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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

jeyben [28]

Answer:

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'

$\frac{∂x}{∂u} = 16(1)+16(0)=16$

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'

$\frac{∂z}{∂w} =6 uv(1)=6uv$

Step :-(ii)

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

Final answer:-

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

6 0

3 years ago

the middle School golf team is selling golf balls to raise $850 for new equipment they sell golf balls for $2 each a case has 24

aniked [119]

Answer:

The number of cases of golf ball that team needed to raise money for equipment is 3 .

Step-by-step explanation:

Given as :

The amount needed for new equipment = $850

The cost of each golf ball = $2

The number of packs of golf ball in each case = 24

The number of golf ball in each pack = 6

Let The number of cases of golf ball team needed to raise money for equipment = n cases

Now, According to question

∵ 1 pack has 6 balls

so, 24 pack has 6 × 24

i.e 24 packs has 144 balls

So, The number of balls in each case` = 144 balls

Again

∵ cost of 1 ball = $2

So, cost of 144 balls = $2 × 144

i.e cost of 144 balls in each case = $288

Again

∵ The amount needed for new equipment = $850

So, The number of cases of golf ball team needed to raise money for equipment = $\dfrac{amount needed for new equipmen}{cost of 144 balls in each case }$

Or, n = $\dfrac{850}{288}$

∴ n = 2.9 ≈ 3

So, The number of cases of golf ball that team needed to raise money for equipment = n = 3

Hence, The number of cases of golf ball that team needed to raise money for equipment is 3 . Answer

3 0

3 years ago

Using the discriminatory, determine the number of real solution 2x^2+7x-15=0

Scilla [17]

Answer:

c. two real solutions

Step-by-step explanation:

x = -5 , x = 1.5

6 0

3 years ago

Nick has $7.00. Bagels cost $0.75 each, and a small container of cream cheese costs $1.29. Write an inequality to find the numbe

lbvjy [14]

$0.75b+$1.29≤$7.00
b being bagels

8 0

3 years ago

Read 2 more answers

It takes $8$ cups of chocolate chips to make $12$ cookies. How many cups of chocolate chips will it take to make $15$ cookies? P

Yuri [45]

Hello!!!

Answer:

11 cups of chocolate chips

Step-by-step explanation:

If we use the information we got from the problem we can see that 8 gives us 12. So all we need to do is add more to the orignal number(8) unitll we get 15. So 11 cups gives us 15 cookies.

Have a nice day!!!

4 0

3 years ago