A shopkeeper bought 50 kg of sugar and sold 1/4th of the sugar. find the mass of sugar that was left

37.5kg

Step-by-step explanation:

When you hear "of", it indicates multiplication. When you multiply by 1/4, you can also divide by 4 to get the same answer. 50/4 = 12.5kg sold

But that isnt our net sugar because thats how much he sold. Subtract that from what he has currently, and youll get the sugar he has after selling the 1/4th.

50 - 12.5 = 37.5kg

n

step-by-step explanation:

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