All categories

2 years ago

A large national park has an area of 91,417 acres. What is its area in hectares

Mathematics

1 answer:

aliya0001 [1]2 years ago

3 0

Answer:

36995.1474

Step-by-step explanation:

multiply the area value by 2.471

You might be interested in

You find an interest rate of 10% compounded quarterly. Calculate how much more money you would have in your pocket if you had us

Elena-2011 [213]

Answer:

see the explanation

Step-by-step explanation:

we know that

step 1

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$r=10\%=10/100=0.10\\n=4$

substitute in the formula above

$A=P(1+\frac{0.10}{4})^{4t}$

$A=P(1.025)^{4t}$

Applying property of exponents

$A=P[(1.025)^{4}]^{t}$

$A=P(1.1038)^{t}$

step 2

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$r=10\%=10/100=0.10$

substitute in the formula above

$A=P(e)^{0.10t}$

Applying property of exponents

$A=P[(e)^{0.10}]^{t}$

$A=P(1.1052)^{t}$

step 3

Compare the final amount

$P(1.1052)^{t} > P(1.1038)^{t}$

therefore

Find the difference

$P(1.1052)^{t} - P(1.1038)^{t}$ ----> Additional amount of money you would have in your pocket if you had used a continuously compounded account with the same interest rate and the same principal.

3 0

3 years ago

Prove the divisibility of the following numbers:

ratelena [41]

Make use of prime factorizations:

$16^5+2^{15}=(2^4)^5+2^{15}=2^{20}+2^{15}$

Both terms have a common factor of $2^{15}$ :

$16^5+2^{15}=2^{15}\left(2^5+1\right)=2^{15}\cdot33$

- - -

The second one is not true! We can write

$15^7+5^{13}=(3\cdot5)^7+5^{13}=3^7\cdot5^7+5^{13}$

Both terms have a common factor of $5^7$ :

$15^7+5^{13}=5^7\left(3^7+5^6\right)$

Since $30=5\cdot6$ , and $5\mid5^7$ , we'd still have to show that $5^6(3^7+5^6)$ is a multiple of 6. This is impossible, because $6=3\cdot2$ and there is no multiple of 2 that can be factored out.