Circular and simultaneous inequalities (HSC SSCE Mathematics Extension 1): Flashcards

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Circular and Simultaneous Inequalities
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What do circular inequalities describe in a coordinate grid?

They describe regions inside or outside a circle.

What is the inequality for points inside a circle?

(xh)2+(yk)2<r2(x - h)^2 + (y - k)^2 < r^2 describes the interior.

What does the inequality (xh)2+(yk)2>r2(x - h)^2 + (y - k)^2 > r^2 mean?

It describes points outside the circle.

What is the boundary condition for circular inequalities?

(xh)2+(yk)2=r2(x - h)^2 + (y - k)^2 = r^2 is the boundary.

How can graphing help with circular inequalities?

It shows shaded areas where inequalities apply.

What is an example of simultaneous inequalities?

Finding overlaps of y<1x2y < 1 - x^2 and y>x1y > x - 1.

How can inequalities be applied in real-world scenarios?

They model network coverage and spatial planning.

What is a method to find solution areas for inequalities?

Use test points to ensure shading is accurate.

What does the inequality x2+y2<9x^2 + y^2 < 9 represent?

It shows points less than 3 units from the center.

Why is technology useful in solving inequalities?

It helps quickly visualize and find solutions.

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