Which of the following correctly shows the equation G=H−TS

Question

rearranged for the quantity of interest T
?(1 point)
Responses

T=GS+H
upper T equals Start Fraction upper G over upper S End Fraction plus upper H

T=G−HS
upper T equals Start Fraction upper G minus upper H over upper S End Fraction

T=−G+HS
upper T equals Start Fraction negative upper G plus upper H over upper S End Fraction

T=GS−H

Answer 1

To rearrange the equation \( G = H - TS \) for \( T \), we can start by isolating \( T \).

1. Rearranging the equation gives us \( TS = H - G \).
2. Next, we divide both sides by \( S \) to solve for \( T \):

\[ T = \frac{H - G}{S} \]

This means that none of the provided options perfectly fit this derived equation. However, if you look at option \( T = \frac{G - H}{S} \), it's the negative of the correct arrangement.

To summarize:

1. Start with the equation: \( G = H - TS \)
2. Rearrange:
   • Add \( TS \) to both sides: \( G + TS = H \)
   • Then rearrange to isolate \( T \): \( TS = H - G \)
   • Finally, divide by \( S \): \( T = \frac{H - G}{S} \)

To emphasize the correct rearrangement:

The correct equation for \( T \) is: \[ T = \frac{H - G}{S} \]

If you need to select the closest one, it would be none specifically listed unless you re-check, but if given the option again, keep in mind the math leading to \( T = \frac{H - G}{S} \).