Your heart rate rises when you exercise.
during aerobic exercise, your heart rate
should be at least 0.7(220 - a), but no
more than 0.85(220 - a), where a is your
age. find the target range if you are 14
years old.

ANSWER:  

While doing the aerobic exercise, heart rate must be in the range of 144.2 bpm to 175.1 bpm for a 14 years old person.

SOLUTION:

Given, your heart rate rises when you exercise.  

During aerobic exercise, your heart rate should be at least 0.7(220 - a), but no more than 0.85(220 - a), where “a” is your age.  

We need to find the target range if you are 14 years old.

Here a = 14

For 14 years old, lower range is

0.7(220 – 14)

0.7(206)

144.2

Now, for 14 years old, upper range is

0.85(220 – 14)

0.85(206)

175.1

Hence, while doing the aerobic exercise, heart rate must be in the range of 144.2 bpm to 175.1 bpm for a 14 years old person.

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