The easiest way to build a unit for energy is to remember that
'work' is energy, and
Work = (force) x (distance).
So energy is (unit of force) x (unit of distance)
[Energy] = (Newton) (meter) .
'Newton' itself is a combination of base units, so
energy is really
(kilogram-meter/sec²) (meter)
= kilogram-meter² / sec² .
That unit is so complicated that it's been given a special,
shorter name:
Joule .
It doesn't matter what kind of energy you're talking about.
Kinetic, potential, nuclear, electromagnetic, food, chemical,
muscle, wind, solar, steam ... they all boil down to Joules.
And if you generate, use, transfer, or consume 1 Joule of
energy every second, then we say that the 'power' is '1 watt'.
If you are asking for a proof on having at least 3 dimensions in space, you can find the physical proof anywhere in your daily life activities. Just the fact that solids have volumes is a proof already that we live in a three-dimensional space. We can move forwards, backwards, sidewards and in all other directions possible.
When you go right into detail, the fundamental laws governing these proofs are very technical. They have differential equations to show as proof. It is too detailed to discuss here. The important things is that, these fundamental laws are what explains the science in our basic activities and natural phenomena:
*Gravitation and planetary motion
* Translation, rotation, magnetic field, forces
* Integrals of equations:
The statement about pointwise convergence follows because C is a complete metric space. If fn → f uniformly on S, then |fn(z) − fm(z)| ≤ |fn(z) − f(z)| + |f(z) − fm(z)|, hence {fn} is uniformly Cauchy. Conversely, if {fn} is uniformly Cauchy, it is pointwise Cauchy and therefore converges pointwise to a limit function f. If |fn(z)−fm(z)| ≤ ε for all n,m ≥ N and all z ∈ S, let m → ∞ to show that |fn(z)−f(z)|≤εforn≥N andallz∈S. Thusfn →f uniformlyonS.
2. This is immediate from (2.2.7).
3. We have f′(x) = (2/x3)e−1/x2 for x ̸= 0, and f′(0) = limh→0(1/h)e−1/h2 = 0. Since f(n)(x) is of the form pn(1/x)e−1/x2 for x ̸= 0, where pn is a polynomial, an induction argument shows that f(n)(0) = 0 for all n. If g is analytic on D(0,r) and g = f on (−r,r), then by (2.2.16), g(z) =
Answer:
The angle of separation is 
Explanation:
From the question we are told that
The angle of incidence is 
The refractive index of violet light in diamond is 
The refractive index of red light in diamond is 
The wavelength of violet light is 
The wavelength of red light is 
Snell's Law can be represented mathematically as
Where 
is the angle of refraction
=> 
Now considering violet light
substituting values
Now considering red light
substituting values
The angle of separation between the red light and the violet light is mathematically evaluated as
substituting values
Answer:
0.0928km/min (4dp)
Explanation:
To find the jogger's speed in km per minute, we just need to divide the number of km jogged by the time in minutes it took to jog that distance. This will give us the distance they jogged every minute which is their speed.
4km in 32 minutes:
4/32 = 0.125km/min
2km in 22 minutes:
2/22 = 0.091 (3dp)km/min
1km in 16 minutes:
0.0625km/min
Now to find the average speed of these 3 speeds, we just add them all together and divide by how many values there are (3 values).
Average (mean) = 
Average = 0.2785/3
Average speed of jogger = 0.0928 (4dp) km/min
Hope this helped!
