# Circle A has a center at #(5 ,7 )# and an area of #56 pi#. Circle B has a center at #(9 ,2 )# and an area of #44 pi#. Do the circles overlap?

We have to compare sum of the radii of the circles to the distance between their centers.

Conclusion: they do not overlap.

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To determine if the circles overlap, we need to calculate the distance between their centers and compare it to the sum of their radii. The formula to calculate the distance between two points (x1, y1) and (x2, y2) is given by:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

For Circle A with center (5, 7) and Circle B with center (9, 2):

Distance = √((9 - 5)^2 + (2 - 7)^2) = √(4^2 + (-5)^2) = √(16 + 25) = √41

Now, we need to find the radii of both circles. Since the area of a circle is given by the formula A = πr^2, we can rearrange it to solve for the radius:

For Circle A: 56π = πr^2 r^2 = 56 r = √56

For Circle B: 44π = πr^2 r^2 = 44 r = √44

Now, we can compare the sum of the radii to the distance between the centers:

Sum of radii = √56 + √44

If the sum of the radii is greater than or equal to the distance between the centers, then the circles overlap. Otherwise, they do not overlap.

After calculating, if the sum of the radii is greater than or equal to the distance between the centers, then the circles overlap. Otherwise, they do not overlap.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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