Answer:
Step-by-step explanation:
Applying the Laplace transform:
![\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%2B5%5Cmathcal%7BL%7D%5By%27%5D%2B4%5Cmathcal%7BL%7D%5By%27%5D%3D0)
With the formulas:
![\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%27%5D%3Ds%5E2%5Cmathcal%7BL%7D%5By%5D-y%280%29s-y%27%280%29)
![\mathcal{L}[y']=s\mathcal{L}[y]-y(0)](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5By%27%5D%3Ds%5Cmathcal%7BL%7D%5By%5D-y%280%29)
![\mathcal{L}[x]=L](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5Bx%5D%3DL)
Solving for 
Apply the inverse Laplace transform with this formula:
![\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}](https://tex.z-dn.net/?f=%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs-a%7D%5D%3De%5E%7Bat%7D)
![y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}](https://tex.z-dn.net/?f=y%3D3%5Cmathcal%7BL%7D%5E%7B-1%7D%5B%5Cfrac1%7Bs%2B4%7D%5D%3D3e%5E%7B-4t%7D)
Find the midpoint of (1,-4) and (7,1) to find the rest stop. To do this add the x values and divide by 2, then add the y values and divide by 2. (4,-1.5) is the midpoint.
To find the distance, use the distance formula then multiply the result by 5.38. The distance is 42 miles
The only non-linear equation from your choices is the area of a circle as it is:
A=πr^2 and if you take the derivative of A you have:
dA/dr=2πr
So the rate of change changes as r changes, it is not constant thus the function has acceleration, so velocity changes.
This is in contrast to any linear equation which is of the form:
y=mx+b now taking the derivative you see that:
dy/dx=m, now m is a constant value, which means that there is no acceleration and the velocity remains constant.
Not the best, teachers are so annoying lol. Hope you are doing well though, don’t give up❤️
Answer:
10 7/12
hope this is right
Step-by-step explanation:
4 5/6 = 29/6 as an improper fraction
5 3/4 = 23/4 as an improper fraction
you times the two denominators together = 24
you times 29 by 4 = 116
you times 23 by 6 = 138
you add 116 and 138 = 254
you put this over 24 = 254/24
simplify this = 127/12
you make this a mixed number = 10 7/12
the answer is 10 7/12
