Question

complete the statement that describes the situation. the drone is at a height of 35 feet when leahs dad calls her in for lunch. the height of the drone decreases ___ on its way to the ground. 5 feet every 3 seconds 3 feet every 5 seconds 5 feet every second 1 foot every 5 seconds

Explanation:

Step1: Analyze the graph's slope

The initial height (at \( x = 0 \)) is 35 feet. Let's check the change in height over time. For example, from \( x = 0 \) (height 35) to \( x = 5 \) (let's estimate height at \( x = 5 \): looking at the graph, at \( x = 5 \), height is around 30? Wait, no, let's take another point. Wait, the x - axis is time in seconds (0 to 10), y - axis is height. Let's take two points: (0, 35) and (5, 30)? Wait, no, maybe (0, 35) and (5, 30) is not right. Wait, let's calculate the rate of change (slope). The formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take \( (0, 35) \) and \( (5, 30) \)? Wait, no, maybe better to see the options. Let's check each option:

Option 1: 5 feet every 3 seconds. Let's see, in 3 seconds, height decreases by 5. So rate is \( \frac{5}{3}\approx1.67 \) ft per second.

Option 2: 3 feet every 5 seconds. Rate is \( \frac{3}{5} = 0.6 \) ft per second.

Option 3: 5 feet every second. Rate is 5 ft/s (too fast, since from 35 to 20 in 10 seconds is 15 feet over 10 seconds, 1.5 ft/s, so no).

Option 4: 1 foot every 5 seconds. Rate is \( \frac{1}{5}=0.2 \) ft/s (too slow).

Wait, let's calculate the actual slope. From \( x = 0 \) (height 35) to \( x = 10 \) (height 20). So change in height \( \Delta y=20 - 35=- 15 \) feet, change in time \( \Delta x = 10-0 = 10 \) seconds. So slope \( m=\frac{-15}{10}=-1.5 \) ft per second. Now let's check the options:

Option 1: 5 feet every 3 seconds: \( \frac{5}{3}\approx1.67 \) (close to 1.5? Wait, maybe my initial point was wrong. Wait, maybe the graph at \( x = 3 \), height is 32? Wait, let's re - examine. Wait, the first point is (0, 35), at \( x = 3 \), height is 32? Then change in height from 0 to 3 seconds: 35 - 32 = 3? No, that's not. Wait, maybe the correct way: let's take (0, 35) and (3, 32) – no, that's 3 feet in 3 seconds, no. Wait, the options: let's check "3 feet every 5 seconds". So in 5 seconds, height decreases by 3. So rate is \( \frac{3}{5}=0.6 \)? No, that's not. Wait, maybe I made a mistake. Wait, the correct approach: let's see the options. Let's check "5 feet every 3 seconds" – no, "3 feet every 5 seconds" – wait, no, let's calculate the rate from the graph. From x = 0 (35) to x = 5 (let's say height is 30? Then 35 - 30 = 5 feet in 5 seconds? No, that's 1 foot per second. Wait, I'm confused. Wait, the graph: at x = 0, y = 35; at x = 5, y = 30 (so 5 feet decrease in 5 seconds? No, 35 - 30 = 5, 5 seconds, so 1 foot per second? No, that's not. Wait, maybe the correct answer is "5 feet every 3 seconds" is wrong. Wait, no, let's check the options again. Wait, the options are:

1. 5 feet every 3 seconds

2. 3 feet every 5 seconds

3. 5 feet every second

4. 1 foot every 5 seconds

Wait, let's take two points: (0, 35) and (3, 30). So in 3 seconds, height decreases by 5 (35 - 30 = 5). So that's 5 feet every 3 seconds. Let's check the slope: \( \frac{5}{3}\approx1.67 \), and our earlier calculation from 0 to 10 was - 1.5, which is close (maybe my estimation of the height at x = 10 was wrong). Maybe the height at x = 10 is 22? Wait, the graph shows at x = 10, height is around 22. So from 35 to 22 in 10 seconds: 13 feet over 10 seconds, 1.3 ft/s. The first option: 5/3≈1.67, which is close. Alternatively, maybe the correct answer is "5 feet every 3 seconds" is not, wait, no, let's check the options again. Wait, the correct answer is "5 feet every 3 seconds" is incorrect? Wait, no, let's think again. Wait, the problem is about the rate of decrease. Let's see the graph: when time increases by 3 seconds, how much does height decrease? At x = 0, y = 35; at x = 3, y = 32? No, maybe the graph is such that from x = 0 (35) to x = 3 (30), so 5 feet decrease in 3 seconds. So the height decreases 5 feet every 3 seconds.

Step2: Eliminate other options

- Option 3: 5 feet every second: this would mean in 1 second, height drops 5 feet. In 10 seconds, it would drop 50 feet, but initial height is 35, so impossible.
- Option 4: 1 foot every 5 seconds: in 5 seconds, drop 1 foot. In 10 seconds, drop 2 feet, but from 35 to ~22, that's a drop of 13, so too slow.
- Option 2: 3 feet every 5 seconds: in 5 seconds, drop 3 feet. In 10 seconds, drop 6 feet, from 35 to 29, but graph shows lower, so no.
- Option 1: 5 feet every 3 seconds: in 3 seconds, drop 5 feet. In 10 seconds, drop \( \frac{5}{3}\times10\approx16.67 \) feet, from 35 to \( 35 - 16.67\approx18.33 \), close to the graph's height at 10 seconds (around 20 - 22, maybe my estimation was off, but this is the most reasonable among the options).

Answer:

5 feet every 3 seconds