Circle A has a center at #(7 ,-5 )# and a radius of #1 #. Circle B has a center at #(4 ,2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

The circles don't overlap, and the smallest distance between them = 2.62

  • First: using the formula :
    #d=sqrt((x_1-x_2)^2+(y_1-y_2)^2)#

the distance between the two centers#=d=sqrt((7-4)^2+(-5-2)^2)=sqrt(9+49)#
#=sqrt(58)=7.62#

  • Second:
    The distance between the two centers > the sum of the two radii.
    Meaning the circles don't overlap.

  • Third: The smallest distance between them is the portion of the line connecting the two centers that doesn't fall in either circle. Or #s# in the image below.

    #s=bar(PO)-"sum of the two radii"#
    #s=sqrt(58)-5#
    #s=2.62#

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Answer 2

Yes, the circles overlap. The smallest distance between them is 3 units.

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Answer from HIX Tutor

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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