Let the rational number be {tex}\frac{x}{{x + 8}}{/tex}
According to the question,
{tex}\frac{{x + 7}}{{x + 8 - 1}} = \frac{3}{2}{/tex}
∴ {tex}\frac{{x + 17}}{{x + 7}} = \frac{3}{2}{/tex}
∴ {tex}\frac{{x + 17}}{{x + 7}} \times (x + 7) = \frac{3}{2} \times (x + 7){/tex}  . . . . [ Multiplying both sides x + 7, ]
∴ {tex}x + 17 = \frac{{3(x + 7)}}{2}{/tex}
2(x + 17) = 3(x + 7)  . . . . [ Multiplying both sides 2 ] 
∴  2x + 34 = 3x + 21
∴ 34 – 21 = 3x – 2x  . . . . [ Transposing 21 to L.H.S. and 2x to R.H.S. ]
∴ 13 = x
∴ x = 13
∴ x + 8 = 13 + 8 = 21 hence, the rational number {tex}\frac{{13}}{{21}},{/tex}
Verification
21 = 13 + 8
{tex}\frac{{13 + 7}}{{21 - 1}} = \frac{{30}}{{20}} = \frac{{30 \div 10}}{{20 \div 10}} = \frac{3}{2}{/tex} hence, the result is verified.

Minerals are naturally occurring substances. They have a definite chemical composition.  Minerals are formed in different types of geological environments, under varying conditions.

Power Resources

We need power resources for industry, agriculture, transport, communication, and defence. Therefore, we must understand the importance of these resources and conserve them. Power resources are of two types:

• Conventional Resources: are those that have been in common use for a long time. Firewood and fossil fuels are two main conventional energy sources.
• Non-conventional Resources: of energy are renewable. Solar energy, wind energy, tidal energy, etc. are non-conventional sources of energy.

Fertilizer are the inorganic compounds which supply specific nutrients.

For example: NPK (Nitrogen Phosphorous Potassium), ammonium sulphate, ammonium phosphate etc.

The Battle of Plassey was fought between the forces of the Nawab of Bengal Siraj-ud-Daulah and the English East India Company, led by Robert Clive. It was fought on 23 June 1757 at Plassey near Murshidabad. A major portion of the 50,000 strong army of the Nawab was controlled by Mir Jafar who was hand in gloves with the British. His men did not join the battle at a crucial time. As a result, the Nawab’s men suffered heavy casualties and he himself left the battlefield after the death of his commander Mir Madan. This was a major blow to the Nawab’s army which was, as a result, easily defeated by the British. Later, the Nawab himself was caught and killed, and Mir Jafar was instituted as the new Nawab of Bengal.

Let take √5 as a rational number
If a and b are two co-prime number and b is not equal to 0.
We can write √5 = a/b
Multiply by b both side we get
b√5 = a
To remove root, Squaring on both sides, we get
5b² = a² ……………(1)
Therefore, 5 divides a² and according to a theorem of rational number, for any prime number p which is divided 'a²' then it will divide 'a' also.
That means 5 will divide 'a'. So we can write
a = 5c
and putting the value of a in equation (1) we get
5b² = (5c)²
5b² = 25c²
Divide by 25 we get
b^2/5 = c²
again using the same theorem we get that b will divide by 5
and we have already get that a is divided by 5
but a and b are co-prime number. so it is contradicting.
Hence √5 is an irrational number

9.87511349546

In tsunami Ignesious , the manager of a cooperative society, lost two of his children, wife and father-in-law as he could not get alarmed by the tremor. Sanjeev was a policeman. He jumped into the water to rescue his cook’s wife, but they were both swept away. Both Meghna’s and Almas’ families were washed away. Both of them kept floating in the sea for days. Meghna floated in the sea for two days holding on to a wooden door. She was brought to the shore by a wave. Similarly, Almas climbed on to a log of wood and fainted. She woke up in a hospital. Both the girls were traumatized after the incident. While Meghna was seen walking on the seashore in daze, Almas does not talk about the incident to anyone. Both of them were not noticed by relief helicopters.Tilly Smith (a British school girl ) was able to save many lives when the tsunami struck Phuket beach in Thailand as she had seen the sea behaving in the same way in a video in her class of a tsunami that had hit the Hawaiian islands in 1946. She had won a number of awards. The tourist thanked Tilly and her geography lesson that had warned her.Before tsunami in India and SriLanka, wild and domestic animals fled to safety, elephants ran for higher grounds; dogs refuse to go outdoors; flamingoes abandoned their low-lying breeding areas as seemed to know what was about to happen. It is believed that animals either posses a sixth sense or have more acute hearing that helps them to hear or feel earth’s vibration. Near about 150,000 people killed in tsunami in a dozen countries but not many animals reported dead.

12701290000

There are about 50 different determiners:

• Articles - a, an, the.
• Demonstratives - this, that, these, those, which etc.
• Possessives - my, your, our, their, his, hers, whose, my friend's, our friends', etc.
• Quantifiers -few, a few, many, much, each, every, some, any etc.

Types of plastics: Plastics are of two types – thermoplastics and thermosetting plastics.

1. Thermoplastics – Thermoplastics get soft when heated and hard again when they are cooled.  Example – polythene and poly vinyl chloride. Such plastics are used in making toys, containers, plastic bags, raincoats and combs. Thermoplastics are used in making those articles which do not get too hot, and are flexible.
2. Thermosetting plastics – Thermosetting plastics get soft only one, the first time they are heated after being made. When such plastics are heated for the first time, they become soft and can be moulded to make an article of any desired shape. On cooling, the article becomes hard and rigid. Example – Bakelite and melamine. They are used in making handles of cooking utensils, plates, cups, floor tiles, electrical fittings, telephone instruments, etc.

A fertiliser is an inorganic salt.Fertilisers are prepared in factories.they have all the three important plant nutrients nitrogen, phosphorous and potassium. They do not emit any bad smell but they cause alot of pollution.ex ammonium sulphate . A fertiliser does not provide any humus to the soil.
Manure is a natural substance obtained by the decomposition of cattle dung, human waste and plant residues. Manure is a natural product. it is prepared naturally in the field. And it mostly doesn't have the three important plant nutrients .  Manure provides a lot of humus to the soil.

Symbiotic relationships are a special type of interaction between species. Sometimes beneficial, sometimes harmful, these relationships are essential to many organisms and ecosystems, and they provide a balance that can only be achieved by working together.