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The given formula for estimating the weight of a fish is:

\[
w = \frac{l \cdot g^2}{800}
\]

Where:
- \( w \) is the weight of the fish in pounds,
- \( l \) is the length of the fish in inches,
- \( g \) is the girth of the fish (distance around its midsection) in inches.

We are asked to estimate the girth (\( g \)) of a 700-pound yellow tuna that is 8 feet (96 inches) long.

The problem provides:
- \( w = 700 \) lbs,
- \( l = 8 \, \text{ft} = 96 \, \text{inches} \).

We need to find \( g \). We can rearrange the formula to solve for \( g \):

\[
g^2 = \frac{w \cdot 800}{l}
\]

\[
g = \sqrt{\frac{w \cdot 800}{l}}
\]

Substituting the values for \( w \) and \( l \):

\[
g = \sqrt{\frac{700 \cdot 800}{96}}
\]

Let's calculate the value of \( g \).The estimated girth of the 700-pound yellow tuna that is 8 feet long is approximately 76.38 inches.

Would you like further details or have any other questions?

Here are 5 related questions:
1. How does the girth affect the weight estimation in this formula?
2. If the length of the tuna were increased, how would the girth be affected to maintain the same weight?
3. How can we rearrange the formula to solve for \( l \) given the weight and girth?
4. What are the practical applications of such formulas in fisheries or wildlife conservation?
5. How accurate is this formula for different species of fish?

**Tip**: Remember to consistently check units (feet vs. inches, pounds vs. grams) when solving word problems, as unit conversion errors are common.

An ancient fisherman’s formula for estimating the weight of a fish is: w = (l * g^2) / 800, where w is the weight, in pounds, l is the length, in inches, and g is the girth (distance around the mid-section), in inches. Estimate the girth of a 700-lb yellow tuna that is 8 ft long.

Learn how to estimate the girth of a 700-lb yellow tuna using an ancient fisherman’s weight estimation formula. This problem involves algebraic concepts such as solving for unknowns and applying formulas, as well as unit conversion from feet to inches. Suitable for students in Grades 9-11.

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