Explain two ways on how 5/6 is greater then 2/3

here's 3 approaches...

I: If you convert them into the same denominator (via 2/3 = 4/6) you can show that 5/6 > 4/6 since 5>4.

II: Multiply both by 6, and you get 5 > 4.

III: Convert both to decimal notation, 0.83333... > 0.66666...

1. 5/6 as a decimal is 0.83 repeating and 2/3 as a decimal is 0.6 repeating so 5/6 is greater.

2. With 6 as a common denominator, 2/3 = 4/6 so 5/6 is greater than 2/3.

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

21

step-by-step explanation: