Answer
398.4k+ views
Hint: First try to get an equation in terms of variables and constant by removing the proportionality. Substitute the variables by the given values to get the value of the constant. Then again substitute the value of the constant in the base equation to get the required expression.
Complete step by step answer:
According to the question; y is directly proportional to the square of x
\[\Rightarrow y\propto {{x}^{2}}\]
\[\Rightarrow y=k{{x}^{2}}\](Where k is the proportionality constant)
Therefore, y would be in the form \[y=k{{x}^{2}}\] (where k is a constant)
Now the given values are x=4 and y=25.
Putting these values in the above equation we get,
$\begin{align}
& 25=k\times {{4}^{2}} \\
& \Rightarrow 25=16k \\
\end{align}$
The value of the constant k obtained from the equation is $\dfrac{25}{16}$
Now we have to find an expression of y in terms of x.
This can be expressed by substituting the value of the constant k in the base equation \[y=k{{x}^{2}}\]
Putting the value of constant $k=\dfrac{25}{16}$(in fraction form);
We get the expression $y=\dfrac{25}{16}{{x}^{2}}$.
Note: A proportionality constant ‘k’ should be added after removing the proportionality sign. The proportionality constant ‘k’ can be obtained by putting the values of ‘x’ and ‘y’ in the proportionality equation.
Complete step by step answer:
According to the question; y is directly proportional to the square of x
\[\Rightarrow y\propto {{x}^{2}}\]
\[\Rightarrow y=k{{x}^{2}}\](Where k is the proportionality constant)
Therefore, y would be in the form \[y=k{{x}^{2}}\] (where k is a constant)
Now the given values are x=4 and y=25.
Putting these values in the above equation we get,
$\begin{align}
& 25=k\times {{4}^{2}} \\
& \Rightarrow 25=16k \\
\end{align}$
The value of the constant k obtained from the equation is $\dfrac{25}{16}$
Now we have to find an expression of y in terms of x.
This can be expressed by substituting the value of the constant k in the base equation \[y=k{{x}^{2}}\]
Putting the value of constant $k=\dfrac{25}{16}$(in fraction form);
We get the expression $y=\dfrac{25}{16}{{x}^{2}}$.
Note: A proportionality constant ‘k’ should be added after removing the proportionality sign. The proportionality constant ‘k’ can be obtained by putting the values of ‘x’ and ‘y’ in the proportionality equation.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)