Identify the domain and range of the following relation {(3,,-,,1)}

Domain of the following relation is {3}

and Range = { 7, 8, -2, 4, 1}

Step-by-step explanation:

Let R be the set of relation i.e,

R = {(3, 7), (3, 8) , (3, -2) , (3, 4) , (3,1)}

Let R be a relation from set X to set Y,  then  

*Domain of R: The set of all first components of the ordered pairs belonging to R is;

Dom(R) = {x∈A: (x, y) ∈ R for some y∈ Y}.  

*Range of R: The set of all second components of the ordered pairs belonging to R is;

Range of R = {y ∈ Y: (x, y) ∈R for some x∈X}.  

Then, From the given relation R

The Domain of  R is { 3}  and

the range of R is { 7, 8, -2, 4, 1}

people went from manufacturing one object at a time by hand to manufacturing many objects in factories

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12