Question

1.8 feet per second. balloon b is 3 feet off the ground and starts to rise at a rate of 2.4 feet per second. allison wrote 2 equations to represent the height of the balloons, h, after t seconds as shown below. balloon a ( h = 6 + 1.8t ) balloon b ( h = 3 + 2.4t ) when allison graphed the equations on the desmos graphing calculator, as shown below, the lines intersected at the point ( (5, 15) ). what does this point mean in relationship to the scenario above? after 5 balloons are launched, the balloons are 15 feet high. after 5 seconds, 15 balloons are in the air. after 5 seconds, the balloons are 15 feet in the air. after 15 seconds, the balloons are 5 feet apart.

Explanation:

Step1: Analyze the variables in the equations

In the equations \(h = 6+1.8t\) (Balloon A) and \(h = 3 + 2.4t\) (Balloon B), \(t\) represents time in seconds and \(h\) represents height in feet.

Step2: Interpret the intersection point \((5,15)\)

The \(x -\)coordinate of the intersection point of two lines \(y = f(x)\) and \(y = g(x)\) (in our case \(h=f(t)\) and \(h = g(t)\)) gives the value of \(x\) (here \(t\)) for which \(f(x)=g(x)\) (here \(f(t)=g(t)\)). The \(y -\)coordinate gives the common value of \(y\) (here \(h\)).

When \(t = 5\) (seconds), for Balloon A: \(h=6 + 1.8\times5=6+9 = 15\) feet. For Balloon B: \(h=3+2.4\times5=3 + 12=15\) feet.

Answer:

After 5 seconds, the balloons are 15 feet in the air.