Annabelle lives at Bermondsey in London. She has to speak at a conference in Birmingham at 10.30am.

Response:

.

Detailed explanation:

We have a set of equations provided. Our task is to find the solution for this system.

Starting from equation (2), we will derive:

Next, by inserting this value into equation (1), we will achieve:

After multiplying both sides by 3, we will arrive at:

Now substituting this back into equation (2), we will find:

Thus, the solution to our specified set of equations is .

a(t) = 210 - 5t

(1) What does t represent?

Since t is given in minutes, it stands for time.

Interpreting t as the balloon’s altitude is incorrect since a(t) represents altitude.

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Time elapsed since the balloon starts descending

This is the correct interpretation.

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Time for the balloon to reach ground level is incorrect because that would be a fixed moment, not a variable t.

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(2) What does a(t) represent?

The balloon’s altitude

This is the correct answer.

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Time since descent began is incorrect because that is represented by t.

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Time to reach the ground is inaccurate since a(t) is altitude, not time.

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(3) What does a(5.5) signify?

It does not represent the time to reach 5.5 feet altitude.

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The altitude of the balloon after 5.5 minutes

This is the correct interpretation since a(5.5) is altitude when t = 5.5 minutes.

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It is not the time needed to reach the ground.

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5.5 minutes alone is not correct because a(t) denotes altitude, not time.

a(5.5) refers to altitude at t = 5.5 minutes.

The circumcenter of the triangle is at the coordinates (2,1). To find this, we can outline the triangle based on the coordinates of points A (-1,5), B (-1,-3), and C (5,-3). Utilizing the distance formula helps us confirm that the triangle satisfies Pythagoras' theorem, hence it is a right triangle. In a right triangle, the circumcenter is located at the midpoint of the hypotenuse, which is determined to be (2,1).

To determine the slope, subtract the y coordinates from each other and the x coordinates as well. That gives us: 10000 - 4000 over 0 - 15, which simplifies to 6000 over -15. When divided, it results in -400. So, the slope amounts to -400. I hope this aids you!:D