Find the value of the tangent for /_A.

Part a) The equation in point slope form is

Part b)

Step-by-step explanation:

Part a) Determine the equation of the line in point slope form

Let

x -----> the time in minutes

y -----> the height of the candle in inches

we know that

After 37 minutes, the candle was 11.2 inches tall

so

we have the point

(37,11.2)

Eighteen minutes later, it was 10.75 inches tall

so

we have the point

(37+18,10.75) -----> (55,10.75)

Find the slope of the linear  equation

The formula to calculate the slope between two points is equal to

substitute the values

 ----> is negative because is a decreasing function

The equation of the line in point slope form is equal to

we have

substitute

Part b) Determine the height of the candle after 4 hours

Remember that

so

For x=240 min

substitute in the linear equation

Round to the tenth place