Sense-Making. Ray-Ray is building a deck in his back yard. The plans for the deck show that it is to be 30 feet by 30 feet. Ray-Ray realizes that he does not have that much space in the back yard, so he has to reduce the dimensions. He wants to reduce one dimension by a number of feet and increase the other dimension by the same number of feet. If the area of the reduced deck is 275 square feet, what are the dimensions of the deck?​

the balance is found at the link

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

55% are girls and 45% are boys : ) hope this

step-by-step explanation:

i think it will be zero as slope has a formula of difference between initial and final distance divided by itz time interval