%29%7D%26%7B-2e%5E%7B-2u%7D%20cos%285v%29%7D%5Cend%7Barray%7D%5Cright%5D%20%20%7C)
So
![\frac{\delta (x,y)}{\delta (u, v)} | = |det \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] |](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdelta%20%20%28x%2Cy%29%7D%7B%5Cdelta%20%28u%2C%20v%29%7D%20%7C%20%3D%20%7Cdet%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5C%5C%5Cend%7Barray%7D%5Cright%5D%20%7C)
=> 
substituting for a, b, c,d
=> 
=> 
=>
37 + 6.70t < 90.60
6.70t < 90.60 - 37
6.70t < 53.6
t < 53.6 / 6.70
t < 8 <=== they could rent the meeting room for less then 8 hrs
Answer:
Step-by-step explanation:
0.5 gal/day * 7 days/week = 3.5 gal/week
3.5 gal * 16 cups/gal = 56 cups
The equation for that line is y=x+5
Answer:
Step-by-step explanation:
The largest factor that will divide evenly into both 32 and 48 is 16.
Thus, 32 - 48 = 16(2 - 3), or 16 (-1), or just -16.
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