PLEASE HELP ME RN NO LINKS !!!
1 answer:
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Given:
The different recursive formulae.
To find:
The explicit formulae for the given recursive formulae.
Solution:
The recursive formula of an arithmetic sequence is and the explicit formula is
, where a is the first term and d is the common difference.
The recursive formula of a geometric sequence is and the explicit formula is
, where a is the first term and r is the common ratio.
The first recursive formula is:
for
.
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:
Therefore, the correct option is A, i.e., .
The second recursive formula is:
for
.
It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:
Therefore, the correct option is F, i.e., .
The third recursive formula is:
for
.
It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:
Therefore, the correct option is D, i.e., .
Answer:
.894
Step-by-step explanation:
First thing to do is to solve for the height of the triangle, BD. That's easy. We have the length of the hypotenuse and the base, so Pythagorean's Theorem gives us that the height is 8.003255588 which rounds nicely to 8. Now you have to call on the fond memories you have of the geometric mean in right triangles to solve the rest. For the sin of x you need the hypotenuse of that smaller right triangle on the left, side AB. First let's use geometric mean to find AD. The formula for that, now that we know the height, is
Filling that in with numbers we have
and
64 = 16(AD). Solve for AD to get that AD has a length of 4. Now we know two of the three sides in that smaller triangle on the left and can solve for the hypotenuse.
and
so
c=√80 which simplifies to 4√5. That means that the sin ratio for x is
which divides out to .894