Consider lim t → 0+ ( −2 sin(4t) sin(4t) + 2 t cos(4t) ) . using a table of values, the limiting value is
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Using an arithmetic sequence, it is found that the total length of wood required to make 50 rungs is of 34.6875 m.
<h3>What is an arithmetic sequence?</h3>- In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
The sum of the first n terms is given by:
In this problem:
- A ladder has 50 rungs, hence the sequence has 50 terms, that is,
.
- The bottom rung is 1 m long, hence, considering it as the first term,
.
- Each rung is 12,5 mm shorter than the rung beneath it, hence, in meters, the common difference is of
.
Then the 50th term is:
The total length is the <u>sum of the first 50 terms</u>, hence:
The total length of wood required to make 50 rungs is of 34.6875 m.
You can learn more about arithmetic sequence at brainly.com/question/6561461