Write an inequality to describe the region. The solid cylinder that lies on or below the plane z = 9 and on or above the disk in
the xy-plane with center the origin and radius 3
1 answer:
Answer:
0 ≤ z ≤ 9, x^2 + y^2 ≤ 9
Step-by-step explanation:
z = 9
radius = 3
The region that lies on or below has a plane z= 9
This means that z ≤ 9
The region that lies on or above the disk in the xy plane is described by z ≥ 0
The combination inequality is 0 ≤ z ≤ 9
To restrict the disk centred at the origin with radius 3 is to restrict the x and y values. We have
x^2 + y^2 ≤ r^2
x^2 + y^2 ≤ 3^2
x^2 + y^2 ≤ 9
The full set of inequalities is
0 ≤ z ≤ 9, x^2 + y^2 ≤ 9
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