Have vehicles gotten more fuel-efficient over the years? between 1960 and 1999 the size and shape of automobiles in the united states has changed almost annually. the amount of fuel consumed by these vehicles has also changed. the following table describes the average fuel consumption per year per passenger car in gallons of gasoline.

year, t 1960 1970 1980 1990 1995 1997 1998 1999
gallons consumed per passenger car
668
760
576
520
530
538
544
552

determine the average rate of change, in gallons of fuel used per passenger car, from 1960 to 1970.

9.20 gallons of fuel used per passenger car.

Step-by-step explanation:

The given table shows average fuel consumption per year per passenger of fuel consumed by the vehicles in United States.

We have to determine the average rate of change in gallons of used per passenger car between 1960 to 1970.

On a graph average rate of change, of fuel used per passenger car

=

=

Therefore, answer is 9.20 gallons of fuel used per passenger car.

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

complete the steps to find the area of the trapezoid.

area of rectangle = 256   square units

area of triangle 1 = 24  square units

area of triangle 2 = 16  square units

area of triangle 3 =   96 square units

area of trapezoid = 120  square units

step-by-step explanation: