The relative value of currencies fluctuates every day. When this problem was written, one Netherland Antillean Guilder (Used on the Caribbean island of CuraÇao) was worth .558659 US dollar.
a. Find a function that gives the U.S. dollar value f(x), of x Netherland guilder.
b. Find f-1. What does f-1 represent?
c. How much guilders would $2,500 in U.S. Currency be worth?
4) A man is running around a circular track that is 200m in circumference. An observer uses a stopwatch to record the runner’s time at the end of each lap, obtaining the data in the tale below.
a. What was the man’s average speed (rate) between 68 s and 152 s?
b. What was the man average speed between 263 s and 412 s?
c. Calculate the
a. To find the function that gives the U.S. dollar value f(x) of x Netherland guilder, we can set up a proportion using the exchange rate provided:
1 Netherland Antillean Guilder = 0.558659 US dollar
So, for x Netherland guilders, we can set up the proportion:
x Netherland guilders = f(x) US dollars
0.558659 US dollars
----------------- = -----------------
1 Netherland guilder = x
Cross-multiplying, we get:
0.558659 * x = 1 * f(x)
Simplifying, we have:
f(x) = 0.558659x
Therefore, the function that gives the U.S. dollar value f(x) of x Netherland guilder is f(x) = 0.558659x.
b. To find f-1, we need to solve the equation for x in terms of f(x) in the function f(x) = 0.558659x:
f(x) = 0.558659x
First, let's interchange x and f(x):
x = 0.558659f(x)
Now, solve for f(x):
f(x) = x / 0.558659
Therefore, f-1(x) = x / 0.558659.
The function f-1 represents the inverse of the function f(x). It allows us to find the Netherland guilder value x for a given U.S. dollar value f(x).
c. To find out how much guilders $2,500 in U.S. currency would be worth, we can use the function f(x) = 0.558659x:
f(x) = 0.558659x
f($2,500) = 0.558659 * $2,500
f($2,500) = $1,396.6475
Therefore, $2,500 in U.S. currency would be worth approximately 1,396.6475 Netherland guilders.
4) To answer the questions related to the runner on a circular track:
a. The average speed (rate) between 68 s and 152 s can be found by dividing the total distance covered in that time by the total time taken:
Total distance = 200m (circumference of the circular track)
Total time = 152s - 68s = 84s
Average speed = Total distance / Total time
= 200m / 84s
Calculate the value to find the average speed.
b. Similarly, for the average speed between 263s and 412s, we can use the same formula:
Total distance = 200m (circumference of the circular track)
Total time = 412s - 263s = 149s
Average speed = Total distance / Total time
= 200m / 149s
Calculate the value to find the average speed.
c. The final question seems to be incomplete, as "calculate the" is incomplete. Please provide the complete question, and I will be happy to help further.