The height of an object moving up and down is described by 𝑦 = 72 + 40𝑐𝑜𝑠18𝑡 (in degree mode). This is an example of simple harmonic motion. To at least three decimal places, confirm that the average speed of the object is 2/π times its greatest speed.

Answer 1

18° = π/10 radians
So, the period is 2π/(π/10) = 20
During one period, it travels a distance of 4*40=160
So, the average speed is 160/20 = 8

Now, what is the greatest speed?
Not sure what tools you have to determine the maximum speed, but I'm sure you can figure out that it is 40*π/10 = 4π

8 = 2/π * 4π