a. I've attached a plot of the surface. Each face is parameterized by
• with and ;
• with and ;
• with and ;
• with and ; and
• with and .
b. Assuming you want outward flux, first compute the outward-facing normal vectors for each face.
Then integrate the dot product of <em>f</em> with each normal vector over the corresponding face.
c. You can get the total flux by summing all the fluxes found in part b; you end up with 42π - 56/3.
Alternatively, since <em>S</em> is closed, we can find the total flux by applying the divergence theorem.
where <em>R</em> is the interior of <em>S</em>. We have
The integral is easily computed in cylindrical coordinates:
as expected.
Answer:
Explanation:
The formula for potential energy is:
where <em>m </em>is the mass, <em>g</em> is the gravitational acceleration, and <em>h</em> is the height.
The mass of the book is 0.4 kilograms. The gravitational acceleration on Earth is 9.8 m/s². The height of the book is 2 meters.
Substitute the values into the formula.
Multiply the first two numbers.
- 0.4 kg*9.8 m/s²= 3.92 kg*m/s²
- If we convert the units now, the problem will be much easier later on.
- 1 kg*m/s² is equal to 1 Newton. So, our answer of 3.92 kg*m/s² is equal to 3.92 N
Multiply.
- 3.92 N* 2 m=7.84 N*m
- 1 Newton meter is equal to 1 Joule (this is why we converted the units).
- Our answer is equal to<u> 7.84 Joules.</u>
For the velocity graph: start at 0s and 4m/s and draw a straight line to 2s and 2 m/s. Then draw a straight horizontal line to 4s and 2m/s
For the acceleration graph: start with a horizontal line from 0s and 2m/s/s to 2s and 2m/s/s. The draw another line from 2 s and 0m/s/s to 4 s and 0m/s/s
A. W
Explanation:
The wave that would be produced by the interaction of the two waves shown in the diagram is wave W.
There is no wave in the diagram W.
This type of interference is known as destructive interference.
- Destructive interference occurs when two waves out of phase comes together.
- In this way, they cancel out each other and are terminated.
- If the two waves are in phase, they will reinforce one another.
- When waves reinforce one another, a constructive interference has occurred.
learn more:
Color in soap bubbles brainly.com/question/8733443
#learnwithBrainly
Explanation:
We know that the sky appears to us like a sphere called as celestial sphere which appears to rotate around an imaginary axis because of Earth's rotation. Since the axis cuts the celestial sphere at celestial poles all the object seems to circle around the celestial poles.
Condition 1: The stars rise and set perpendicular to the horizon
The observer is at the equator
Condition 2: The stars circle the sky parallel to the horizon
The observer is at the Pole of the Earth
Condition 3: The celestial equator passes through the zenith
The observer is at the equator
Condition 4: In the course of a year, all stars are visible
The observer is at the equator
Condition 5: The Sun rises on March 21 and does not set until September 21 (ideally)
The observer is at North Pole