Answer:
QC - PB = 6
Step-by-step explanation:
Given PQ is parallel to BC then it divides the sides proportionally, that is
=
=
=
, then
=
( cross- multiply )
8PB = 5QC → *
Given PB + QC = 26 , then
PB = 26 - QC
Substitute into *
8(26 - QC) = 5QC ← distribute left side
208 - 8QC = 5QC ( subtract 5QC from both sides )
208 - 13QC = 0 ( subtract 208 from both sides )
- 13QC = - 208 ( divide both sides by - 13 )
QC = 16
Thus PB = 26 - QC = 26 - 16 = 10
QC - PB = 16 - 10 = 6
Answer:
11.1 years
Step-by-step explanation:
The formula for interest compounding continuously is:
Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:
We will simplify this first a bit by dividing 2000 by 1150 to get
To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with
ln(1.739130435)=.05t
Taking the natural log of that decimal on our calculator gives us
.5533852383=.05t
Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.