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Quadratic Equation

is a quadratic equation in the variable x. Here a, b, c are real numbers and a ≠ 0
If α is the root of quadratic equation
Then

Quadratic Formula :

For a given quadratic equation, The roots can be given by

Exercise 4.1 (NCERT Solution) - Part - 1

1. Check whether the following are quadratic equations:

Since, the equation is in the form of So, it is a quadratic equation.

Since, the equation is in the form of So, it is a quadratic equation.

Since, the equation is not in the form of So, it is not a quadratic equation.

Since, the equation is in the form of So, it is a quadratic equation.

Since, the equation is in the form of So, it is a quadratic equation.

Since, the equation is not in the form of So, it is not a quadratic equation.

Since, the equation is not in the form of So, it is not a quadratic equation.

Since, the equation is in the form of So, it is a quadratic equation. 

Exercise 4.1 (NCERT Solution) - Part - 2

Question: 2 – Represent the following situation in the form of quadratic equation:
(i) The area of a rectangular plot is 528 m2. The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot.

Solution:

Since, the equation is in the form of So, it is a quadratic equation.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

Solution:

Since, the equation is in the form of So, it is a quadratic equation.

(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find the Rohan’s age.

Solution:

Since, the equation is in the form of So, it is a quadratic equation.

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Solution:

Since, the equation is in the form of So, it is a quadratic equation. 

Water resources notes

Water resources

Water resources are sources of water that are useful or potentially useful. Uses of water include agricultural, industrial, household, recreational and environmental activities. The majority of human uses require fresh water.
97 percent of the water on the Earth is salt water and only three percent is fresh water; slightly over two thirds of this is frozen in glaciers and polar ice caps.^[1] The remaining unfrozen freshwater is found mainly as groundwater, with only a small fraction present above ground or in the air.^[2]
Fresh water is a renewable resource, yet the world's supply of groundwater is steadily decreasing, with depletion occurring most prominently in Asia and North America, although it is still unclear how much natural renewal balances this usage, and whether ecosystems are threatened.^[3] The framework for allocating water resources to water users (where such a framework exists) is known as water rights

Top 5 Reasons for Water Pollution

Water pollution is the contamination or adulteration of the water bodies, such as rivers, lakes, seas, oceans, and ground water by number of human activities. Since water is essential for all our basic needs, water pollution is a threat to us. Many communicable diseases spread through unclean water, which even results in death. Although there are different factors that contribute to water pollution, listed below are the most dangerous causes of water pollution.

• Factories and nuclear plants play a major role in polluting the water. Wastes from factories include toxins, such as lead, mercury, and other contaminants. These chemicals are very harmful and can lead to serious health hazards.
• Nonpoint sources are one of the major causes of water pollution. Oil spills from cars, trucks, and other vehicles on land get mixed with rainwater and runoff into streams and lakes polluting them. These nonpoint sources are very difficult to monitor and control, so it falls on each individual to make sure that their vehicles used does not in any way contribute to further pollution. Proper maintenance of vehicles and oil spill cleanup using eco-friendly products, such as Oil Gone Easy S-200 will help to a great extent.
• Fertilizers and pesticides used in agricultural farms, homeowners lawns, and roadsides are a threat to the natural water source. When runoff into local streams or rivers or when drained down into groundwater, they contaminate the water completely.
• Mining is another major reason for water pollution. Heavy metals and sulfur components which are buried in the earth are exposed during mining and during rainfall these toxic chemicals are exposed, which ultimately result in “acid rain drainage”
• Surprising though it may seem, air pollution is also a cause of water pollution. Pollutants, such as sulfur dioxide, nitric acid, and mercury, when deposited out of air results in nutrient pollution and acidification of lakes.

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Rainwater harvesting is the accumulation and deposition of rainwater for reuse before it reaches the aquifer. Uses include water for garden, water for livestock, water for irrigation, and indoor heating for houses etc. In many places the water collected is just redirected to a deep pit with percolation. The harvested water can be used as drinking water as well as for storage and other purpose like irrigation

Advantages

Rainwater harvesting provides an independent water supply during regional water restrictions and in developed countries is often used to supplement the main supply. It provides water when there is a drought, can help mitigate flooding of low-lying areas, and reduces demand on wells which may enable ground water levels to be sustained. It also helps in the availability of potable water as rainwater is substantially free of salinity and other salts.

Quality

The concentration of contaminants is reduced significantly by diverting the initial flow of run-off water to waste.^[1] Improved water quality can also be obtained by using a floating draw-off mechanism (rather than from the base of the tank) and by using a series of tanks, with draw from the last in series. The stored rainwater may need to be analyzed properly before use in a way appropriate to ensure its safe use
The quality of collected rainwater is generally better than that of surface water. Contamination is always possible by airborne dust and mists, bird feces, and other debris, so some treatment may be necessary, depending on how the water will be used.

System setup

Rainwater harvesting systems can be installed with minimal skills. The system should be sized to meet the water demand throughout the dry season since it must be big enough to support daily water consumption. Specifically, the rainfall capturing area such as a building roof must be large enough to maintain adequate flow. The water storage tank size should be large enough to contain the captured water.^{[citation needed}

India

• In the state of Tamil Nadu, rainwater harvesting was made compulsory for every building to avoid ground water depletion. It proved excellent results within five years, and every states took it as role model. Since its implementation, Chennai saw a 50 percent rise in water level in five years and the water quality significantly improved.^[13]
• In Rajasthan, rainwater harvesting has traditionally been practiced by the people of the Thar Desert. There are many ancient water harvesting systems in Rajasthan, which have now been revived ^[14] Water harvesting systems are widely used in other areas of Rajasthan as well, for example the chauka system from the Jaipur district.^[15]
• Kerala:

Main article: Rainwater harvesting in Kerala

• At present, in Pune (in Maharashtra), rainwater harvesting is compulsory for any new society to be registered.
• An attempt has been made at Dept. of Chemical Engineering, IISc, Bangalore [1] to harvest rainwater using upper surface of a solar still, which was used for water distillation^[16

Kabir