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To measure voltage [tex]\((V)\)[/tex], the formula [tex]\(V = \sqrt{P \cdot R}\)[/tex] is used. In this formula, [tex]\(P\)[/tex] represents power measured in watts and [tex]\(R\)[/tex] represents resistance measured in ohms. What is the resistance (to the nearest ohm) if the volts are 130 and power is 1200 watts?

The solution is [tex]\(\square\)[/tex].



Answer :

GinnyAnswer
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].

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