Suppose a single bacterium is placed in a bottle at 11:00am. It grows and at 11:01 divides into two bacteria. These two bacteria each grow and at 11:02 divide into four bacteria. Which grow and at 11:03 divide into eight bacteria, and so on. Now, suppose the bacteria continue to double every minute until the bottle is full at 12:00.

a. How many bacteria are in the bottle at 11:53?

b. What fraction of the bottle is full at that time?

Number of bacteria at 11:53 for 53 min =   = 9.007199 ×  

fraction that is full =

Step-by-step explanation:

solution

Number of bacteria is express as here

Number of bacteria =    ............1

so

bacteria at 1 min , 2 min and 3 min are

Number of bacteria at 1 min = = 2

Number of bacteria at 3 min = = 4

Number of bacteria at 3 min =  = 8

and

as that Number of bacteria at 11:53 is for 53 min is

Number of bacteria at 11:53 for 53 min =   = 9.007199 ×  

and

bottle is full at 12:00

so Number of bacteria at 12:00 for 60 min =  

so fraction that is full =

fraction that is full =

the second option

step-by-step explanation:

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²