Ralph read 1/8 of his book. what fraction of the book does he still have left to read?

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

What is the true solution to ln 20+ln 5= 2 ln x

Aleks [24]

Ln20+ln5=2lnx
ln(20x5)=lnx^2
ln100=1nx^2
100=x^2
square root
x=10

5 0

3 years ago

Read 2 more answers

Can someone help me with this question in so confused

Svetlanka [38]

Answer:

D(1, 2) → D'(2, 7)

E(-3, -5) → E'(-10, 0)

F(4, -1) → F'(11, 4)

Step-by-step explanation:

D(1, 2) → D' ________

Translate image (3x - 1, y + 5)

(1, 2), x = 1 and y = 2

3x - 1 = 3(1) - 1 = 3 - 1 = 2

y + 5 = (2) + 5 = 7

E(-3, -5) → E' ________

(-3, -5), x = -3 and y = -5

3x - 1 = 3(-3) - 1 = -9 - 1 = -10

y + 5 = (-5) + 5 = 0

F(4, -1) → F' ________

(4, -1), x = 4 and y = -1

3x - 1 = 3(4) - 1 = 12 - 1 = 11

y + 5 = (-1) + 5 = 4

3 0

1 year ago

You are designing a container in the shape of a cylinder. The radius is 6 inches. You want the container to hold at least 324π c

goldfiish [28.3K]

Answer: 9 inches

Explaination: The volume of a cylinder, V = (πr^2)H, so H = V/(πr^2).

Using the parameters you specified, H = 324π/[(π)(6^2)] = 324π/36π = 324/36 = 9 inches

4 0

3 years ago

Researcher Sandy Beach found a correlation coefficient of +2.3 between variables X and Y. She is thrilled because that correlati

tia_tia [17]

Correlation coefficient is always between -1 and +1. So it cannot be +2.3

7 0

2 years ago

Ralph read 1/8 of his book. what fraction of the book does he still have left to read?​

Ralph read 1/8 of his book. what fraction of the book does he still have left to read?