Question

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

Answer 1

Answer:

$g(t) = aLt - aLT + L$

$Slope = aL$

The vertical component is: $L - aLT$

Step-by-step explanation:

Given

$g - L = aL(t - T)$

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

$g - L = aL(t - T)$

Open Bracket

$g - L = aLt - aLT$

Add L to both sides

$g - L + L= aLt - aLT + L$

$g= aLt - aLT + L$

Represent as s function

$g(t) = aLt - aLT + L$

Since the function is a function is t:

The slope is the coefficient of t;

Hence:

$Slope = aL$

To get the vertical intercept, we set t to 0

$g(0) = aL * 0 - aLT + L$

$g(0) = - aLT + L$

Hence, the vertical component is: $L - aLT$