Combinations

WS#1G9

1. In a game, there are 10 players, and the coach needs to choose a captain and a vice-captain. How many different combinations of captain and vice-captain are possible?
   
   
2. A school has 5 different clubs, and each student can join only one club. If there are 25 students in the school, how many different ways are there for the students to join the clubs?

Equation of parabola from graph

Transformed equation of parabola is: \(y=af(x-h)^2+k\) \(……(1)\)

Where \(a=\)Vertical stretch or compression, \(h=\)horizontal shift (left or right) \(k=\)Vertical shift (up or down) From graph, \(h=3\) and \(k=-2\); plug \(h\) and \(k\) values in eqn \((1)\) \(y=a(x-3)^2-2\) /(……(2)\) To find \(‘a’\), use the given point \((1,0)\) as: \(0=a(5-3)^2-2\) \(0=4a-2\) \(a=1/2\);plug in eqn.(2) \(y=1/2 (x-3)^2-2\);which is the reqd.eqn.

Trigonometric Co-ratios

Learn to convert and use trigonometric co-ratio functions to solve trigonometric problems.

Operations with integers

A number without a decimal or fractional element is known as an integer, which includes both positive and negative numbers, including zero. Some examples are \(-3, -2, 0, 2, 3\) etc. Every integer has an opposite. For example, \(3\) has opposite as \(-3\) and \(-5\) has opposite as \(5\). 

Absolute value: A number's absolute value is its numerical value without taking the sign into consideration, and it is represented by the sign \(|a|\); where a is any number. \(e.g.\)\(|a|=a\) and \(|-a|=a\) 

Water pollution

 

What is water pollution?

Water pollution is when waste, chemicals, or other particles cause a body of water (i.e. rivers, oceans, lakes) to become harmful to the fish and animals that need the water to survive.

What causes water pollution?

(1) Natural causes:

• Volcanoes
• Algae blooms
• Animal waste
• Silt from storms and floods.

Air Pollution

What is air pollution?

Air pollution is when unwanted chemicals, gasses, and particles enter the air and the atmosphere causing harm to animals and damaging the natural cycles of the Earth.

What causes air pollution?

    Natural causes:

• Eruptions of volcanoes  
  
• Dust storms
  
• Forest Fires
  
  Human activities responsible for air pollution:
  
  

HSPT Vocabulary Set-1