Question

The designer of a miniature golf course is going to cut holes that can be modeled using the equation x2 + y2 = 6.25 where the radius is measured in inches. Complete the statements to describe how the parts of the circle it describes relate to the holes in the golf course. The holes have a radius of inches. If the holes in a standard golf course are 4.25 inches wide, the miniature golf holes are .

Answer 1

1: 2.500

2: larger

Answer 2

2.5 inches

Explanation:

The general form of the equation of a circle is

`(x-a)^2+(y-b)^2=r^2`

Where

`a=x\ \text{coordinate of center}`

`b=y\ \text{coordinate of center}`

`r=\text{Radius of the circle}`

If the circle's center is on the origin the equation becomes

`x^2+y^2=r^2`

Here the equation is of the form

`x^2+y^2=6.25\\\Rightarrow x^2+y^2=2.5^2`

So, the radius of the circle is 2.5 inches.

Hence the miniature golf holes are 2.5 inches wide.