Question

select all the correct answer. a company decides to drain the water heater to flush out sediments. the water heater has a capacity of 500 gallons. it drains 100 gallons in 20 minutes. after 20 minutes, they open another drain valve and it drains 200 gallons in the next 20 minutes. the drain valves are closed for 10 minutes, while the workers take a break and then the water heater is drained until the water heater is completely empty. what are the domain and the range of this relation? chart: a graph with x-axis labeled time (minutes) from 0 to 100, y-axis labeled water (gallons) from 0 to 500. the graph shows a line starting at (70, 500) and decreasing with different slopes, with a horizontal segment around 40 - 50 minutes? (exact details from the chart as per image). multiple choice options (checkboxes): 0 ≤ y ≤ 70, y ≥ 0, 0 ≤ x ≤ 70, 0 ≤ x ≤ 500, x ≥ 0, 0 ≤ y ≤ 500

Explanation:

Step1: Determine the domain

The x - axis represents time (in minutes). From the graph and the problem description, the time starts at 0 minutes (when the draining starts) and goes up to 70 minutes (when the water heater is empty). So the domain is the set of all x - values, which is \(0\leq x\leq70\).

Step2: Determine the range

The y - axis represents the amount of water (in gallons). The water heater starts with 500 gallons and drains down to 0 gallons. So the range is the set of all y - values, which is \(0\leq y\leq500\). Also, we can check the other options:

• \(x\geq0\): This is too broad as the draining stops at 70 minutes, so this is incorrect.
• \(0\leq x\leq500\): x is time, not gallons, so this is incorrect.
• \(y\geq0\): This is too broad as the maximum water is 500 gallons, so this is incorrect.
• \(0\leq y\leq70\): y is gallons, not time, so this is incorrect.

Answer:

The correct options for domain and range are \(0\leq x\leq70\) and \(0\leq y\leq500\) (the checkboxes corresponding to \(0\leq x\leq70\) and \(0\leq y\leq500\) should be selected).