# Two circles have the following equations: #(x +3 )^2+(y -5 )^2= 64 # and #(x -2 )^2+(y +4 )^2= 81 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

No. One circle does not contain the other.

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The circles do not contain each other. The greatest possible distance between a point on one circle and another point on the other can be found by adding the radii of the circles and subtracting the distance between their centers. The radii are √64 = 8 and √81 = 9. The distance between the centers of the circles can be calculated using the distance formula. The centers of the circles are (-3, 5) and (2, -4). Therefore, the distance between the centers is √((2 - (-3))^2 + (-4 - 5)^2) = √(5^2 + 9^2) = √(25 + 81) = √106. So, the greatest possible distance between a point on one circle and another point on the other is 8 + 9 - √106.

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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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