Which of the following is a geometric sequence? 3, 6, 12, 24, … 4, 8, 12, 16, … 2, 4, 16, 256, …
Svetlanka [38]
Answer:
The geometric sequence would be 3, 6, 12, 24 . . .
Step-by-step explanation:
A <u>geometric sequence</u> is when the you find the next term in the sequence by multiplying by a <em>common ratio</em>. (A common ratio is the constant value that you <em>multiply</em> by each time in a geometric sequence.) In order to solve your problem, you would find the relationship between each term in the sequence. For the first sequence, 3, 6, 12, 24, etc., you can see that the ratio between one term and the next would be two: 3×2 = 6, 6×2 = 12, 12×2 = 24, and so on. This makes it a geometric sequence, but you still need to check the other sequences to make sure. For the sequence 4, 8, 12, 16, . . . , you need to add four each time. This means that the sequence has a <em>common difference</em>, or the constant value you <em>add or subtract</em> by in an <u>arithmetic sequence</u>. So, we know that the second sequence is not the answer. Finally, we check the last sequence, and if you look at it you can see that the you square the previous term to get the current one. This is different from a geometric sequence, and has a different name. However, it is not a geometric sequence because you are not multiplying by the <em>same</em> value each time (it doesn't have a common ratio). So, the first sequence, 3, 6, 12, 24, . . . , is a geometric sequence.
So 9 x 8 = 72
72/2 = 36
36 x 10 = 360
so 360in
Hope this helps
I'm going to show you step by step. I posted 2 pictures of the work
Answer:
x = 31.12
Step-by-step explanation:
First find the base (hypotenuse) of the smaller triangle (the isosceles triangle): Its three sides are 11, 11 and b. b can be found using the Pythagorean Theorem: b^2 = 11^2 + 11^2 = 242. Then b = √242, or b = approximately 15.56.
b (which is approximately 15.56) is the shorter leg of the large (right) triangle. The trig function needed to solve for x is the cosine:
adjacent side
cos 60 degrees = ----------------------
hypotenuse,
15.56
which becomes (1/2) = ------------
x
Solving this for x, we get: x = 2(15.56) = 31.12
