A small airplane can hold 13 people per trip. How many trips would it take the airplane to transport 9,165 people?
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Answer:
The 13th term is 81<em>x</em> + 59.
Step-by-step explanation:
We are given the arithmetic sequence:
And we want to find the 13th term.
Recall that for an arithmetic sequence, each subsequent term only differ by a common difference <em>d</em>. In other words:
Find the common difference by subtracting the first term from the second:
Distribute:
Combine like terms. Hence:
The common difference is (7<em>x</em> + 5).
To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:
Where <em>a</em> is the initial term and <em>d</em> is the common difference.
The initial term is (-3<em>x</em> - 1) and the common difference is (7<em>x</em> + 5). Hence:
To find the 13th term, let <em>n</em> = 13. Hence:
Simplify:
The 13th term is 81<em>x</em> + 59.
Given parameters:
Length of earring hook = 1.5cm
Length of given wire = 45cm
Dimension of the triangle = 3.2cm, 3.2cm and 2.1cm
Unknown:
Number of earrings that can be made from the wire = ?
To solve this problem, we need to calculate the total length of the earring we want to make.
Total earring length = Perimeter of earring + length of earring hook
= 3.2 + 3.2 + 2.1 + 1.5
= 10cm
Now the length of the wire is 45cm,
Number of earrings = = 4.5 earrings
But this is not reasonable, therefore, we can only forge 4 complete earrings from the given length with 5cm of wire remaining.
The number of earrings that can be made is 4.