The rectangle below has an area of 81-x^281−x 2 81, minus, x, squared square meters and a width of 9-x9−x9, minus, x meters. What expression represents the length of the rectangle?

Length = 9 + x meters

Step-by-step explanation:

The rectangle below has an area of 81- x² square meters and a width of 9-x meters. What expression represents the length of the rectangle?

Area of a rectangle = Length × Width

Area = 81 - x²

Width = 9 - x

Hence

Length = Area /Width

= 81 - x²/9 - x

= 9 + x meters

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

b is 38 degrees.

a is 52 degrees.

this is because if b is 38 and a is 14 degrees more than b than 38+14=52 and 52+38=90 degrees. hope this .