I assume your question amounts to finding the period of f(t)=8sin(4 pi t). A period L is a positive number such that f(t+L)=f(t) for all t. Since sin(x) is 2 pi perodic we can find the least number L such that 4pi(t+L)=4*pi*t+2*pi. Multiplying out we get
4pi(t+L)=4*pi*t+4*pi*L and we want to find L such that we get 4*pi*t+2*pi, notice if we take L=1/2 we get the desiered result 4*pi*t+4*pi*1/2=4*pi*t+2*pi. This proves that L=1/2 and your function has a period of 1/2.
Answer:
480 miles
Equation:

Step-by-step explanation:
#First we calculate the average time it takes to walk one mile:

#We then calculate the number of miles he walks in 8 weeks.
-Given he walks one mile per day, 4 times a week;

#Multiply the distance traveled by the average time per mile to get total time spent:

Hence, the walking time over the 8 period will be 480 minutes
#This can be represent as:
Let w be the number of weeks and t be the time in minutes.
The time spent on walking per week is 
Therefore the time spent walking in w weeks is represented as:

Answer:
2 dimes and one nickel
Step-by-step explanation: