Respuesta :
(a) 0.05 ° C
(b) 12.17 ohms
Explanation
Assuming that the resistance changes uniformly with temperature we can set the equation of the line
so
Step 1
find the equation of the line:
the equation of a line has the form:
[tex]\begin{gathered} y=mx+b \\ where\text{ m is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]to do that, we need 2 points from the line, so let
x represents the temperature
y represents resistance
[tex]\begin{gathered} P1(0,10.40) \\ P2(100,14.35) \end{gathered}[/tex]now, to find the slope of a line we need to use the expression
[tex]\begin{gathered} slope=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}[/tex]then, replace the values in the formula
[tex]slope=\frac{14.35-10.4}{100-0}=\frac{3.95}{100}=0.0395[/tex]so, the slope is 0.0395
b) now, use the slope point formula to find the equation of the line
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ m is the slope and P1\lparen x}_1,y_1) \\ replace \\ y-10.4=0.0395(x-0) \\ y=0.0395x+10.4 \end{gathered}[/tex]so, the equation of the lines is
y=0.0395x+10.4
Step 2
Now, we can use the equation to find the asked values
(a) The temperature when the resistance is 11.19 ohms?
let
[tex]\begin{gathered} resistance\text{ = 11.19,so y=11.19} \\ replace\text{ in the equation and solve for x} \\ y=0.0395x+10.4 \\ 11.19=0.0395x+10.4 \\ 11.19-10.4=0.0395x \\ 0.79=0.0395x \\ x=\frac{0.0395}{0.79}=0.05 \end{gathered}[/tex]therefore
(a) 0.05 ° C
Step 3
(b) The resistance of the thermometer when the temperature is 45 C?
let
[tex]tempereature\text{ = x= 45 C}[/tex]now, replace in the expression to find the resistance
[tex]\begin{gathered} y=0.0395x+10.4 \\ y=0.0395(45)+10.4 \\ y=12.17 \end{gathered}[/tex]therefore,
(b) 12.17 ohms
I hope this helps you
