setup an equation or expression to model the situation:
a rectangle that would fit inside of the curve y=-x^2+8
To model the situation of a rectangle that fits inside the curve y = -x^2 + 8, we need to establish the dimensions and position of the rectangle.
Let's assume that the rectangle is aligned with the x and y axes, and its sides are parallel to the axes. We can represent the rectangle's position using its bottom left corner as a reference point. Let's denote the x-coordinate of the bottom left corner as "a" and the y-coordinate as "b."
Since the rectangle needs to fit inside the curve y = -x^2 + 8, we need to ensure that the rectangle's top right corner does not exceed the curve.
The top right corner of the rectangle will have coordinates of (a + w, b + h), where "w" represents the width of the rectangle, and "h" represents its height.
To make sure the top right corner does not exceed the curve, we can set up the following inequality:
b + h ≤ -(a + w)^2 + 8
This inequality ensures that the y-coordinate of the top right corner (b + h) is not higher than the corresponding y-value on the curve -(a + w)^2 + 8.
Therefore, the equation or expression to model the situation is:
b + h ≤ -(a + w)^2 + 8