length L at temp @ given by L = 0.000008@^2 - 0.0007@ + 5

[davey2015]

Hello Guys, I have the queston below which i am struggling with a and b.

The length of a metal rod L meters at temperature \(\displaystyle \, \theta\, \) °C is given by: \(\displaystyle L\, =\, 0.000\,008\, \theta^2\, -\, 0.000\, 7\,\theta\, +\, 5\)

(a) Using the concept of derivative, find the rate of change of length with respect to temperature.

(b) Hence determine the rate of change of length in metres / °C, when the temperature of 90°C.

i dont even know where to start. Any help if you guys dont mind?

 

[stapel]

The length of a metal rod L meters at temperature \(\displaystyle \, \theta\, \) °C is given by: \(\displaystyle L\, =\, 0.000\,008\, \theta^2\, -\, 0.000\, 7\,\theta\, +\, 5\)

(a) Using the concept of derivative, find the rate of change of length with respect to temperature.

(b) Hence determine the rate of change of length in metres / °C, when the temperature of 90°C.

i dont even know where to start. Any help if you guys dont mind?

A good place to start would probably be with the stated starting point: "the concept of derivative". You have learned that the derivative of a function is related to the rate of change of that function. How then might the derivative of L with respect to temperature relate to finding the rate of change in L with respect to temperature? :wink:

 

[davey2015]

i see the sum but i dont know which part is the tempature. is it the first bit?


i see its 3 figures, 0 - 0 + length...

is it room tempature - material temp + length??? im unsure

 

[stapel]

i see the sum but i dont know which part is the tempature.

The exercise states as follows:

The length of a metal rod L meters at temperature θ °C is given by: L=0.000008θ2−0.0007θ+5[/q

This tells you which variable represents the temperature, and which item's temperature this is.