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skelet666 [1.2K]
3 years ago
13

Calculate curls of the following vector functions (a) AG) 4x3 - 2x2-yy + xz2 2

Physics
1 answer:
aleksandr82 [10.1K]3 years ago
6 0

Answer:

The curl is 0 \hat x -z^2 \hat y -4xy \hat z

Explanation:

Given the vector function

\vec A (\vec r) =4x^3 \hat{x}-2x^2y \hat y+xz^2 \hat z

We can calculate the curl using the definition

\nabla \times \vec A (\vec r ) = \left|\begin{array}{ccc}\hat x&\hat y&\hat z\\\partial/\partial x&\partial/\partial y&\partial/\partial z\\A_x&X_y&A_z\end{array}\right|

Thus for the exercise we will have

\nabla \times \vec A (\vec r ) = \left|\begin{array}{ccc}\hat x&\hat y&\hat z\\\partial/\partial x&\partial/\partial y&\partial/\partial z\\4x^3&-2x^2y&xz^2\end{array}\right|

So we will get

\nabla  \times \vec A (\vec r )= \left( \cfrac{\partial}{\partial y}(xz^2)-\cfrac{\partial}{\partial z}(-2x^2y)\right) \hat x - \left(\cfrac{\partial}{\partial x}(xz^2)-\cfrac{\partial}{\partial z}(4x^3) \right) \hat y + \left(\cfrac{\partial}{\partial x}(-2x^2y)-\cfrac{\partial}{\partial y}(4x^3) \right) \hat z

Working with the partial derivatives we get the curl

\nabla  \times \vec A (\vec r )=0 \hat x -z^2 \hat y -4xy \hat z

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The elements least likely to form bonds are found in what group
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The histogram below shows the number of downloads of a song over time.
Allisa [31]

Given data:

  • It is a graphical display where the data is grouped in to ranges
  • A diagram consists rectangles, whose area is proportional to frequency of a variable and whose width is equal to the class interval.
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<em>From Figure:</em>  

        Each box in the graph (small rectangle box) is assumed to be one download. So, in the graph the time between 8 p.m to 9 p.m, the number of downloads are 8.75 approximately (because the last box is incomplete, therefore 8 complete boxes and 9th is more than half).

<em>So, We conclude that the total number of downloads are approximately 9 in the time span of 8 p.m. to 9 p.m.</em>

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2 years ago
Four different resistors have various amounts of electric current flowing through them. Given the values of current I and resist
Artemon [7]

You did not provide the options. However, the options are

I = 6.0, R= 4.0 ohms

I = 9.0, R= 2.0ohms

I = 3.0, R= 2.0ohms

I = 8.0, R= 8.0 ohms

Answer:

The order of  the resistors from the highest to the lowest is:

I = 8.0, R= 8.0 ohms

I = 6.0, R= 4.0 ohms

I = 9.0, R= 2.0ohms

I = 3.0, R= 2.0 ohms

Explanation:

ohm's law states that voltage across a conductor is directly proportional to the current flowing through it.  V = IR

Based on this formula, the voltages in each of the resistors are calculated below from the highest to the lowest

  • For I = 8.0, R= 8.0 ohms

       V = 8 * 8 =64 volts

  •  For I = 6.0, R= 4.0 ohms

      V = 6 * 4 =24 volts

  • For I = 9.0, R= 2.0 ohms

       V = 9 * 2 =18 volts

  • For I = 3.0, R= 2.0 ohms

       V = 3 * 2 =6 volts

3 0
2 years ago
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Answer:

-0.912 m/s

Explanation:

When the package is thrown out, momentum is conserved. The total momentum after is the same as the total momentum before, which is 0, since the boat was initially at rest.

(m_c + m_b)v_b + m_pv_p = 0

where m_c = 24.6 kg, m_b = 39 kg, m_p = 5.8 kg are the mass of the child, the boat and the package, respectively. , v_p = 10m/s, v_b are the velocity of the package and the boat after throwing.

(24.6 + 39)v_b + 5.8*10 = 0

63.6v_b + 58 = 0

v_b = -58/63.6 = -0.912 m/s

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