Identify 2 objects you could find in a grocery store that hold less than 100 millimeters.

The function in Exercise represents the rate of flow of money in dollars per year. Assume a 10-year period at 8% compounded cont

anzhelika [568]

Answer:

a) The present value is 688.64 $

b) The accumulated amount is 1532.60 $

Step-by-step explanation:

a) The preset value equation is given by this formula:

$P=\int^{T}_{0}f(t)e^{-rt}dt$

where:

T is the period in years (T = 10 years)
r is the annual interest rate (r=0.08)

So we have:

$P=\int^{T}_{0}(0.01t+100)e^{-rt}dt$

Now we just need to solve this integral.

$P=\int^{T}_{0}0.01te^{-rt}dt+\int^{T}_{0}100e^{-rt}dt$

$P=e^{-0.08t}(-1.56-0.13t)|^{10}_{0}+1250e^{-0.08t}|^{10}_{0}$

$P=0.30+688.34=688.64 $$

The present value is 688.64 $

b) The accumulated amount of money flow formula is:

$A=e^{r\tau}\int^{T}_{0}f(t)e^{-rt}dt$

We have the same equation but whit a term that depends of τ, in our case it is 10.

So we have:

$A=e^{r\tau}\int^{T}_{0}(0.01t+100)e^{-rt}dt=e^{0.08\cdot 10}P$

$A=e^{0.08\cdot 10}688.64=1532.60 $$

The accumulated amount is 1532.60 $

Have a nice day!

6 0

3 years ago

What is the quotient of (x^3 - 3x^2 + 3x - 2) ÷ (x^2 - x + 1)?

Ugo [173]

Answer:

x-2

The choose (1)

Step-by-step explanation:

(x³-3x²+3x-2)÷(x²-x+1)

(x-2)(x²-x+1) ÷ (x²-x+1)

Delete (x²-x+1)

so = (x-2)

4 0

3 years ago

Does anyone know what has integers as it's square root?

Snezhnost [94]

It shouldn't be too tough to find one of those, seeing that there are
an infinite number of them.

To create one, take any integer, positive or negative, and multiply it by itself.

Here are a few to put you in the mood:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, ...

784, 841, 900, 1024, 1225, 1600, 2500, 3600, 4900, 10000, 1 million, ...

3 0

3 years ago

Alex and Freddy collect stamps. The number of stamps in Alex’s collection to the number of stamps in Freddy’s collection is in t

vazorg [7]

Remark

The trick here is to realize that you have to find the number both have in order to find the difference. That means you take (effectively) 3/8 and 5/8 to find out how much each of them has. The 8 stands for the 136

Step One

Find the number of stamps Alex has. Remember his ratio is the smaller so he will have 3/8

Alex = 3/8 * 136

Alex = 408/8 = 51

Step 2

Find the number that Freddy has.

The total is 136

Formula

Freddy = Total - Alex

Freddy = 136 - 51

Freddy = 85

Check

Let us see if 5/8 * 136 = 85

5*136/8 = 680 / 8 = 85 So your answers are correct.

Difference

Difference = 85 - 51 = 34 which is how many more stamps Freddy has than Alex.

5 0

3 years ago

Numbers like 10 100 1000 and so on are called

Ad libitum [116K]

Powers of ten, and they're easy to represent as exponents.

6 0

3 years ago

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