Your parents are renting an apartment for you when you go away to college. an annual contract is $502.00/month with a 2-month penalty if you break the lease. the month-to-month contract is $615.00/month. say you leave after 6 months. how much is the difference in the amount paid between the two contracts?

The difference in the amount paid between the two contracts is $326.

Step-by-step explanation:

Given : An annual contract is $502.00/month with a 2-month penalty if you break the lease. The month-to-month contract is $615.00/month. Say you leave after 6 months.

To find :  How much is the difference in the amount paid between the two contracts?

Solution :

Annual contract: The annual contract means a contract for 12 months. There is a month penalty for breaking the lease. 

In our case the penalty is 2 month means if you left after 6 months, you will have to pay for 8 month.

Total paid = Monthly payment × 8

Total paid = 502 × 8 = $4016

Month-to-month contract: The payment is for actual month stayed.

You will only paid for the 6 months you stayed,

Total paid = Monthly payment × 6

Total paid = 615 × 6= $3690

To get the difference in the amount paid between the two contracts is

Difference = Annual contract - Month-month contract

Difference = 4016 - 3690 = $326

Therefore,The difference in the amount paid between the two contracts is $326.

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