This is the countiue question to the last one I posted. so please help
2 answers:
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Considering the vertex of the parabola, the correct statement is given by:
The range of the function is all real numbers less than or equal to 9.
<h3>What is the vertex of a quadratic equation?</h3>A quadratic equation is modeled by:
The vertex is given by:
In which:
Considering the coefficient a, we have that:
- If a < 0, the vertex is a maximum point, which means that the range is all real numbers less than or equal to
.
- If a > 0, the vertex is a minimum point, which means that the range is all real numbers greater than or equal to
In this problem, we have that:
- a = -1 < 0, hence the vertex is a maximum point.
- The vertex is (-2,9).
Hence the range is described by:
The range of the function is all real numbers less than or equal to 9.
More can be learned about the vertex of a parabola at brainly.com/question/24737967
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In cylindrical coordinates, we have , so that
correspond to the upper and lower halves of a sphere with radius . In spherical coordinates, this sphere is
.
means our region is between two cylinders with radius 1 and
. In spherical coordinates, the inner cylinder has equation
This cylinder meets the sphere when
which occurs at
where . Then
.
The volume element transforms to
Putting everything together, we have