Arunner tries to keep a consistent stride length in a marathon. but, the length will change during the race. a runner has a strde length of 5 feet for the first half of the race and a stride length of 4.5 feet for the second half

1. 70,000 feet

2. 14,000 strides

3. About 15,555.55 strides

Step-by-step explanation:

Complete Question:

A runner tries to keep a consistent stride length in a marathon. But, the length will change during the race. A runner has a stride length of 5 feet for the first half of the race and a stride length of 4.5 feet for the second half.

1.)A marathon is 26 miles 385 yards long. That is about 1.4 × 105 feet. How many feet long is half a marathon?

2.)How many strides would it take to finish the first half of the marathon?

3.)How many strides would it take to finish the second half of the marathon?

1.

1.4 * 10^5 is in scientific notation. To get the number, we move the decimal place 5 units to the right. So the number is:

140,000 feet

So, half a marathon is half of that which is

140,000 / 2 = 70,000 feet

2.

Each stride is 5 feet and first half is around 70,000 feet.

Hence,

Number of strides = 70,000/5 = 14,000 strides

3.

Here, each stride would be 4.5 feet and second half is about 70,000 feet.

Hence,

Number of strides = 70,000/4.5 = About 15,555.55 strides

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

answer: plz give a pic and answer choices so i can answer!

step-by-step explanation: