Question

Question 1: Describe in words the region of double-struck R3 represented by the equation: x2 + z2 ≤ 36.

Answer 1

Step-by-step explanation:

1) i will asume x2 and z2 are squares here.

ok, here we only have restrictions to x and z, so y can take all the values in R.

$x^{2} + z^{2} \leq 36$ is a circle of radius 6, you can see this if for example we set z = 0, then x goes from -6 to 6, the same if we set x = 0 then z goes from -6 to 6.

and the equation $x^{2} + z^{2}$ describes a circle.

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

2) you tipped the same inequality but different numbers in the right side, here i think you are saying that the inequalities describes the set of all points whose distance from the y-axis is equal or less tan 6.