Paul is comparing two high-speed internet service providers (isps) for his business. the graph represents the cost of each isp as a function of t, the duration in months of a service contract.
if c(t) = 180 + 10t represents isp a and c(t) = 25t represents isp b, how long would the service contracts need to be for the total costs to be the same?
6 months
8 months
10 months
12 months

The correct option is 4. The total costs will be the same at 12 months.

Step-by-step explanation:

The given equations represents the cost of each ISP as a function of t, the duration in months of a service contract.

ISP A:

ISP B:

Equate both the functions to find the time at which the total costs to be the same.

Subtract 10t from both the sides.

Divide both sides by 15.

The total costs will be the same at 12 months. Therefore the correct option is 4.

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