A hemispherical tank is filled with water and has a diameter of 17 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

The total weight = 1286 × 62.4 = 80246 pounds.  

Step-by-step explanation:

The formula of the volume of the sphere is

V = 4/3×π×r³

Given

d = 17 feet

as

d = 2r

so

r = d/2 = 17/2 = 8.5 feet

as

V = 4/3×π×r³

Since we need half of the volume as it is a hemispherical tank.

    = 1286 ft³

Given that the weighs 62.4 pounds per cubic foot

Thus,

The total weight = 1286 × 62.4 = 80246 pounds.                

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}