A triangle with angle measures 30°, 60°, 90° has a perimeter of 18+6√3. What is the length of the longest side of the triangle?

# Students in a Science lab are working in groups to build both a small and a large electrical circuit…

Students in a Science lab are working in groups to build both a small and a large electrical circuit. A large circuit uses 4 resistors and 2 capacitors, and a small circuit uses 3 resistors and 1 capacitor. There are 100 resistors and 70 capacitors available, and each group must have enough resistors and capacitors to make one large and one small circuit. What is the maximum number of groups that could work on this lab project?

# 4, 7, 3, 4,….In the sequence above, the first term is 4, the second term is 7, and each term after the second term is the nonnegative difference…

4, 7, 3, 4,….

In the sequence above, the first term is 4, the second term is 7, and each term after the second term is the nonnegative difference between the previous two terms. If the nth term is the first term of the sequence that is equal to zero, what is the value of n?

Okay I know this number can be solved through first principles(finding each number in the sequence manually) but I can’t help but wonder if there’s a certain algebraic formula or method one can utilize to solve it.