Set 5: Linear Inequalities (Advanced)

Explanation

Answer: A

Which inequality represents the region outside the circle of radius 3 centered at the origin? (Note: This is a non-linear preview)

$x^2 + y^2 > 9$

✓ Correct

$x^2 + y^2 < 9$

$x^2 + y^2 \geq 9$

$x + y > 3$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Distance from origin $> 3$ . 1. Distance Formula: $\sqrt{x^2 + y^2} > 3$ 2. Square both sides: $x^2 + y^2 > 9$ Strategic Tip: $<$ is inside, $>$ is outside. Choice B is incorrect because it represents the inside. Choice C is incorrect because it includes the boundary (not strictly outside). Choice D is incorrect because it represents a half-plane, not a circle.

Key Steps:

•

The correct answer is $x^2 + y^2 > 9$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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