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2 years ago

Write the number in different ways

Mathematics

1 answer:

mina [271]2 years ago

3 0

4. 15 tens, 1 hundred, 5 tens
150
5. 18 tens, 1 hundred, 8 tens
180

note: I hope this helps. I haven't done this in a long time. Sorry X(

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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

The graph represents the function f(x) = x2 + 3x + 2. If g(x) is the reflection of f(x) across the x-axis, g(x) = . (Write the f

Tanya [424]

Answer:

g(x) = - (x² + 3x + 2) = - x² - 3x - 2

Step-by-step explanation:

The graph represents the function f(x) = x² + 3x + 2.

Now, g(x) is the function which is obtained by reflecting f(x) across the x-axis.

While a graph of a function reflects across x-axis then its y-values will change sign for a fixed value of x.

Therefore, the function g(x) will be given by

g(x) = - (x² + 3x + 2) = - x² - 3x - 2 (Answer)

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2 years ago

Need help as fast as possible will mark brainliest

MissTica

Answer:

Option C. is correct choice.

Step-by-step explanation:

$20\pm 0.1\:^{\circ}\:C$

Regards: Umer

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2 years ago

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sertanlavr [38]

y=1/2x the first bubble

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2 years ago

Read 2 more answers

Pls answer question 1-4 Ill give extra 100 points

Vlad1618 [11]

I can’t really see the image I don’t know if it’s my internet but I’ll tell you the answer when it loads

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2 years ago