Find the Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables. If x = f(u, v, w), y = g(u, v, w), and z = h(u, v, w), then the Jacobian of x, y, and z with respect to u, v, and w is ∂(x, y, z) ∂(u, v, w) = ∂x ∂u ∂x ∂v ∂x ∂w ∂y ∂u ∂y ∂v ∂y ∂w ∂z ∂u ∂z ∂v ∂z ∂w . x = 1 6 (u + v), y = 1 6 (u − v), z = 6uvw

The Jacobian ∂(x, y, z) ∂(u, v, w) for the indicated change of variables

= -3072uv

Step-by-step explanation:

Step :-(i)

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'

Step :-(ii)

The Jacobian ∂(x, y, z)/ ∂(u, v, w) =

   Determinant       16(-16×6uv-0)-16(16×6uv)+0(0) = - 1536uv-1536uv

                                                                                 = -3072uv

Final answer:-

The Jacobian ∂(x, y, z)/ ∂(u, v, w) = -3072uv

i think the answer is fried chicken ; >

step-by-step explanation:

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: