Answer:
4
Step-by-step explanation:
taxes are collected for the government
Answer:
After 2009 the quality of the forests in this country improving.
Step-by-step explanation:
Consider the provided function.
![f(t) = \frac{1}{3}t^3-\frac{5}{2}t^2 + 80](https://tex.z-dn.net/?f=f%28t%29%20%3D%20%5Cfrac%7B1%7D%7B3%7Dt%5E3-%5Cfrac%7B5%7D%7B2%7Dt%5E2%20%2B%2080)
![f'(t) = t^2-5t](https://tex.z-dn.net/?f=f%27%28t%29%20%3D%20t%5E2-5t)
Substitute f'(t)=0.
![t^2-5t=0](https://tex.z-dn.net/?f=t%5E2-5t%3D0)
![t(t-5)=0](https://tex.z-dn.net/?f=t%28t-5%29%3D0)
![t=0\ or\ t=5](https://tex.z-dn.net/?f=t%3D0%5C%20or%5C%20t%3D5)
It is given that (0 ≤ t ≤ 10)
The test interval are (0,5) and (5,10)
For (0 < t < 5) the value of
For (5 < t < 10) the value of
Hence, the function is increasing from (5,10).
t = 0 corresponds to 2004.
Therefore, after 2009 the quality of the forests in this country improving.
recall that a/b to decimal is just a ÷ b, so 2/9 is just 2 ÷ 9.
check the picture below.
Answer:
The value of first coin will be $151.51 more than second coin in 15 years.
Step-by-step explanation:
You have just purchased two coins at a price of $670 each.
You believe that first coin's value will increase at a rate of 7.1% and second coin's value 6.5% per year.
We have to calculate the first coin's value after 15 years by using the formula
![A=P(1+\frac{r}{100})^{n}](https://tex.z-dn.net/?f=A%3DP%281%2B%5Cfrac%7Br%7D%7B100%7D%29%5E%7Bn%7D)
Where A = Future value
P = Present value
r = rate of interest
n = time in years
Now we put the values
![A=670(1+\frac{7.1}{100})^{15}](https://tex.z-dn.net/?f=A%3D670%281%2B%5Cfrac%7B7.1%7D%7B100%7D%29%5E%7B15%7D)
![A=670(1+0.071)^{15}](https://tex.z-dn.net/?f=A%3D670%281%2B0.071%29%5E%7B15%7D)
![A=670(1.071)^{15}](https://tex.z-dn.net/?f=A%3D670%281.071%29%5E%7B15%7D)
A = (670)(2.797964)
A = 1874.635622 ≈ $1874.64
Now we will calculate the value of second coin.
![A=670(1+\frac{6.5}{100})^{15}](https://tex.z-dn.net/?f=A%3D670%281%2B%5Cfrac%7B6.5%7D%7B100%7D%29%5E%7B15%7D)
![A=670(1+0.6.5)^{15}](https://tex.z-dn.net/?f=A%3D670%281%2B0.6.5%29%5E%7B15%7D)
![A=670(1.065)^{15}](https://tex.z-dn.net/?f=A%3D670%281.065%29%5E%7B15%7D)
A = 670 × 2.571841
A = $1723.13
The difference of the value after 15 years = 1874.64 - 1723.13 = $151.51
The value of first coin will be $151.51 more than second coin in 15 years.
parallel when a=2
perpendicular when a=-1/2