To find the resistance [tex]\( R \)[/tex], given that the voltage [tex]\( V \)[/tex] is 130 volts and the power [tex]\( P \)[/tex] is 1200 watts, you can follow these steps:
1. Understand the given formula:
[tex]\[
V = \sqrt{P + R}
\][/tex]
2. Identify the known quantities and the target variable:
- [tex]\( V = 130 \)[/tex] volts
- [tex]\( P = 1200 \)[/tex] watts
- We need to solve for [tex]\( R \)[/tex].
3. Rearrange the formula to solve for [tex]\( R \)[/tex]:
[tex]\[
130 = \sqrt{1200 + R}
\][/tex]
Square both sides to eliminate the square root:
[tex]\[
130^2 = 1200 + R
\][/tex]
4. Calculate [tex]\( 130^2 \)[/tex]:
[tex]\[
130^2 = 16900
\][/tex]
5. Isolate [tex]\( R \)[/tex]:
[tex]\[
16900 = 1200 + R
\][/tex]
Subtract 1200 from both sides:
[tex]\[
R = 16900 - 1200
\][/tex]
6. Perform the subtraction:
[tex]\[
R = 15700
\][/tex]
7. Round to the nearest ohm (if necessary):
- Since 15700 is already a whole number, rounding is not needed.
So, the resistance [tex]\( R \)[/tex] to the nearest ohm is:
[tex]\[
R = 15700 \, \text{ohms}
\][/tex]
The solution is [tex]\(\boxed{15700}\)[/tex].
