Answer:
32, 46
Step-by-step explanation:
Remember, a is congruent to b modulo d if d divides a-b.
Now, the problem says that b=4 and d=14.
Let a=32. Observe that a-b=28 and , then 32 is congruent to 4 modulo 14.
Let a=46. Observe that a-b=46-4=42 and , then 46 is congruent to 4 modulo 14.
Given:
The sequence is:
To find:
The 6th term of the given sequence.
Solution:
We have,
Here, the first term is:
The ratio between consecutive terms are:
The given sequence has a common ratio 5. So, the given sequence is a geometric sequence.
The nth term of a geometric sequence is:
Where, a is the first term and r is the common ratio.
Substitute to get the 6th term.
Therefore, the 6th term of the given sequence is 50000.
Trigonometric ratios are useful in calculating the side lengths of a triangle.
<u>(a) Length, z</u>
First we calculate (h) using the following sine ratio
Make h the subject
Next, we calculate (z) using the following sine ratio
Make z the subject
Substitute
Hence, the length of the zip line is 222.5 ft
<u>(b) The height, h</u>
In (a), we have
Evaluate
Hence, the height where the ladder rests against the tree is 38.6 ft
<u />
<u>(c) The distance, b</u>
To do this, we make use of the following sine ratio
Make b the subject
Hence, the distance between the base of the ladder and that of the tree is 10.4 ft
<u />
<u>(d) Distance, B</u>
To do this, we make use of the following sine ratio
Make B the subject
Substitute
Hence, the distance between the base of the tree and the spot where the zip line is anchored to the ground is 219.1 ft
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Read more about trigonometry ratios at: