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Describe in words the region of double-struck R3 represented by the equation: x2 + z2 ≤ 36.

1 Answer

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Answer:

Explanation:

Given that:


x^2 + z^2 \leq 36

if we assume that x is zero, then
z^2 = 36 ,
z = \pm √(36)
z = \pm 6 i.e the radius of the circle goes from -6 to +6, Similarly, if we assume that z is zero, then
x^2 = \pm 36 ,
x = \pm √(36) ,
x = \pm 6 . This implies that
x^2 + z^2 describes the circle with radius 6


x^2 + z^2 \leq 36 is an equation at region which consist of those points whose distance from the centre is at least with radius -6 and at most 6.

Therefore, the region is the solid cylinder of radius 6, where the Y axis is also the axis of the cylinder.

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