A race car driver won a 300 mile race with a speed of 183.2 mph find the drivers time

The time taken by the driver is: t = 1.6 seconds

Step-by-step explanation:

Given

Distance covered by a race car = d = 300 mile

Speed of a car = s = 183.2 mph

To determine

The time of the driver = t = ?

Using the formula to determine the time of the driver

distance = speed x time

d = st

t = d/s

substitute d = 300 and s = 183.2

t = 300 / 183.2

t = 1.6 seconds

Therefore, the time taken by the driver is: t = 1.6 seconds

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