(i) You are given that $$ y $$ is inversely proportional to $$ \sqrt{x} $$. $$ y=65 $$ when $$ x=51.84 $$. Find an expression for $$ y $$ in terms of $$ x $$.

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UpStudy AI · Accepted Answer

Given that $$ y $$ is inversely proportional to $$ \sqrt{x} $$, we can express this relationship as:

$$
y = \frac{k}{\sqrt{x}}
$$

where $$ k $$ is the constant of proportionality.

**Step 1: Determine the constant $$ k $$**

We are given that $$ y = 65 $$ when $$ x = 51.84 $$. Plugging these values into the equation:

$$
65 = \frac{k}{\sqrt{51.84}}
$$

First, compute $$ \sqrt{51.84} $$:

$$
\sqrt{51.84} = 7.2 \quad \text{(since $$ 7.2 \times 7.2 = 51.84 $$)}
$$

Now, solve for $$ k $$:

$$
65 = \frac{k}{7.2} \
k = 65 \times 7.2 \
k = 468
$$

**Step 2: Write the expression for $$ y $$ in terms of $$ x $$**

Substitute the value of $$ k $$ back into the original equation:

$$
y = \frac{468}{\sqrt{x}}
$$

**Final Answer:**

$$
y = \frac{468}{\,\sqrt{x}\,}
$$
$$ y = \frac{468}{\sqrt{x}} $$

(i) You are given that is inversely proportional to .
when .
Find an expression for in terms of .

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(i) You are given that is inversely proportional to . when . Find an expression for in terms of .