Make a conjecture about the next item in each sequence -2, 1 , -1/2, 1/4, -1/8

Mathematics

2 answers:

Semenov [28]3 years ago

7 0

Answer: 1/16

Step-by-step explanation:

Each number in the series is half of the previous number. The negatives alternate with the positives. So they must be multipling by -1/2.

-1/8(-1/2) = 1/16

After that would be

1/16(-1/2) = -1/32

Hope this helps. (And maybe worth Brainliest)

Georgia [21]3 years ago

4 0

Answer:

-2,2 -1/3 1/4 -1/9

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Find the volume of the solid formed by rotating the region bounded by the given curves about the indicated axis. Y = 1x, y = 1,

Goryan [66]

The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.

Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is

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and the volume of a stack of n such disks is

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where $y_i$ is a point sampled from the interval [1, 5].

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