Answer :
Final answer:
A system of equations representing the heights of the two hot-air balloons as functions of time is h1(t) = 500 + 120t for the ascending balloon and h2(t) = 1500 - 200t for the descending balloon.
Explanation:
To write a system of equations for the two hot-air balloons, let's define t as the time in minutes after the observations begin. Let h1(t) represent the height of the first balloon which is ascending and h2(t) represent the height of the second balloon which is descending.
Since the first balloon starts at 500 feet and rises at the rate of 120 feet per minute, we can write the equation for the first balloon as:
h1(t) = 500 + 120t
The second balloon starts at 1500 feet and descends at 200 feet per minute, so the equation for the second balloon is:
h2(t) = 1500 - 200t
These two equations make up our system of equations:
- h1(t) = 500 + 120t
- h2(t) = 1500 - 200t
Final answer:
A hot-air balloon rising at 120 feet per minute from 500 feet and another descending at 200 feet per minute from 1500 feet can be described by the system of equations: Height1(t) = 500 + 120t for the rising balloon and Height2(t) = 1500 - 200t for the descending balloon.
Explanation:
To write a system of equations representing the positions of each hot-air balloon over time, let's define t as the time in minutes since the observation started.
For the first hot-air balloon rising at 120 feet per minute from an initial height of 500 feet, the position equation is:
- Height1(t) = 500 + 120t
For the second hot-air balloon descending at 200 feet per minute from an initial height of 1500 feet, the position equation is:
- Height2(t) = 1500 - 200t
Writing these as a system of equations, we have:
- Height1(t) = 500 + 120t
- Height2(t) = 1500 - 200t
