Kip is using a recipe that call for One fourth cup of juice. He has a 6 -fluid -ounce of juice. There are 8 fluid ounces of juice in 1 cup . How many batches of the recipe can kip make

Step-by-step explanation:

Given:

Recipe:

1/2 cup of juice

Kip has:

6 fluid ounce of juice

I cup = 8 fluid ounces of juice

Therefore, kip has = 1 cup/8 fluid ounces × 6 fluid ounces

= 3/4 cup of juice

The recipe requires 1/4 cup of juice

Therefore, total cup kip has = recipe × number of batches

3/4 = 1/4 × y

y = 3/4 × 4/1

= 3 batches

= approximately 3 batches.

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

s

step-by-step explanation: