Odd numbers are defined as any number which cannot be divided by two.

The most simple way to remember an odd number is ‘it is not a multiple of 2. The examples of odd numbers are 1, 3, 5, 7, etc

To compare the chemical energy of coal to its gravitational potential energy we nee to calculate the height to which 1 kg of coal can be lifted using the chemical energy released by burning 1 kg coal

Given Data:

The Chemical energy released by burning 1 kg of coal 

E = 3 x 10^6 Joules 

The mass of coal that is being lifted 

m = 1 kg 

acceleration due to gravity,

g = 9.81 m/s^2

The formula for gravitational potential energy (GPE)

GPE = mgh 

Let's solve for h

h = GPE/mg

h = 3 x 10 ^6 /1 x 9.81

h = 3035812.69 meters 

So, using all the chemical energy released by burning 1 kg of coal,  we could lift another 1 kg of coal to a height of approximately 305,813 meters.

This comparison demonstrates the huge amount of energy that coal contains since it can raise its own weight to a height that is much higher than the Earth's atmosphere.

a) F = ma and the force of gravity.

F= ma = Force of gravity  = mg
       m - mass of the book

       g - Acceleration due to gravity 

Using equation of motion,

v^2=u^2?+2as

v- Final velocity when book reaches the floor

u- Initial velocity = 0 

a- acceleration - In this case acceleration due to gravity - g ( approx.= 9.8 m/s^2)

s- distance travelled = h

So,

v^2= 0^2 + 2gh

v^2 = 2gh

Solving for v 

v = sqrt. (2gh) - velocity of book when it reaches floor calculated using force of gravity

Why do you use the force of gravity?

We use use force of gravity because it provides constant acceleration that  book experiences during fall.

b) gravitational potential energy and kinetic energy

Gravitational potential Energy = GPE = mgh

       m - mass of the book

       g - Acceleration due to gravity 

       h- distance travelled 

Kinetic Energy = KE = 1/2mv^2

When book hits the floor all KE will be converted in PE 

So, KE = PE 

mgh = 1/2 mv^2

gh = 1/2 v^2 

Let's solve it of v 

v^2 = 2gh

v = sqrt.2gh

In both the methods we arrive at same formula for the final velocity. 

This consistency shows that whether you use Newton's laws of motion or the principles of energy conservation, you will obtain the same result for the velocity of the book just before impact.

An assembly file, also known as an assembly language file or assembly source file, is a text file that contains instructions written in assembly language. Assembly language is a low-level programming language that is specific to a particular computer architecture or processor. Each assembly language instruction typically corresponds to a single machine language instruction that the computer's central processing unit (CPU) can directly execute.

An odd number is an integer that is not divisible evenly by 2, meaning that when you divide an odd number by 2, there is a remainder of 1.

To solve the expression $||x+3| - 4|$ piecewise, we need to consider the cases when $x+3$ is positive and when it is non-positive.

1. When $x+3 \geq 0$: In this case, $|x+3| = x+3$. Therefore, $||x+3| - 4| = |x+3| - 4 = (x+3) - 4 = x - 1$.

2. When $x+3 < 0$: In this case, $|x+3| = -(x+3)$. Therefore, $||x+3| - 4| = |-(x+3) - 4| = |-x-7| = x + 7$.

So, the piecewise definition for $||x+3|-4|$ is: