Abicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes. (use set notation for the domain and range of the function that models this situation.)

Domain: ,

Range:

Step-by-step explanation:

We have been given that a bicyclist travels at a constant speed of 12 miles per hour for a total of 45 minutes. We are asked to write the domain and range of the function in set notation.

Since the bicycle travels at constant rate, so the distance traveled by bicycle at any time t (in minutes) would be .

We know that domain of a function is set of all values of independent variable. We can see that independent variable is time (t).

Since the bicycle travels for a total of 45 minutes that is 0.75 hours , so domain of our function is restricted to interval that is in set notation.

To find the upper limit of range of our given function, we will substitute in our function as:

Therefore, the range of our given function would be that is in set notation.

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