George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan. Recall the formulas for area and perimeter: A = lw and P = 2l + 2w.

A rectangle labeled Dog run has a length of 30 feet and width of (30 minus x) feet.

How many feet of fencing will George need for the dog run?
22 feet
68 feet
76 feet
82 feet

76 feet

Step-by-step explanation:

Area of Dog Run = 240

Length of Dog Run = 30

Width of Dog Run = 30 - x

Area of Dog Run:  30 * (30 - x) = 240

240 / 30 = 30 - x

8 = 30 - x

x = 24

Width of Dog Run = 8

How many feet of fencing will George need for the dog run?

Perimeter of Dog Run = 2Length + 2Width

Perimeter of Dog Run = (2 * 30) + (2 * 8)

Perimeter of Dog Run = 60 + 16

Perimeter of Dog Run = 76

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