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

Question 2: Here x2 + z2 ≤ 36, or equivalently x2 + z2 ≤ 6, describes the set of all points in double-struck R3 whose distance from the -axis is a _______.

Answer :

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.

[tex]x^{2}  + z^{2}  \leq 36[/tex] 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 [tex]x^{2}  + z^{2} \\[/tex] 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.

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