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pantera1 [17]
2 years ago
5

4> Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o

Mathematics
1 answer:
harina [27]2 years ago
7 0

Answer:

y=3e^{-4t}

Step-by-step explanation:

y''+5y'+4y=0

Applying the Laplace transform:

\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0

With the formulas:

\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)

\mathcal{L}[y']=s\mathcal{L}[y]-y(0)

\mathcal{L}[x]=L

s^2L-3s+5sL-3+4L=0

Solving for L

L(s^2+5s+4)=3s+3

L=\frac{3s+3}{s^2+5s+4}

L=\frac{3(s+1)}{(s+1)(s+4)}

L=\frac3{s+4}

Apply the inverse Laplace transform with this formula:

\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}

y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}

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Subtract 7 2/9 - 1 5/6
fiasKO [112]

Answer:5 7/18

Step-by-step explanation:

7 2/9 - 1 5/6

65/9-1 5/6

65/9-11/6

97/18

5 7/18

5 0
2 years ago
Read 2 more answers
One angle of a right triangle measures 78°. What is the measure of the other acute angle?
muminat

Answer:

12°

Step-by-step explanation:

a right triangle implies there is an angle that is 90°

another angle is 78°

the third angle is 180 - (90 + 78)  =  180 - 168  = 12°

6 0
3 years ago
Need help ASAP. i forgot all the steps after the Area is solved with 5. or if 25pi is the right answer.
maxonik [38]

Answer:

42.5\:\mathrm{m^2}

Step-by-step explanation:

The area of a sector with measure \theta in degrees is given by r^2\pi\cdot\frac{\theta}{360}, where r is the radius of the sector.

What we're given:

  • r of 5
  • \theta of 195^{\circ}

Solving, we get:

A_{sector}=5^2\pi\cdot \frac{195}{360}=13.5416666667\pi=42.5424005174\approx \boxed{42.5\:\mathrm{m^2}}

*Notes:

  • units should be in square meters (area)
  • the problem does not say whether to round or leave answers in term of pi, so you may need to adjust the answer depending on what your teacher specifically wants
7 0
2 years ago
Help me plz idk this at all
worty [1.4K]

Step-by-step explanation:

sin theta = opp / hyp

sin theta × hyp = opp

sin60 × 30 = opp

.866 × 30 = opp

25.98° = opp

*Theta is the 0 with a line through it

8 0
2 years ago
Can you guys please help me I really need to past this ASAP thank you!!!
Dmitry_Shevchenko [17]

Answer: ???

Step-by-step explanation:  what do you need help with

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7 0
2 years ago
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