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)
The rate of change is +2 degrees per hour (an increase of 2 degrees per hour)
Volume of reg sq. pyramid = vp
vp = 1/3×s^2×h, where s = side and h = height
Volume of cone = vc =1/3×h×pi×r^2
Now we know that h is the same for both, and the cones diameter = s of square base, so radius (r) = 1/2 s
so now vc = 1/3×h×pi×(1/2s)^2
let's remove the same items for both vc and vp
so 1/3 and h
now let's plug an arbitrary number into each:
vc = pi (10/2)^2 = 3.14×25 = 78.54
vp = s^2 = 10^2 = 100
So any square pyramid has slightly more volume than the cone
Answer: its 4
Step-by-step explanation:
gg
Answer:
-52.5 or -53
Step-by-step explanation:
Start by subtracting 18 from both sides. With you get 0.4=-21. Now divide 0.4 into both sides.
