You are hiking in an area with steep trails. It takes you twice as long to hike uphill as it takes you to hike downhill. When you get to the bottom of the trail, you take a 30-minute break. On your way back up the trail, you take a 15-minute break. A. Write an expression for the total time of your hike in hours. Explain what the terms represent in the situation. B. Evaluate the expression to find the total time of a hike when the trip downhill take 1.25 hours. C. The next time you want to bike a trail, it will take only one and a half times as long to hike uphill as it takes to bike downhill. The breaks will stay the same. Explain how you would change expression. Then evaluate the expression to find the total time when the trip downhill takes 2 hours.

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

b. x + 1

step-by-step explanation:

i'am smart

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.