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)
Answer:
9 1/6 miles
Step-by-step explanation:
Add the mixed number by the improper fraction.
1 + 1/3 + 35/6
Solve the fractions first.
In order to have both of the fractions have the same denominator, find the Least Common Multiple of both of the fractions.
1/3 = 2/6
2/6 + 35/6 = 37/6
Turn the improper fraction into a mixed number by dividing the the numerator by the denominator. When you get your quotient, use the remainder as the new numerator over the denominator.
37/6 = 6 1/6
Now, add the 1.
6 1/6 + 1 = 7 1/6
Now, add the 2 miles that Carol walked on Wednesday.
7 1/6 + 2 = 9 1/6
So, Carol walked about 9 1/6 miles on Monday, Tuesday, and Wednesday all together.
Answer:
x = 2
4 (x + 6) - 3x = 26
solve the parenthesis
4x + 24 - 3x = 26
subtract 24 from both sides to get x by itself
4x - 3x = 2
solve
x = 2
✧・゚: *✧・゚:* *:・゚✧*:・゚✧
Hello!
✧・゚: *✧・゚:* *:・゚✧*:・゚✧
❖ There will be 16 girls.
The relationship is x4. If we multiply 3 x 4, we get 12. What we do to one number we do to the other so 4 x 4 = 16.
~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡
~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ
Answer:
x =76.45 degrees
Step-by-step explanation:
72 + 252 – 2(7)(25)cos _x__=242
combine like terms
324-350cosx = 242
subtract 324 from each side
-350x = -82
divide by -350
cos x = -82/-350
cos x = 82/350
take the arccos of each side
arccos (cos x) = arccos (82/350)
x =76.45 degrees