# Hot Air Balloons!

### By Jeremy Basso & Abhi C

## Graphs And Explanations.

## Our Graph and Table (Question 2 & 3) On the left there is a table of values for Balloon 1 for every 5 minutes, and the right is our graph based on that graph data. 5 minutes before it was sighted, (or -5 for 0 minutes on the x axis represents when spotted) the balloon was 100 feet above when first spotted, making it at 900 ft. 800- (-100) = 800+100 = 900 | ## Question 4 As seen on the graph, the balloon descended to 20 feet after 39 minutes, or the coordinates (39,20). This is because it declined at a steady rate of 20 feet. Another way is finding when it reached 20 feet is finding when it landed and subtracting a minute from that. This method works because it descends 20 feet per minute, so if it descended to 0 at 40minutes, the real answer would be 39 minutes for when you subtract a minute you are adding 20 feet. | ## Question 5 The second balloons function would be: f(x) = 1200-20x. As shown on the graph, it would take 20 more minutes for the second balloon to land. Both ballons descend at the same rate of 20 feet making them parallel on the graph. Because the second ballons function is f(x) = 1200-20x, it means that the y intercept would be 1200, and descend from that would take longer than 800. |

## Our Graph and Table (Question 2 & 3)

800- (-100) = 800+100 = 900

## Question 4

## Question 5

As shown on the graph, it would take 20 more minutes for the second balloon to land. Both ballons descend at the same rate of 20 feet making them parallel on the graph. Because the second ballons function is f(x) = 1200-20x, it means that the y intercept would be 1200, and descend from that would take longer than 800.

## Question 6 The function for the third balloon would be f(x) = 800-30x. The third balloon landed 13 1/3 minutes faster than the first balloon. While the first balloon landed at 40 minutes, the third balloon landed at 26 2/3 minutes. Although both balloons were spotted at 800 feet, the third balloon had a faster descent (steeper slope) of 30 feet per minute causing it to land faster. | ## Question 7 The function for the 4th balloon would be f(x) = 30x.This function would not be negative for it had a positive correlation (since it is going upwards) and is ascending at 30 feet per minute while the other balloons are descending. The 4th balloon and the first balloon would both reach the same altitude after 16 minutes, with both at the altitude of 480 feet. Graphically this would be the point of intersection between the two lines/balloons. The 4th balloon is represented by the green line while the 1st balloon is represented by the blue line. | ## Question 8 The third balloon would have to start it's descent at 1200 feet to reach the ground at the same time as the 1st balloon. An equation for this line would be 0 = -30x + y. x is when the first balloon landed. (40 minutes) 0= -1200 + y. y (or when the 3rd balloon has to start its descent) would then have to equal 0 to finish the equation. 0 = -1200 + 1200 |

## Question 6

The third balloon landed 13 1/3 minutes faster than the first balloon. While the first balloon landed at 40 minutes, the third balloon landed at 26 2/3 minutes. Although both balloons were spotted at 800 feet, the third balloon had a faster descent (steeper slope) of 30 feet per minute causing it to land faster.

## Question 7

__30x.__

This function would not be negative for it had a positive correlation (since it is going upwards) and is ascending at 30 feet per minute while the other balloons are descending.

The 4th balloon and the first balloon would both reach the same altitude after 16 minutes, with both at the altitude of 480 feet. Graphically this would be the point of intersection between the two lines/balloons. The 4th balloon is represented by the green line while the 1st balloon is represented by the blue line.

## Question 8

__start__it's descent at 1200 feet to reach the ground at the same time as the 1st balloon.

An equation for this line would be 0 = -30x + y.

x is when the first balloon landed. (40 minutes)

0= -1200 + y.

y (or when the 3rd balloon has to start its descent) would then have to equal 0 to finish the equation.

0 = -1200 + 1200