Q:

The resistance in ohms of a metal wire temperature sensor varies directly as the temperature in degrees Kelvin​ (K). If the resistance is 510 ohms at a temperature of 170 ​K, find the resistance at a temperature of 250 K?

Accepted Solution

A:
Answer:The resistance at a temperature of 250 K is 750 ohmsStep-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 getLet 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.