Question

How do you write the equation if $R$is inversely proportional to the square of $I$and $I = 25$when $R = 100$?

Answer 1

In order to determine equation, express the relation between $R$and the square of $I$as $R \propto \dfrac{1}{{{I^2}}}$which can be resolved into$R = (k)\dfrac{1}{{{I^2}}}$.

Determine the value of k by putting$I = 5$and$R = 65$and then put the value of k into $R = (k)\dfrac{1}{{{I^2}}}$to determine the equation.

Complete step by step solution:
In order to write any mathematical expression from some words and figures, we must first find the relationship and the quantities specified.

Here in this question the relation between $R$ and${I^2}$is that its saying that $R$ varies inversely with the square of $I$.

Here, inversely means that when the value of ${I^2}$increases the value of
$R$ decreases.

So we are replacing the ‘inversely varies’ word from the sentence with the Proportional
symbol $R \propto \dfrac{1}{{{I^2}}}$

Resolving the proportionality symbol with the inclusion of proportionality constant$k$on the right- hand side

$R = (k)\dfrac{1}{{{I^2}}}$where k is the proportionality constant ---(1)

According to question, when$I = 25$ then $R = 100$so putting values of $R$ and$I$ in above expression

$R = (k)\dfrac{1}{{{I^2}}} \\\ \Rightarrow 100 = (k)\dfrac{1}{{{{(25)}^2}}} \\\ \Rightarrow k = 100 \times {(25)^2} \\\ \Rightarrow k = 100 \times 625 \\\ \Rightarrow k = 62500 \\\$

Hence, the value of proportionality constant $k = 13$.

Therefore, the Equation becomes$R = \dfrac{{62500}}{{{I^2}}}$.

Additional Information: 1.Mathematical equation: A Mathematical equation can be defined as the mathematical statement which contains an equal symbol $=$ in between two algebraic expressions that share the same value.

Algebraic expression can contain any number of variables generally we take 2-3 variables
Let assume a expression $5x + 9 = 24$

It is a mathematical equation having LHS (Left-Hand-Side) equal to RHS (Right-Hand-Side)
Where $x$ is the variable 5 is the coefficient of variable $x$

And $24,9$are the constants 2.$2x + 98 + 78y$is not a mathematical equation because it does not contain equality $=$ symbol .

It is only a mathematical expression.

Note: 1. Read the statement carefully in order to convert them into mathematical expressions.
2.If the relation between $x$and $y$is directly proportional when the expression will be
$y \propto x \\\ y = (k)x \\\$
Where k is the proportionality constant.