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diamong [38]
3 years ago
7

A hot air balloon in flight begins to ascend at a steady rate of 120 feet per minute. After 1.5 minutes, the balloon is at an al

titude of 2150 feet. After 3 minutes, it is at an altitude of 2330 feet. Use an equation in point-slope form to determine whether the balloon will teach an altitude of 2500 feet in 4 minutes.
Mathematics
1 answer:
azamat3 years ago
4 0

Answer:

The balloon will not reach 2,500 feet after 4 minutes.

Step-by-step explanation:

The equation of the line in the point-slope form is

y-y_1=m(x-x_1)

A hot air balloon in flight begins to ascend at a steady rate of 120 feet per minute, then the slope is

m=120

After x_1=1.5 minutes, the balloon is at an altitude of y_1=2,150 feet. This means, the line passes through the point (1.5, 2,150).

Substitute the slope and point coordinates into the equation:

y-2,150=120(x-1.5)

We know that after 3 minutes, the balloon is at an altitude of 2,330 feet. Check this:

2,330-2,150=180\\ \\120(3-1.5)=120\cdot 1.5=180\\ \\2,330-2,150=120(3-1.5)

Now, find the height after 4 minutes:

y-2,150=120(4-1.5)\\ \\y=120\cdot 2.5+2,150=300+2,150=2,450

Thus, the balloon will reach only 2,450 feet after 4 minutes.

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