Gfind the jacobian of the transformation. x = 6e−3r sin 2θ, y = e3r cos 2θ

Definition:

The Jacobian of the transformation x = f(r, θ) and y = g(r ,θ)  is:

=             ......[1]

Given: and  

then,  

and      

Substitute these value in [1] ;  

=

 =

On simplify:

 =  

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therefore, the jacobian transformation of and   is;    

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation:

nope.   happens to me as well.

-aparri