How to draw and label a diagram to show how you would separate each mixture

Consider the vector field. f(x, y, z) = xy2z2i x2yz2j x2y2zk (a) find the curl of the vector field?

Marat540 [252]

Observe that the given vector field is a gradient field:

Let $f(x,y,z)=\nabla g(x,y,z)$ , so that

$\dfrac{\partial g}{\partial x} = x y^2 z^2$

$\dfrac{\partial g}{\partial y} = x^2 y z^2$

$\dfrac{\partial g}{\partial z} = x^2 y^2 z$

Integrating the first equation with respect to $x$ , we get

$g(x,y,z) = \dfrac12 x^2 y^2 z^2 + h(y,z)$

Differentiating this with respect to $y$ gives

$\dfrac{\partial g}{\partial y} = x^2 y z^2 + \dfrac{\partial h}{\partial y} = x^2 y z^2 \\\\ \implies \dfrac{\partial h}{\partial y} = 0 \implies h(y,z) = i(z)$

Now differentiating $g$ with respect to $z$ gives

$\dfrac{\partial g}{\partial z} = x^2 y^2 z + \dfrac{di}{dz} = x^2 y^2 z \\\\ \implies \dfrac{di}{dz} = 0 \implies i(z) = C$

Putting everything together, we find a scalar potential function whose gradient is $f$ ,

$f(x,y,z) = \nabla \left(\dfrac12 x^2 y^2 z^2 + C\right)$

It follows that the curl of $f$ is 0 (i.e. the zero vector).

5 0

1 year ago

By what factor must the amplitude of a sound wave be increased in order to increase the intensity by a factor of 9?a. 9 b. 2 c.

Marta_Voda [28]

Answer:

option D

Explanation:

given,

$intensity\ \alpha \ (Amplitude)^2$

increase the intensity by factor of 9

I₁ = I₀

I₂ = 9 I₀

now,

$\dfrac{I_1}{I_2}=\dfrac{A_1^2}{A_2^2}$

$\dfrac{I_0}{9I_0}=(\dfrac{A_1}{A_2})^2$

$(\dfrac{A_1}{A_2})^2=\dfrac{1}{9}$

$\dfrac{A_1}{A_2}=\dfrac{1}{3}$

A₂ = 3 A₁

hence, amplitude increase with the factor of 3

so, the correct answer is option D

4 0

2 years ago

Read 2 more answers

During the experiment it is determined that, as the cart rolls between two points on the track, the work done on the cart by the

natita [175]

Answer:

Explanation:

If the work done on the cart is NET work

Then the work will result in an increase in kinetic energy

KE₀ + W = KE₁

½mv₀² + W = ½mv₁²

½(0.80)(0.61²) + 0.91 = ½(0.80)v₁²

v₁ = 1.626991...

v₁ = 1.6 m/s

4 0

2 years ago

A sound wave has a frequency of 265 hz and a wavelength measured at 1.3

pochemuha

Answer:

V = f λ speed of wave in terms of frequency and wavelength

t = S / V time for wave to travel a distance S

t = 91.4 m / 344.5 m/s = .265 sec time to travel 91.4 m

8 0

2 years ago

A train travels 77 kilometers in 1 hour, and the 66 kilometers in 1 hour. What is the average speed?

Kipish [7]

Average speed = (total distance covered) / (time to cover the distance)

Total distance = (77km + 66km) = 143 kilometers

Time to cover the distance = 2 hours

Average speed = (143 km) / (2 hours) = 71.5 km per hour

6 0

3 years ago