The formula gives the temperature change $r$ , in degrees Celsius per minute, of tortellini while it is being cooked, given the initial temperatures of the tortellini, $T_{t}$ , and the water, $T_{w}$ , in degrees Celsius, and a heat conductivity of the tortellini of $k$ joules per square centimeter per second. Which equation correctly gives the heat conductivity of the tortellini in terms of the temperature change per minute and the initial temperatures of the water and tortellini? $\newline$ Choose $1$ answer: $\newline$ (A) $k=\frac{200(r+T_{w})}{-181T_{t}}$ $\newline$ (B) $k=\frac{200r}{-181(T_{t}-T_{w})}$ $\newline$ (C) $k=\frac{200r+T_{W}}{-181T_{t}}$

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Q. The formula gives the temperature change

r

, in degrees Celsius per minute, of tortellini while it is being cooked, given the initial temperatures of the tortellini,

T_{t}

, and the water,

T_{w}

, in degrees Celsius, and a heat conductivity of the tortellini of

k

joules per square centimeter per second. Which equation correctly gives the heat conductivity of the tortellini in terms of the temperature change per minute and the initial temperatures of the water and tortellini?

\newline

Choose

1

answer:

\newline

(A)

k=\frac{200(r+T_{w})}{-181T_{t}}

\newline

(B)

k=\frac{200r}{-181(T_{t}-T_{w})}

\newline

(C)

k=\frac{200r+T_{W}}{-181T_{t}}

Given Formula Manipulation: The given formula is $r=\frac{-181 k(T_{t}-T_{w})}{200}$ . We need to solve for $k$ .
Multiply by $200$ : First, multiply both sides of the equation by $200$ to get rid of the denominator: $\newline$ $200r = -181k(T_{t} - T_{w})$
Divide by $-181(T_{t} - T_{w})$ : Next, divide both sides of the equation by $-181(T_{t} - T_{w})$ to solve for $k$ : $k = \frac{200r}{-181(T_{t} - T_{w})}$
Check Answer Choices: Check the answer choices to see which one matches the derived equation for $k$ . The correct equation is: $\newline$ $k = \frac{200r}{-181(T_{(t)} - T_{(w)})}$
Match with Option (B): Comparing the derived equation with the answer choices, we find that option (B) matches: $\newline$ (B) $k = \frac{200r}{-181(T_{t} - T_{w})}$