The percent of a country's households with broadband Internet access can be modeled by the function f left parenthesis x right 0.11 x squared plus 6.51 x plus 3, where f left parenthesis x right parenthesis is the projected percent of households with broadband Internet access and x is the number of years since 2000. a. Will this function have a maximum or a minimum? How can you tell?

b. According to this model, in what year will the percent of homes with broadband Internet access be at its maximum or minimum?

c. What is the predicted maximum/minimum percent of homes with broadband Internet access?

a) The function has a maximum at  x = 29,59

b) 99,32 %

Step-by-step explanation:

f(x) = -0,11*x² + 6,51*x + 3

Then:

f´(x) = -0,22*x + 6,51

If   f´(x) = 0   then    - 0,22*x + 6,51 = 0

0,22*x = 6,51

x = 6,51/0,22    ⇒     x = 29,59

if we get the second derivative

f´´(x) = - 0,22       f´´(x) < 0   then we have a maximun at x = 29,59

a) the function has a maximum

b) 29,59 years after 2000   ( in 2030 )

c) f(x) = - 0,11*x² + 6,51*x + 3

f(29,59) = - (0,11)* (29,59)² + 6,51*29,59 + 3

f(29,59) = 99,32 %

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: 193

explanation:

200-7 = 193