Final answer:
To find the depth of the hole that Jack should dig, we use the proportion 3 feet deep for every 5 feet of tree height to calculate that for a 17-foot tree, Jack should dig a hole 10.2 feet deep.
Step-by-step explanation:
The question involves determining how deep to dig a hole for a tree based on its height, using a given ratio. Since the ratio is 3 feet deep for every 5 feet of tree height, we can set up a proportion to find out how deep Jack should dig for a tree that is 17 feet high. The proportion is:
(3 feet deep / 5 feet height) = (x feet deep / 17 feet height)
To solve for x, the depth of the hole, multiply both sides by 17 feet height (3/5 = x/17) to get:
x = (3/5) × 17
x = 51/5
x = 10.2
Therefore, Jack should dig a hole that is 10.2 feet deep for a tree that is 17 feet high.