Circle A has a center at #(2 ,5 )# and a radius of #2 #. Circle B has a center at #(4 ,-1 )# and a radius of #6 #. Do the circles overlap? If not, what is the smallest distance between them?
James AtkinsYes
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Wyatt AndersonThe circles do not overlap. The distance between their centers is ( \sqrt{(4-2)^2 + (-1-5)^2} = \sqrt{36 + 36} = \sqrt{72} = 6\sqrt{2} ) units. The sum of their radii is ( 2 + 6 = 8 ) units. Since the distance between their centers is greater than the sum of their radii, the circles do not overlap. The smallest distance between them is the difference between the distance between their centers and the sum of their radii, which is ( 6\sqrt{2} - 8 ) units.
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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.
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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