1. The amortization formula can tell you the present value if the string of payments is made at the end of the month.
A = P(i/n)/(1 -(1 +i/n)^(-nt))
where A is the payment (200), P is the present value, n is the number of compoundings per year (12), and t is the number of years (4).
200 = P(.034/12)/(1 -(1 +.034/12)^-48)
200 = P*0.0223115558
P = 200/0.0223115558 ≈ 8,963.96
This matches the selection ...
a) $8963.96
[Please note that an actual sale would probably require the first payment be made immediately, hence the present value would actually be $8,989.36.]
2. A financial calculator (HP-12c) computes the IRR at 3.889% (per quarter). Hence the annual rate of return is about
4*3.889% ≈ 15.55%
This matches selection ...
a.) 15.55%
The answer to the question
We need to find the percent increase from 38.8 to 82.4, so
x * 38.8 = 82.4
x = 82.4/38.8
x = 2.1237
Multiply by 100 to convert to percentage (move decimal 2 places to the right)
2.1237 = 212.37%
Now we can apply this percentage increase to the onion dip...
0.48 x 212.37% =
0.48 x 2.1237 = 1.019
Round to the nearest cent $1.02 is the amount of increase. Now add it to the original price to get today's price...
$1.02 + .48 = $1.50
the question in English
The route of a stage of a cycle tour is 213 km long and a cyclist covers 2/3 of the route in five hours.
a) How many kilometers are left to finish the stage?
b) If he continues with the same average speed, how much time does he have left to finish the stage?
Step 1
we know that
1) Total kilometers of a stage is 
2) The cyclist covers
of the route
so
the kilometers remaining to finish the stage is equal to

therefore
<u>the answer Part a) is </u>

Step 2
<u>Find the average speed of the cyclist</u>
we know that
the speed is equal to

we have

substitute

Step 3
<u>Find the time remaining to finish the stage</u>
we know that

Solve for the time

we have

substitute

therefore
<u>the answer Part b) is</u>

Answer: The coordinate of the center is (4,-3)
radius = 8
Step-by-step explanation:
Given ;

re - arranging , we have

comparing with the general equation

This means that



also




The coordinate of the center is (-g,-f)
Therefore;
the coordinate of the center = (4,-3)
the formula for calculating r is given by:




METHOD 2

using completing the square method , we have

completing the square , we have


comparing with the general equation

where a and b are the coordinate of the center , that is
the coordinate of the center is ( 4 , -3)

