# Two circles have the following equations #(x -1 )^2+(y -4 )^2= 36 # and #(x +5 )^2+(y -7 )^2= 49 #. 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, the circle:

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The circles represented by the equations ((x - 1)^2 + (y - 4)^2 = 36) and ((x + 5)^2 + (y - 7)^2 = 49) do not contain each other. To find the greatest possible distance between a point on one circle and another point on the other circle, you would compute the sum of their radii and subtract the distance between their centers.

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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.

- Two circles have the following equations #(x +3 )^2+(y -6 )^2= 64 # and #(x +7 )^2+(y +2 )^2= 9 #. 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?
- A circle has a center that falls on the line #y = 7/4x +4 # and passes through # ( 3 ,7 )# and #(7 ,1 )#. What is the equation of the circle?
- A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/12 #, and the triangle's area is #12 #. What is the area of the triangle's incircle?
- The circumference of a circle measures #22pi# units. How do you find the area of the circle?
- A circle has a chord that goes from #( 3 pi)/4 # to #(5 pi) / 4 # radians on the circle. If the area of the circle is #16 pi #, what is the length of the chord?

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