A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.

The equation for this sequence is:

a_n = a_n-1 + 8

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 8
a₆ = 33 + 8
a₆ = 41

In order to find how many additional workers are needed to staff the extra crews you first need to calculate how many workers are on a crew. There are 10 workers at the company now and that's enough to staff 5 crews so there are \( \frac{10}{5} \) = 2 workers on a crew. 9 crews are needed for the busy season which, at 2 workers per crew, means that the roofing company will need 9 x 2 = 18 total workers to staff the crews during the busy season. The company already employs 10 workers so they need to add 18 - 10 = 8 new staff for the busy season.

To subtract these radicals together their radicands must be the same:

7\( \sqrt{8} \) - 3\( \sqrt{2} \)
7\( \sqrt{4 \times 2} \) - 3\( \sqrt{2} \)
7\( \sqrt{2^2 \times 2} \) - 3\( \sqrt{2} \)
(7)(2)\( \sqrt{2} \) - 3\( \sqrt{2} \)
14\( \sqrt{2} \) - 3\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

If the tiger has consumed 98 pounds of food in 7 days that's \( \frac{98}{7} \) = 14 pounds of food per day. The tiger needs to consume 182 - 98 = 84 more pounds of food to reach 182 pounds total. At 14 pounds of food per day that's \( \frac{84}{14} \) = 6 more days.