2. The greatest volcanic eruption in recorded history took place in 1815 on the Indonesian island of Sumbawa, when the volcano Tambora expelled an estimated 100 cubic kilometers of molten rock. Suppose all of the expelled rock fell on a region with an area of 600 square kilometers. Find the average depth of the resulting layer of ash and rock.

Mount Tambora, also called Mount Tamboro, Indonesian Gunung Tambora, volcanic mountain on the northern coast of Sumbawa island, Indonesia, that in April 1815 exploded in the largest volcanic eruption in recorded history. It is now 2,851 metres (9,354 feet) high, having lost much of its top in the 1815 eruption. The volcano remains active; smaller eruptions took place in 1880 and 1967, and episodes of increased seismic activity occurred in 2011, 2012, and 2013.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

lo.lll

step-by-step explanation: