For small changes in temperature, the formula for the expansion of a metal rod under a change in temperature is: g-L=aL(t-T), where g is the length of the object at temperature t,and L is the length at temperature T,and a is a constant which depends on the type of metal a) express g as the linear function of t.Find the slope and vertical intercept in terms of L,T,a

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MrRoyal MrRoyal · Answer 1 · 2020-10-07T00:47:18+02:00

Answer:

[tex]g(t) = aLt - aLT + L[/tex]

[tex]Slope = aL[/tex]

The vertical component is: [tex]L - aLT[/tex]

Step-by-step explanation:

Given

[tex]g - L = aL(t - T)[/tex]

Solving (a): Write g as a function of t

[tex]g - L = aL(t - T)[/tex]

Open Bracket

[tex]g - L = aLt - aLT[/tex]

Add L to both sides

[tex]g - L + L= aLt - aLT + L[/tex]

[tex]g= aLt - aLT + L[/tex]

Represent as s function

[tex]g(t) = aLt - aLT + L[/tex]

Since the function is a function is t:

The slope is the coefficient of t;

Hence:

[tex]Slope = aL[/tex]

To get the vertical intercept, we set t to 0

[tex]g(0) = aL * 0 - aLT + L[/tex]

[tex]g(0) = - aLT + L[/tex]

Hence, the vertical component is: [tex]L - aLT[/tex]