High School

An iron bar is heated. Its length, L, in mm can be modelled by a linear function, L=mT+c where T is the temperature measured in degrees Celsius. At 150 C the length of the iron bar is 180 mm.
(a) Write down an equation that shows this information. At 210 C the length of the iron bar is 181.5 mm

Answer :

L = 0.025T + 176.25, is an equation that shows this information. At 210 C the length of the iron bar is 181.5 mm.

To find the linear function L = mT + c, we can use the given information: At 150°C, L = 180 mm, and at 210°C, L = 181.5 mm.

We can write these two conditions as linear equations:

  • 180 = 150m + c
  • 181.5 = 210m + c

We can solve this system of equations to find the values of m and c. Subtract the first equation from the second:

  • (181.5 - 180) = (210m - 150m) + (c - c)
    1.5 = 60m
    m = 1.5 / 60
    m = 0.025

Now substitute m = 0.025 into the first equation to find c:

  • 180 = 150(0.025) + c
    180 = 3.75 + c
    c = 180 - 3.75
    c = 176.25

So, the equation that models the length of the iron bar as a function of temperature is:

  • L = 0.025T + 176.25

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