Answer:
30=15
Step-by-step explanation:
30=40-30+6-4-27
30=10+2-27
40=12-27
30=-15
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)
Using the formula for the nth term of an arithmetic progression.
an = a + (n - 1)d
a(4) = a + 3d = 55
a(9) = a + 8d = 90
a(9) - a(4) => 5d = 35
d = 35/5 = 7.
From a(4): a = 55 - 3d = 55 - 3(7) = 55 - 21 = 34
a(2) = a + d = 34 + 7 = 41.
Answer:
b = 4.66666667
Step-by-step explanation:
The equation for finding the area of a triangle is
0.5b x h = a
b = base
h = height
a = area
So I calculated 14 divided by 6
And got 2.3333333
And since that number is half of the base, I multiplied it by 2
2.333 x 2 ≈ 4.66666667
25/80 + 24/80 = 49/80. 16 and 20 both go into 80. !6 goes in 5 times so you multiply 5 by 5. 20 goes into 80 4 times so you multiply 4 by 4. 24/80 + 25/80 = 49/80.
