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nlexa [21]
3 years ago
15

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), wh

ere 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
Mathematics
1 answer:
nasty-shy [4]3 years ago
3 0

Answer:

g(t) = aLt - aLT + L

Slope = aL

The vertical component is: L - aLT

<em></em>

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

<em>Hence, the vertical component is: </em>L - aLT<em></em>

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(1) The train travels 4 miles per gallon.

(2) The slope of the graph is m=\frac{1}{4}

Explanation:

(1) The miles that train travels per gallon is given by

Miles= \frac{800}{200}

Dividing, we have,

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