From 1990 through 1999, the female population F and the male population M of the United States (in thousands) is modeled by the following equations, where n is the number of years since 1990. Source: U. S.
Census Bureau

F =1247n +126,971 M= 1252n +120,741

a) Find an equation that models the total population T in thousands of the United States for this time period.
b) If this trend continues, what will the population of the United States be in 2010?
3. The measures of two sides of a triangle are given. If P is the perimeter, find the measure of the third side.

answer;

the correct answer

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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

180-142=38 for the acute angle next to the entry

90+38=128

180-128=52

a=52

step-by-step explanation: