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3 years ago

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Mathematics

1 answer:

UNO [17]3 years ago

8 0

Answer:

Step-by-step explanation:

We have to multiply it by two because they have us 2 numbers for the legs, we use the Pythagorean theorem thing, but we have to basically add them, or we can multiply y 2(since they are the same number). Anyways $18\sqrt{2} (2)= 36\sqrt{2}$

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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

What is the distance between points (2,2) and (8,7)

Ganezh [65]

Answer: 1

Step-by-step explanation:

Please see attached

5 0

3 years ago

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all arou

Arisa [49]

Complete question :

A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?

1) 2 1/2 feet

2) 3 feet

4) 5 feet

5) 8 1/2 feet

Answer:

2.5

Step-by-step explanation:

Solving for X in the perimeter equation :

2[(12+2x)+15+2x)]=74

Open the bracket

2[(12 + 2x + 15 + 2x)] = 74

2(27 + 4x) = 74

54 + 8x = 74

8x = 74 - 54

8x = 20

x = 20/8

x = 2.5

Hence, width fo border = 2.5

5 0

2 years ago

Question 16

anastassius [24]

Step-by-step explanation:

Distance between 2 towns 360 miles showed length 3 inches

1800 miles = ? inches

360 miles = 3 inches

1 miles = 3/360 inches

1800 miles = 3/360 × 1800

= 15 inches

3 0

3 years ago

Which ordered pair is a solution of the equation y=x-4

Andreyy89

The answer would be y=-4 and x=4, so pick which ever number/letter has this answer.

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3 years ago

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