Answer :
To determine the radius of the circle described by the equation [tex]\(x^2 + y^2 = 16\)[/tex], we need to identify the standard form of a circle equation centered at the origin, which is:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
Here, [tex]\( r \)[/tex] represents the radius of the circle and [tex]\( r^2 \)[/tex] is the square of the radius.
Step-by-step:
1. Identify the given equation: The given equation is [tex]\( x^2 + y^2 = 16 \)[/tex].
2. Compare with the standard form: By comparing [tex]\( x^2 + y^2 = 16 \)[/tex] with the standard form [tex]\( x^2 + y^2 = r^2 \)[/tex], we can see that [tex]\( r^2 = 16 \)[/tex].
3. Solve for [tex]\( r \)[/tex]: To find [tex]\( r \)[/tex], take the square root of both sides of the equation [tex]\( r^2 = 16 \)[/tex]:
[tex]\[ r = \sqrt{16} \][/tex]
4. Calculate the square root: The square root of 16 is 4, as [tex]\( 4 \times 4 = 16 \)[/tex].
Therefore, the radius of the circle is [tex]\( 4.0 \)[/tex].
So, the length of the circle's radius is 4.0 units.
[tex]\[ x^2 + y^2 = r^2 \][/tex]
Here, [tex]\( r \)[/tex] represents the radius of the circle and [tex]\( r^2 \)[/tex] is the square of the radius.
Step-by-step:
1. Identify the given equation: The given equation is [tex]\( x^2 + y^2 = 16 \)[/tex].
2. Compare with the standard form: By comparing [tex]\( x^2 + y^2 = 16 \)[/tex] with the standard form [tex]\( x^2 + y^2 = r^2 \)[/tex], we can see that [tex]\( r^2 = 16 \)[/tex].
3. Solve for [tex]\( r \)[/tex]: To find [tex]\( r \)[/tex], take the square root of both sides of the equation [tex]\( r^2 = 16 \)[/tex]:
[tex]\[ r = \sqrt{16} \][/tex]
4. Calculate the square root: The square root of 16 is 4, as [tex]\( 4 \times 4 = 16 \)[/tex].
Therefore, the radius of the circle is [tex]\( 4.0 \)[/tex].
So, the length of the circle's radius is 4.0 units.
