1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
levacccp [35]
3 years ago
6

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

Mathematics
1 answer:
jeyben [28]3 years ago
6 0

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'

               \frac{∂x}{∂u} = 16(1)+16(0)=16

  Differentiating equation (i) partially with respective to 'v'

              \frac{∂x}{∂v} = 16(0)+16(1)=16

  Differentiating equation (i)  partially with respective to 'w'

               \frac{∂x}{∂w} = 0

Given  y = 1 6 (u − v) …(ii)

  Differentiating equation (ii) partially with respective to 'u'

               \frac{∂y}{∂u} = 16(1) - 16(0)=16

 Differentiating equation (ii) partially with respective to 'v'

               \frac{∂y}{∂v} = 16(0) - 16(1)= - 16

Differentiating equation (ii)  partially with respective to 'w'

               \frac{∂y}{∂w} = 0

Given   z = 6uvw   ..(iii)

Differentiating equation (iii) partially with respective to 'u'

               \frac{∂z}{∂u} = 6vw

Differentiating equation (iii) partially with respective to 'v'

               \frac{∂z}{∂v} =6 u (1)w=6uw

Differentiating equation (iii) partially with respective to 'w'

               \frac{∂z}{∂w} =6 uv(1)=6uv

<u>Step :-(ii)</u>

The Jacobian ∂(x, y, z)/ ∂(u, v, w) =

                                                         \left|\begin{array}{ccc}16&16&0\\16&-16&0\\6vw&6uw&6uv\end{array}\right|

   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

 

               

     

You might be interested in
Casey travels from her house directly west to the bank and then directly north from the bank to the mall. She then travels home
netineya [11]
The answer is D 40miles

4 0
3 years ago
I would like to buy a sandwich and pancakes, which would be $8.50, with a 6% tax and 20% gratuity, how much would that be all in
Luda [366]

Answer:

9.01 maybe my math might be wrong

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
How do you write two hundred fifty-two and thirty-one ten thousandths
ryzh [129]

Answer:

252.3110

Step-by-step explanation:

5 0
3 years ago
Find the midpoint of if A(-3, 8) andB(-7, -6).
Mama L [17]

Answer:

(-5,1)

Step-by-step explanation:

8 0
2 years ago
I just need to know how to solve this question.
Zarrin [17]

Answer:

x = 62

Step-by-step explanation:

x and 118 form a linear pair (added up, they both equal 180 degrees)

So, 180-118 = 62 which is the measurement of x

6 0
2 years ago
Other questions:
  • Laila wants to create a data display to clearly show the median salary, the highest salary,
    13·2 answers
  • PLZZZZZZZZZZZZ HELP ME!!!!!!!!!!!!
    14·1 answer
  • 15x+2x can be written as ____.
    12·2 answers
  • 3x^2+48=0, solve the equation
    5·1 answer
  • WILL GIVE BRAINLIEST!!Soro bought a $50.00 bus card at the beginning of the week. Each bus ride costs $2.50. He needs to have at
    15·2 answers
  • What is the volume of the following figure?<br> A. 40<br> B. 50 <br> C. 30<br> D. 20
    8·2 answers
  • What is the nth term rule of the linear sequence below?
    8·1 answer
  • What is the value of 2|2-9|-3(4+2)?<br> A. -32<br> B. -26<br> C. -15<br> D. -5 <br> E. -4
    6·1 answer
  • 68.1 x 0.8<br> help me please or im gonna fail :(
    15·1 answer
  • What is the maximum of the sinusoidal function? pls help me pls!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!