Your eccentric Aunt Isabella sends money to each niece and nephew on his or her birthday, She gives each child $10 on his or her first birthday. On each

birthday thereafter, you and your cousins get $20 more than on the birthday

before. How old will you be when you have received a total of $4,000 from

Aunt Isabella?

How old will you be when you have Received a total Of $4000 from aunt Isabell?

20 years old

Step-by-step explanation:

Given

Base Amount = $10

Additional Amount = $20

Required

Determine the number of years where the total will accumulate to $4000

This question represents Sum of an AP series.

Such that:

Substitute these values in the above formula:

Divide through by 10

Take square root of both sides

step-by-step explanation:

f

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