Question

1. Find the dimensions of the rectangle with the largest area that

can be formed with its base on the x-axis and its upper vertices
on the graph of the parabola y=9-x^2

Answer 1

The dimensions of the rectangle with the largest area are 0 units for the length and 9 units for the width.

Step-by-step explanation:

To find the dimensions of the rectangle with the largest area, we need to consider the vertices of the rectangle on the graph of the parabola y=9-x^2.

The base of the rectangle will be on the x-axis, so the y-coordinate of the upper vertices of the rectangle will be y=9.

Let's find the x-coordinate of the upper vertices by setting y=9 in the equation:

9=9-x^2

x^2=0

x=0

So, the x-coordinate of the upper vertices is 0.

Now, we can calculate the dimensions of the rectangle.

The length of the rectangle will be 2 times the x-coordinate of the upper vertices, which is 2*0=0.

The width of the rectangle will be the y-coordinate of the upper vertices, which is 9.

Therefore, the dimensions of the rectangle with the largest area are 0 units for the length and 9 units for the width.