4
algebra

Which inequality represents the region strictly between the circles x2+y2=4x^2 + y^2 = 4 and x2+y2=16x^2 + y^2 = 16?

A

4<x2+y2<164 < x^2 + y^2 < 16

B

2<x2+y2<42 < x^2 + y^2 < 4

C

4≤x2+y2≤164 \leq x^2 + y^2 \leq 16

D

x2+y2<4x^2 + y^2 < 4 or x2+y2>16x^2 + y^2 > 16

Correct Answer: A

Choice A is the correct answer. An annulus (ring) shape.

  1. Inner boundary: Radius 4=2\sqrt{4}=2. Outside this: x2+y2>4x^2 + y^2 > 4.
  2. Outer boundary: Radius 16=4\sqrt{16}=4. Inside this: x2+y2<16x^2 + y^2 < 16.
  3. Combine: 4<x2+y2<164 < x^2 + y^2 < 16

?�� Strategic Tip: The equation uses r2r^2, not rr.

Choice B is incorrect because it uses the radii (2 and 4) instead of squares. Choice C is incorrect because it includes the boundaries. Choice D is incorrect because it represents everything EXCEPT the ring.

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Linear Functions Set 77