Find the divergence of each of the following vector fields at all points where they are defined. (a) div(x(x2 y2 z2)1.5i y(x2 y2 z2)1.5j z(x2 y2 z2)1.5k)

the divergence of the vector fields at all points its defined is 0

Step-by-step explanation:

Given that;

div ( [x / (x²+ y² + z²)^1.5]i  +  [y / (x² + y² + z²)^1.5]j  +  [z / (x² + y² + z²)^1.5]k )

= d/dx [x / (x²+ y² + z²)^1.5]  +  d/dx [y / (x² + y² + z²)^1.5] +  d/dx [z / (x² + y² + z²)^1.5]

= [1 / (x²+ y² + z²)^1.5] - [3x² / (x²+ y² + z²)^2.5] + [1 / (x²+ y² + z²)^1.5] - [3y² / (x²+ y² + z²)^2.5] + [1 / (x²+ y² + z²)^1.5] - [3z² / (x²+ y² + z²)^2.5]

= [3 / (x²+ y² + z²)^1.5]  -  [(3x² + 3y² +3z²) / (x²+ y² + z²)^2.5]

= [2 / (x²+ y² + z²)^1.5]   -   [3 / (x²+ y² + z²)^1.5]  = 0

therefore the divergence of the vector fields at all points its defined is 0

solution:

as, mean is defined as sum of all the observations divided by total number of observations.

and , median is mid value of the data whether arranged in ascending order or descending order.

consider, roadsters:

2,3,4,5,6,7,8,9

mean =

also, median= , because number of observations is even, so median is mean of two mid values.

now, coming to bandits

2,3,4,5,6

mean =  

median = 4, as number of observations is odd.

so, roadsters has greater median as well mean than bandits.

→option a is true about the repairs performed on 2 types of cars:

bandits have lower median and mean than roadsters.

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|