A limousine company charges a fixed cost for a limousine and an hourly rate for it's driver. It cost $500 to rent a limousine for 5 hours and $800 to rent a limousine for 10 hours. What is the fixed cost, in dollars, to rent the limousine.

the fixed cost to rent the limousine is $200

Step-by-step explanation:

Let x represent the fixed cost rent the limousine.

Let y represent the cost of of hiring the driver of the limousine per hour.

It cost $500 to rent a limousine for 5 hours. This means that

x + 5y = 500 - - - - - - - - - - -1

It costs 800 to rent a limousine for 10 hours. This means that

x + 10y = 800 - - - - - - - - - - -2

Subtracting equation 2 from equation 1, it becomes

- 5y = - 300

y = - 300 /- 5

y = 60

Substituting y = 60 into equation 1, it becomes

x + 5 × 60 = 500

x + 300 = 500

x = 500 - 300

x = 200

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

step-by-step explanation:

circumference divided by 3.141592654 then timesthe radius twice