Answer:
The resistance at a temperature of 250 K is 750 ohms
Step-by-step explanation:
We know that the resistance of a metal wire temperature sensor varies directly as the temperature, so we can construct a model using direct variation.
The definition of direct variation is:
Let x and y denote two quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero number k such that
[tex]y=kx[/tex]
The number k is called the constant of proportionality.
Applying the definition of direct variation to our situation, we get
Let R be the resistance in ohms, and t the temperature in K
[tex]R=kt[/tex]
Next, find the value of k, we know that when the temperature is 170 K the resistance is 510 ohms
[tex]510=k\cdot 170\\\\k=\frac{510}{170}=3\:\frac{ohms}{K}[/tex]
Substitute k into the equation
[tex]R=3\cdot t[/tex]
Find the resistance at a temperature of 250 K
[tex]R=3\cdot 250=750 \:ohms[/tex]
The resistance at a temperature of 250 K is 750 ohms.
