Question

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

Answer 1

Answer:

Step-by-step explanation:

Given that:

$x^2 + z^2 \leq 36$

if we assume that x is zero, then $z^2 = 36$ , $z = \pm \sqrt{36}$ $z = \pm 6$ i.e the radius of the circle goes from -6 to +6, Similarly, if we assume that z is zero, then $x^2 = \pm 36$ , $x = \pm \sqrt{36}$ , $x = \pm 6$ . 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.