a pet boarder keeps a dog to cat ratio of 5:2 is it a border has a room 98 animals and how many of them can be dogs

I'm not sure how the correct way to do this would be but if you have a ratio that is 5:2 think of it as having 5 groups of animals and 2 groups of animals.

Find the number by dividing the total amount of animals 98/7 = 14.

We know that there are 5 groups of cats, the ratio for 5 cats. 14 x 5 = 70.

The remainder is dogs, which has a ratio of 2:5. 14 x 2 = 28.

70 + 28 = 98.

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