Answer:
graph (b)
Explanation:
The farm started with 40 sheep and the number doubled each year.
So, the equation modeling this situation would be:
N(x) = 40*(2)^2
By getting the equation, we can notice that we already excluded the third and fourth choices as they have the wrong equations.
Now, we will need to select the right graph which is either graph a or graph b.
To do this, we will get the value of N(x) for different values of x as follows:
At x = 0: N(0) = 40*(2)^0 = 40
At x = 1: N(1) = 40*(2)^1 = 80
At x = 1: N(2) = 40*(2)^2 = 160
Now, taking a look at graph a, we will find that:
N(1) = 120
N(2) = 360
These numbers are not the same as the numbers we calculated, therefore, this graph is wrong
Taking a look at graph b, we will find that:
N(1) = 80
N(2) = 160
These numbers are exactly the same as the ones calculated, therefore, this graph is the correct one.
Hope this helps :)
<span>y(t) = a exp(3t) + b exp(4t)
conditions, y(0) = 3
y'(0) = 3
y(0) = a exp(3 x 0) + b exp(4 x 0)
= a exp(0) + b exp(0)
= (a x 1) + (b x 1)
= a + b
y'(0) = 0
so the linear equation is, a + b = 3</span>
Answer:
4 hours and 7 hours
Step-by-step explanation:
Marcus = x hours
Donnell = x + 3 hours
Total = 11 hours
- x + x + 3 = 11
- 2x + 3 = 11
- 2x = 8
- x = 4
So Marcus practiced 4 hours and Donnell practiced 7 hours
Answer:
Step-by-step explanation:
We have to simplify the original function using partial fraction, hence:
![From\ Laplace\ inverse:\\\\But\ L^{-1}[\frac{1}{s-a} ]=e^{at}\\\\Hence:\\\\L^{-1} [\frac{5s}{s^2+3s-4}]=L^{-1}[\frac{1}{s-1} ]+L^{-1}[\frac{4}{s+4} ]=e^{t}+4e^{-4t}\\\\L^{-1} [\frac{5s}{s^2+3s-4}]=e^{t}+4e^{-4t}](https://tex.z-dn.net/?f=From%5C%20Laplace%5C%20inverse%3A%5C%5C%5C%5CBut%5C%20L%5E%7B-1%7D%5B%5Cfrac%7B1%7D%7Bs-a%7D%20%5D%3De%5E%7Bat%7D%5C%5C%5C%5CHence%3A%5C%5C%5C%5CL%5E%7B-1%7D%20%5B%5Cfrac%7B5s%7D%7Bs%5E2%2B3s-4%7D%5D%3DL%5E%7B-1%7D%5B%5Cfrac%7B1%7D%7Bs-1%7D%20%5D%2BL%5E%7B-1%7D%5B%5Cfrac%7B4%7D%7Bs%2B4%7D%20%5D%3De%5E%7Bt%7D%2B4e%5E%7B-4t%7D%5C%5C%5C%5CL%5E%7B-1%7D%20%5B%5Cfrac%7B5s%7D%7Bs%5E2%2B3s-4%7D%5D%3De%5E%7Bt%7D%2B4e%5E%7B-4t%7D)
X^2+19x+48
(x+16)(x+3)
Explanation:
Two factors of 48 that added together equal 19 are 16 and 3 so that’s why they are used
