If $y \propto \dfrac{1}{x}$ and $x = 7$ when $y = 9$, find the constant of variation $\left( k \right)$.
Answer
386.7k+ views
Hint- Here, we will be putting the given values of the variables in the equation obtained after removing the inversely proportional sign.
Given $y \propto \dfrac{1}{x}$
Let the constant of variation introduced be $k$ after removing the proportionality sign.
\[y \propto \dfrac{1}{x} \Rightarrow y = k\left( {\dfrac{1}{x}} \right){\text{ }} \to {\text{(1)}}\]
Also given that when $y = 9$, the corresponding value of $y$ is $y = 9$.
Put $x = 7$ and $y = 9$ in equation (1), we get
\[ \Rightarrow y = k\left( {\dfrac{1}{x}} \right){\text{ }} \Rightarrow 9 = k\left( {\dfrac{1}{7}} \right) \Rightarrow k = 7 \times 9 = 63\]
Therefore, the required value of the constant of variation $\left( k \right)$ is 63.
Note- These types of problems are solved by assuming a constant of proportionality or a constant of variation when the proportionality sign (either directly proportional or inversely proportional) is removed.
Given $y \propto \dfrac{1}{x}$
Let the constant of variation introduced be $k$ after removing the proportionality sign.
\[y \propto \dfrac{1}{x} \Rightarrow y = k\left( {\dfrac{1}{x}} \right){\text{ }} \to {\text{(1)}}\]
Also given that when $y = 9$, the corresponding value of $y$ is $y = 9$.
Put $x = 7$ and $y = 9$ in equation (1), we get
\[ \Rightarrow y = k\left( {\dfrac{1}{x}} \right){\text{ }} \Rightarrow 9 = k\left( {\dfrac{1}{7}} \right) \Rightarrow k = 7 \times 9 = 63\]
Therefore, the required value of the constant of variation $\left( k \right)$ is 63.
Note- These types of problems are solved by assuming a constant of proportionality or a constant of variation when the proportionality sign (either directly proportional or inversely proportional) is removed.
Recently Updated Pages
Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts
Which of the following Chief Justice of India has acted class 10 social science CBSE

Green glands are excretory organs of A Crustaceans class 11 biology CBSE

What if photosynthesis does not occur in plants class 11 biology CBSE

What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

10 slogans on organ donation class 8 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

Students Also Read