A cellar contains only bottles of port, claret, sherry and brandy. Of these, 1/5 of the bottles are port and 1/5 are claret. The cellar also contains 15 dozen bottles of sherry and 30 bottles of brandy. How many bottles of port and claret does it contain?

70 bottles of each

Step-by-step explanation:

let X be bottles of port and claret

X = 2/5

1/2 X = 1/5

180 + 30 = 210 = 3/5

210/3 = 70 = 1/5

70 x 2 = X = 140

2/5 = 140

1/5 = 70

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

70

step-by-step explanation:

2*5=10

4*15=60

60+10=

70