The temperature, t, generated by an electrical circuit is represented by `t=f(m)=0.3m^(2)`, where m is the number of moving parts. The resistance of the same circuits is represented by `r=g(t)=150+5t,` where t is the temperature. What is the resistance in a circuit that has four moving parts?

Options

A. `51`
B. `156`
C. `174`
D. `8,670`

Answer

To find the resistance in a circuit that has four moving parts, we can follow these steps:

### Step 1: Calculate the Temperature
The temperature \( t \) generated by the electrical circuit is given by the function:
\[ t = f(m) = 0.3m^2 \]
where \( m \) is the number of moving parts. For four moving parts, we substitute \( m = 4 \):
\[ t = f(4) = 0.3 \times (4^2) \]
Calculating \( 4^2 \):
\[ 4^2 = 16 \]
Now substituting this back into the equation:
\[ t = 0.3 \times 16 = 4.8 \]

### Step 2: Calculate the Resistance
The resistance \( r \) of the circuit is given by the function:
\[ r = g(t) = 150 + 5t \]
Now we substitute the value of \( t \) we found in Step 1:
\[ r = 150 + 5 \times 4.8 \]
Calculating \( 5 \times 4.8 \):
\[ 5 \times 4.8 = 24 \]
Now substituting this back into the equation for resistance:
\[ r = 150 + 24 = 174 \]

### Final Answer
The resistance in the circuit that has four moving parts is:
\[ \boxed{174} \]