Answer:
0 and 2
Step-by-step explanation:
![f(x) = -x^2e^{-x}+2xe^{-x}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-x%5E2e%5E%7B-x%7D%2B2xe%5E%7B-x%7D)
To find zeros set f(x)=0 and solve for x
![0 = -x^2e^{-x}+2xe^{-x}](https://tex.z-dn.net/?f=0%20%3D%20-x%5E2e%5E%7B-x%7D%2B2xe%5E%7B-x%7D)
![0 = -e^{-x}(x^2-2x)](https://tex.z-dn.net/?f=0%20%3D%20-e%5E%7B-x%7D%28x%5E2-2x%29)
now factor out x
![0 = -xe^{-x}(x-2)](https://tex.z-dn.net/?f=0%20%3D%20-xe%5E%7B-x%7D%28x-2%29)
set each factor =0 and solve for x
![x=0](https://tex.z-dn.net/?f=x%3D0)
no solution for x
![x-2=0, x=2](https://tex.z-dn.net/?f=x-2%3D0%2C%20x%3D2)
zeros of f are 0 and 2
Answer:
a) $3480
b) $4036.8
Step-by-step explanation:
The compound interest formula is given by:
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Suppose that $3000 is placed in an account that pays 16% interest compounded each year.
This means, respectively, that ![P = 3000, r = 0.16, n = 1](https://tex.z-dn.net/?f=P%20%3D%203000%2C%20r%20%3D%200.16%2C%20n%20%3D%201)
So
![A(t) = P(1 + \frac{r}{n})^{nt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D)
![A(t) = 3000(1 + \frac{0.16}{1})^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%203000%281%20%2B%20%5Cfrac%7B0.16%7D%7B1%7D%29%5E%7Bt%7D)
![A(t) = 3000(1.16)^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%203000%281.16%29%5E%7Bt%7D)
(a) Find the amount in the account at the end of 1 year.
This is A(1).
![A(t) = 3000(1.16)^{t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%203000%281.16%29%5E%7Bt%7D)
![A(1) = 3000(1.16)^{1} = 3480](https://tex.z-dn.net/?f=A%281%29%20%3D%203000%281.16%29%5E%7B1%7D%20%3D%203480)
(b) Find the amount in the account at the end of 2 years.
This is A(2).
![A(2) = 3000(1.16)^{2} = 4036.8](https://tex.z-dn.net/?f=A%282%29%20%3D%203000%281.16%29%5E%7B2%7D%20%3D%204036.8)
Answer:
16
+ 2t - 6
Step-by-step explanation:
![(12t^{2} + 5t -y) - (-4t^{2} + 3t -1)](https://tex.z-dn.net/?f=%2812t%5E%7B2%7D%20%20%2B%205t%20-y%29%20-%20%28-4t%5E%7B2%7D%20%2B%203t%20-1%29)
simplify
![12t^{2} + 5t -7 +4t^{2} -3t +1](https://tex.z-dn.net/?f=12t%5E%7B2%7D%20%2B%205t%20-7%20%2B4t%5E%7B2%7D%20-3t%20%2B1)
combine like terms
16
+ 2t - 6
Answer: the second fifth and sixth one
Step-by-step explanation:
Answer:
538.3
Step-by-step explanation:
First of all find the area of the rectangle
L*W
15*30
450
Now find the area of semi circle
1/2![\pi r^{2}](https://tex.z-dn.net/?f=%5Cpi%20r%5E%7B2%7D)
Since radius is half a diameter divided 15 by 2=7.5
1/2
7.5 times 7.5= 56.25
1/2*3.14*56.25
56 times 3.14 is 176.625 now multiply 176.625 by 1/2
Answer is 88.3125
Now add 450 to 88.3125
Final answer: 538.3125