Rate, distance in geometry

In the mathematics we study a lot of concepts which are related to our daily life. These concepts help to solve the problems related to mathematical calculations. In the mathematical field there are many ways to represent the things in the measurable quantity. These measurable quantities provide an easy and convenient way to represent the things, which help in to performing the various tasks related to our daily routine life.
Here we are going to discuss about the rate and distance in geometry. Rate contains the collection of several measurable quantity or measures to specify the quantity of the product or things. In simple terms rates is a ratio, which demonstrates the relationship of a thing to the measurable quantity.

Suppose John makes a trip to Hollywood, in which he covers a distance of 250 miles in 5 hours then what is the speed of his car?
This would be represented by dividing the distance by the time.
            Let’s see                    250/5 = 50 miles per hour
It means john covers the distance at the rate of 50miles/hour. Here ( / )symbol represent ‘ at per’.
Now we show the relationship between rate and distance. As we describe rate termed as ratio, which represents the comparison of two different numbers to display them in measurable quantity.
Now we will see an example to represent the relationship between the rate and distance:
Example: Suppose there is a shop where jack purchases 5 liter milk. Now he pays $15 for the milk. So find the amount of 1 liter milk.
Solution: Here given that purchase milk = 5 liter
                               Paid amount             = $ 15
                         So, amount of 1 liter   =       $15 / 5
                                                                =   $3/liter
                                                 
In the next session we are going to discuss time and angle measures

time and angle measures

Time and angle measures are one of the important types of mathematical problems. We all know that time problems (clock angle measure problem) are all about finding the angles between the hands (Hands are minute hand or hour hand or second hand) of an analog clock. This is very important part of geometry. In geometry the measurement unit for angle is the “Degree”. A circle is divided into 360 equal degrees.  Moreover, degrees are divided into two terms, known as Minutes and Seconds. This division of degree is not universal. (To get help on central board of secondary education books click here)
These problems generally relate to two different measures which are angles and time. For such problems we always consider the change rate of the angle in degree per minute (deg/min) and we may also use arc lengths in this. In an analog clock the hour hand of the clock turns 360 degree in 12 hours which are 720 minutes or we can say 0.5 degree per minute. In the same analogue clock the minute hand turns 6 degree per minute or 360 deg in 1 hour (60 minutes).
Now to solve related problems we need to apply some formulas in form of general equations. These equations are:
1.      Equation for angle of the hour hand of the clock:
Ahr = ½ Me = ½ ( 60 H + M)
Here Ahr is the angle of the hand measured clockwise from the exact time 12’o clock. M is the minute past hour and Me is minute past 12’o clock.
2.      Equation for degree on minute hand of the clock:
Amin  = 6*M
Where Amin is the angle of the hand measured clockwise from the time 12’o clock and its unit is degree.
For example: Time given is 5:30 then the angle of hour hand in degrees:
Ahr  = ½(60*5 + 30) =165 degree
Similarly for the same time the angle of minute hand in degree:
Amin  = 6*30  = 180 degree.
So today we learnt about Times and Angle measures. In the next session I will tell you about arc lengths and In the next session we will discuss about Rate, distance in geometry.