All categories

2 years ago

Question is attached below

Mathematics

1 answer:

Katarina [22]2 years ago

8 0

<span>x y
-3 1
1 3
3 4
5 5

is your answer</span>

You might be interested in

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

Priya bought x grams of flour. Clare bought 3/8 more than that.

iris [78.8K]

Answer:

Step-by-step explanation:

y=x+3/8x

5 0

3 years ago

The members of a cooking club are making cakes, which they will sell at a street fair for $14 apiece. It cost $22 for a booth at

tangare [24]

Is the amount of cakes estimated or rounded??

8 0

3 years ago

Triangles ABC and DEF are similar. what is the length of side EF

Leto [7]

The anwser is either 2.88 or 3, But others are saying it is 3.

8 0

3 years ago

Read 2 more answers

How can I find the volume of L shape blocks

Anvisha [2.4K]

The formula for volume is length multiplied by width multiplied by height
I hope this helps sorry if it doesn't :)

8 0

3 years ago