A rectangular swimming pool is twice as long as it is wide. A small concrete sidewalk surrounds the pool and is a constant 2 feet wide. The total area of the pool and sidewalk is 160 square feet. Find the dimensions of the pool

The dimensions of the pool are:

Width: 8.944 feet

Length: 17.888 feet

Step-by-step explanation:

From Geometry, the area of a rectangle (), measured in square feet, is determined by the following equations:

(1)

Where:

- Width, measured in feet.

- Length, measured in feet.

If we know that , and , then we get the following second order polynomial:

(1)

And we solve the expression for :

Then, the dimensions of the pool are, respectively:

and

i believe

step-by-step explanation:

from my conclusion c

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