If $$ A \propto B^{2} $$, and $$ A=45 $$ whe $$ B=3 $$, find $$ B $$ when $$ A=80 $$

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UpStudy AI · Accepted Answer

Given that $$ A \propto B^{2} $$, we can express this relationship as:
$$
A = k B^{2}
$$
where $$ k $$ is the proportionality constant.

**Step 1: Find the Proportionality Constant $$ k $$**

We're given that when $$ B = 3 $$, $$ A = 45 $$. Plugging these values into the equation:
$$
45 = k \times 3^{2} \
45 = 9k \
k = \frac{45}{9} = 5
$$

**Step 2: Find $$ B $$ When $$ A = 80 $$**

Now, using the value of $$ k $$ found:
$$
80 = 5 B^{2} \
B^{2} = \frac{80}{5} = 16 \
B = \sqrt{16} = 4 \quad (\text{since } B \text{ is typically positive})
$$

**Answer:** $$ B = 4 $$
$$ B = 4 $$

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