Circle A has a center at #(2 ,3 )# and an area of #8 pi#. Circle B has a center at #(13 ,7 )# and an area of #54 pi#. Do the circles overlap?

Answer 1

This straightforward application of distance formula and comparing of the radiuses.
#R=10.18 < D_((B-A))=11.7# so no overlap

This straightforward application of distance formula and comparing of the radiuses. First let calculate the radii: Let A(2,3) and B(13,7) #r_A = pir^2 = 8pi => r=2sqrt(2)# #r_B = pir^2 = 54pi => r=3sqrt(6)# so the sum of the radii, #R = r_B+r_A=2sqrt(2)+3sqrt(6)# #R = sqrt(2)(2+3sqrt(3))#

Now use the distance formula to find the distance from the center of the circles: #D_((B-A)) = sqrt((13-2)^2+(7-3)^2)=sqrt(137)#

Now #R=10.18 < D_((B-A))=11.7# so no overlap

Sign up to view the whole answer

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

Sign up with email

Answer 2

Aaliyah Anderson

Yes, the circles overlap.

Sign up to view the whole answer

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

Sign up with email

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.