Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To solve this problem, we need to understand the standard form of the equation of a circle. The general form of a circle's equation centered at the origin is:
[tex]\[ x^2 + y^2 = r^2 \][/tex]
Here, [tex]\( r \)[/tex] represents the radius of the circle.
Given the equation:
[tex]\[ x^2 + y^2 = z \][/tex]
you can see that the equation is in the form [tex]\( x^2 + y^2 = r^2 \)[/tex]. By comparing both equations, we can directly infer that the constant term [tex]\( z \)[/tex] on the right side of the equation is equal to [tex]\( r^2 \)[/tex], the square of the radius.
To find the radius [tex]\( r \)[/tex], we need to take the square root of the constant term [tex]\( z \)[/tex]:
[tex]\[ r = \sqrt{z} \][/tex]
Thus, the radius is the square root of the constant term [tex]\( z \)[/tex].
Given a specific example where [tex]\( z = 25 \)[/tex]:
1. We recognize that the equation is [tex]\( x^2 + y^2 = 25 \)[/tex].
2. Here, [tex]\( z = 25 \)[/tex].
3. The radius [tex]\( r \)[/tex] is then [tex]\( \sqrt{25} \)[/tex].
4. Calculating [tex]\( \sqrt{25} \)[/tex] gives us [tex]\( 5 \)[/tex].
So, the radius of the circle is [tex]\( 5 \)[/tex].
Therefore, the correct answer to the problem is:
[tex]\[ \text{The radius is the square root of the constant term, } z. \][/tex]
[tex]\[ x^2 + y^2 = r^2 \][/tex]
Here, [tex]\( r \)[/tex] represents the radius of the circle.
Given the equation:
[tex]\[ x^2 + y^2 = z \][/tex]
you can see that the equation is in the form [tex]\( x^2 + y^2 = r^2 \)[/tex]. By comparing both equations, we can directly infer that the constant term [tex]\( z \)[/tex] on the right side of the equation is equal to [tex]\( r^2 \)[/tex], the square of the radius.
To find the radius [tex]\( r \)[/tex], we need to take the square root of the constant term [tex]\( z \)[/tex]:
[tex]\[ r = \sqrt{z} \][/tex]
Thus, the radius is the square root of the constant term [tex]\( z \)[/tex].
Given a specific example where [tex]\( z = 25 \)[/tex]:
1. We recognize that the equation is [tex]\( x^2 + y^2 = 25 \)[/tex].
2. Here, [tex]\( z = 25 \)[/tex].
3. The radius [tex]\( r \)[/tex] is then [tex]\( \sqrt{25} \)[/tex].
4. Calculating [tex]\( \sqrt{25} \)[/tex] gives us [tex]\( 5 \)[/tex].
So, the radius of the circle is [tex]\( 5 \)[/tex].
Therefore, the correct answer to the problem is:
[tex]\[ \text{The radius is the square root of the constant term, } z. \][/tex]
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.