Calculate the average rate of change of the function from

θ = π/10 to θ = π/8.
(Round your answer to two decimal places.)
f(θ) = 9 sin(9θ)

the average rate of change is just

f(π/8)-f(π/10)
-------------------
(π/8 - π/10)

Now just plug and chug. It's just the slope of the line joining the two points on the curve.

1.41

To calculate the average rate of change of the function f(θ) = 9 sin(9θ) from θ = π/10 to θ = π/8, we need to find the difference in the function values at these two points and divide it by the difference in the values of θ.

First, let's find the value of the function at the point θ = π/10:
f(π/10) = 9 sin(9(π/10))
= 9 sin(9π/10)

Next, let's find the value of the function at the point θ = π/8:
f(π/8) = 9 sin(9(π/8))
= 9 sin(9π/8)

Now, we can calculate the average rate of change:
Average rate of change = (f(π/8) - f(π/10)) / (π/8 - π/10)
= (9 sin(9π/8) - 9 sin(9π/10)) / (π/8 - π/10)

Calculating this further may require a calculator or math software to evaluate the trigonometric functions.

Therefore, the average rate of change of the function from θ = π/10 to θ = π/8 is (9 sin(9π/8) - 9 sin(9π/10)) / (π/8 - π/10).

To calculate the average rate of change of the function f(θ) = 9 sin(9θ) from θ = π/10 to θ = π/8, we need to find the slope of the secant line passing through the two points on the function.

The average rate of change (ARC) formula is given by:

ARC = (f(θ2) - f(θ1)) / (θ2 - θ1)

where θ1 represents the initial value of θ, and θ2 represents the final value of θ.

In this case, θ1 = π/10, and θ2 = π/8.

Now let's calculate the average rate of change step by step:

Step 1: Calculate f(θ1):
Replace θ in the function f(θ) = 9 sin(9θ) with θ1 = π/10.

f(θ1) = 9 sin(9 * (π/10))
= 9 sin(9π/10)

Step 2: Calculate f(θ2):
Replace θ in the function f(θ) = 9 sin(9θ) with θ2 = π/8.

f(θ2) = 9 sin(9 * (π/8))
= 9 sin(9π/8)

Step 3: Calculate the difference between f(θ2) and f(θ1):
f(θ2) - f(θ1) = 9 sin(9π/8) - 9 sin(9π/10)

Step 4: Calculate the difference between θ2 and θ1:
θ2 - θ1 = π/8 - π/10

Step 5: Calculate the average rate of change (ARC):
ARC = (f(θ2) - f(θ1)) / (θ2 - θ1)
= (9 sin(9π/8) - 9 sin(9π/10)) / (π/8 - π/10)

To get the final answer, you need to evaluate this expression.