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Sophie [7]
2 years ago
7

20%5Csqrt%7B5%7D%20%29" id="TexFormula1" title="(5 \sqrt{3} + 2 \sqrt{5} - (3 \sqrt{3} - 7 \sqrt{5} )" alt="(5 \sqrt{3} + 2 \sqrt{5} - (3 \sqrt{3} - 7 \sqrt{5} )" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Sophie [7]2 years ago
7 0
Hey mom can you please answer
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Please help me with the below question.
Snezhnost [94]

6a. By the convolution theorem,

L\{t^3\star e^{5t}\} = L\{t^3\} \times L\{e^{5t}\} = \dfrac6{s^4} \times \dfrac1{s-5} = \boxed{\dfrac5{s^4(s-5)}}

6b. Similarly,

L\{e^{3t}\star \cos(t)\} = L\{e^{3t}\} \times L\{\cos(t)\} = \dfrac1{s-3} \times \dfrac s{1+s^2} = \boxed{\dfrac s{(s-3)(s^2+1)}}

7. Take the Laplace transform of both sides, noting that the integral is the convolution of e^t and f(t).

\displaystyle f(t) = 3 - 4 \int_0^t e^\tau f(t - \tau) \, d\tau

\implies \displaystyle F(s) = \dfrac3s - 4 F(s) G(s)

where g(t) = e^t. Then G(s) = \frac1{s-1}, and

F(s) = \dfrac3s - \dfrac4{s-1} F(s) \implies F(s) = \dfrac{\frac3s}{\frac{s+3}{s-1}} = 3\dfrac{s-1}{s(s+3)}

We have the partial fraction decomposition,

\dfrac{s-1}{s(s+3)} = \dfrac13 \left(-\dfrac1s + \dfrac4{s+3}\right)

Then we can easily compute the inverse transform to solve for f(t) :

F(s) = -\dfrac1s + \dfrac4{s+3}

\implies \boxed{f(t) = -1 + 4e^{-3t}}

6 0
1 year ago
Which graph represents the solution set of the inequality Negative 9 greater-than x?
Kamila [148]

Answer:

de answer is A

Step-by-step explanation:

hope i helped

7 0
3 years ago
Read 2 more answers
What is another way to write 42 + 63
satela [25.4K]
You could write this  by going 63+42 or add 63 and 42 
hope that's what you are looking for ;-)<span />
7 0
3 years ago
Read 2 more answers
Solve by completing the square and show steps <br> x^(2)+6x+5=0
Crazy boy [7]
X ^2 +6x+ 5
(x+2)(x+3)

2 + 3 = 5
While also 2•3= 6
The two numbers have to equal b when multiplied and c when added
4 0
3 years ago
Ricky is playing a racing game on PS5.
stepan [7]

Answer:

192 points

Step-by-step explanation:

he earned 120 points for passing 6 levels and getting 20 points per level

he earned 72 points for racing 45 laps and getting 24 points per every 15 laps

8 0
3 years ago
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