Direct Variation With Exponents
Direct Variation With Exponents
Direct Variation:
Two terms are said to be in direct variation if increase or decrease of term will result in the increase or decrease of the other term respectively.
Direct Variation With Exponents:
Two terms are said to be in direct variation with exponents if increase or decrease of term will result in the exponential increase or decrease of the other term respectively.
For example:let us consider the formula to find the area of circle.
The formula for finding the area A of a circle of radius r is
Now let us calculate the value of area for different values of the radius
|
r |
0 | 1 | 2 | 3 | 4 |
|
A |
0 | 3.14 | 12.57 | 28.27 | 50.27 |
If we graph A against r we get the graph below
The graph is not the straight line, it is curve or we can say that it is part of a parabola . So the area is not directly proportional with radius. A is not directly proportional to r.
However suppose we include in the table a row for the values of :
|
r |
0 | 1 | 2 | 3 | 4 |
| 0 | 1 | 4 | 9 | 16 | |
| A | 0 | 3.14 | 12.57 | 28.27 | 50.27 |
The graph of A against is a straight line through the origin O as shown below
so A is directly proportional to . We can say that
. In this case we know from the formula that the proportional constant is
.
Notice from the table that if r is doubled from 1 to 2 both and A are multiplied by 9 .
Illustration: From the following equation state which two variables are directly proportional and determine the proportionality constant k .
.
Solution: On analysing the equation we can say that as
,
.
Hence y is directly proportional to the fourth power of x and the proportionality constant is
.
If p varies directly as the square of q, and p = 20 when q = 5, find p when q = 8. | |||
| Right Option : A | |||
| View Explanation | |||
From the following equation state which two variables are directly proportional. | |||
| Right Option : D | |||
| View Explanation | |||
18 men can do a piece of work in 35 days. For doing the same work in 15 days, how many men are required? | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [10]
My experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thI have spent a wonderful time in Abhyas academy. It has made my reasoning more apt, English more stronger and Maths an interesting subject for me. It has given me a habbit of self studying
Yatharthi Sharma
10thAbhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thMy experience with Abhyas academy is very good. I did not think that my every subject coming here will be so strong. The main thing is that the online tests had made me learn here more things.
Hiya Gupta
8thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thIt was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
10thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
