Question

1. The area of a parabola inscribed in a rectangle 3 meters long with diagonal 5 meters is. 2.A circle having an area of 530.93 square meters is cut into segments by a chord which is 5 meters from the center of the circle. Compute the area of the smallest segment.

Answer 1

The student's question involves the computation of areas - a parabola within a rectangle, and a segment of a circle. Both of these topics involve an understanding of conic sections, parabolas, and circle geometry.

Step-by-step explanation:

The first part of your question refers to the parabola inscribed in a rectangle. This concept relates to the field of conic sections where a plane intersects with a cone to form curves like circles, ellipses, and of course, parabolas. In the case of your question, this might refer to the maximum area a parabola can occupy within a given rectangle. When resolving this, we can use properties and equations associated with parabolas and rectangles.

For the second segment of your question which is about the area of a circle segment, we must apply principles of circle geometry. The area of a circle is determined by πr², where r is the radius of the circle. To find the area of a segment of the circle, we would subtract the area of the sector from the area of the triangle formed by the chord and the radii connecting the chord to the circle's center.

Both of these problems involve understanding geometric shapes, their properties, and how to use and manipulate their respective formulas to find the desired outcome, that is finding the areas in question.

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