Homework #13
Instructions: Work these problems on a separate sheet(s) of paper, and turn in on
Thursday at the final exam.
Problem 1. If ϕis Euler’s phi function, calculate
ϕ(9), ϕ(10), ϕ(11), ϕ(12)
from the definition.
Problem 2. If you look at the properties in your notes, there are easier ways to calculate
some of them. Calculate the following using the easy ways presented in the notes.
ϕ(13), ϕ(22), ϕ(341)
Problem 3. Calculate
ϕ(2), ϕ(4), ϕ(8), ϕ(16)
Do you notice a pattern?
Problem 4. Complete the triangle with side lengths a= 12, b= 10, c= 7.6.
Problem 5. Complete the triangle with side lengths a= 12, b= 13.5, ∠C= 70o.
Problem 6. Elizabeth and John are hungry. Elizabeth wants to eat Cafe Yumm and John
wants to eat at McDonald’s. From where Elizabeth and John are now, the straight paths
to Cafe Yumm and McDonald’s make a 135oangle. If Cafe Yumm is 3.6 miles away, and
McDonald’s is 4.3 miles away, how far is McDonald’s from Cafe Yumm.