Answer
$$ w = 1.28 \ tons$$
Work Step by Step
We first translate the given problem into an equation:
$$ w = \frac{k}{h^2}$$
where w is the maximum weight the column can hold, k is the constant of variation, and h is the height of the column. We now plug in the given data to find the constant of variation:
$$ 2 = \frac{k}{8^2}$$
$$ k = 128$$
This gives the expression:
$$ w = \frac{128}{h^2}$$
Now, we plug in the given value for h, 10.
$$ w = \frac{128}{10^2}$$
Now, we use PEMDAS, a method for simplification. This acronym reminds us that we must first address parentheses, and then exponents. Next, we address multiplication and division, going from left to right. Lastly, we simplify addition and subtraction from left to right. This gives:
$$ w = 1.28 \ tons$$
