Question
The length of a radius of a circle, measured in feet, is represented by the expression z + 3.6. The diameter of the circle is 1145 ft.
What is the value of z?
Enter your answer as a decimal or mixed number in simplest form in the box.
z =
What is the value of z?
Enter your answer as a decimal or mixed number in simplest form in the box.
z =
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To find the value of \( z \), we start by using the relationship between the radius and the diameter of a circle. The diameter \( d \) is twice the radius \( r \):
\[
d = 2r
\]
Given that the diameter of the circle is 1145 feet, we can express this in terms of the radius:
\[
1145 = 2r
\]
To find the radius \( r \), we divide both sides by 2:
\[
r = \frac{1145}{2} = 572.5 \text{ feet}
\]
Next, we have the radius represented by the expression \( z + 3.6 \). Therefore, we can set up the equation:
\[
z + 3.6 = 572.5
\]
To solve for \( z \), we subtract 3.6 from both sides:
\[
z = 572.5 - 3.6
\]
Calculating this gives:
\[
z = 572.5 - 3.6 = 568.9
\]
Thus, the value of \( z \) is:
\[
\boxed{568.9}
\]
\[
d = 2r
\]
Given that the diameter of the circle is 1145 feet, we can express this in terms of the radius:
\[
1145 = 2r
\]
To find the radius \( r \), we divide both sides by 2:
\[
r = \frac{1145}{2} = 572.5 \text{ feet}
\]
Next, we have the radius represented by the expression \( z + 3.6 \). Therefore, we can set up the equation:
\[
z + 3.6 = 572.5
\]
To solve for \( z \), we subtract 3.6 from both sides:
\[
z = 572.5 - 3.6
\]
Calculating this gives:
\[
z = 572.5 - 3.6 = 568.9
\]
Thus, the value of \( z \) is:
\[
\boxed{568.9}
\]
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