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Radical Expressions and Quadratic Equations

Question 1D:

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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?



Answer :

GinnyAnswer
To find the resistance [tex]\( R \)[/tex] when given the volts [tex]\( V \)[/tex] and power [tex]\( P \)[/tex], we use the formula for voltage:

[tex]\[ V = \sqrt{P \cdot R} \][/tex]

We need to rearrange this formula to solve for [tex]\( R \)[/tex]. By squaring both sides of the equation, we get:

[tex]\[ V^2 = P \cdot R \][/tex]

Next, we isolate [tex]\( R \)[/tex] by dividing both sides of the equation by [tex]\( P \)[/tex]:

[tex]\[ R = \frac{V^2}{P} \][/tex]

Now, we can substitute the given values into this equation. We are given:

- [tex]\( V = 130 \)[/tex] volts
- [tex]\( P = 1200 \)[/tex] watts

Substituting these values in, we calculate:

[tex]\[ R = \frac{130^2}{1200} \][/tex]

First, calculate [tex]\( 130^2 \)[/tex]:

[tex]\[ 130^2 = 16900 \][/tex]

Now, divide this by 1200:

[tex]\[ R = \frac{16900}{1200} \approx 14.0833 \][/tex]

Next, we round this value to the nearest whole number. Hence, the resistance [tex]\( R \)[/tex] to the nearest ohm is:

[tex]\[ R \approx 14 \][/tex]

Therefore, the resistance is 14 ohms.

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