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slavikrds [6]
2 years ago
8

Use the laplace transform to solve the given initial-value problem. y' + 5y = e3t, y(0) = 2

Mathematics
1 answer:
Iteru [2.4K]2 years ago
4 0

In mathematics, the Laplace transform, named after its discoverer Pierre Simon Laplace, transforms a function of real variables (usually in the time domain) into a function of complex variables (in the time domain). is the integral transform that Complex frequency domain, also called S-area or S-plane).

Learn more about Laplace transform here brainly.com/question/17062586

#SPJ4

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How can I solve this?<br>Please use the simplest format​
IgorLugansk [536]

Answer:

option D is true.

Step-by-step explanation:

The right-angled triangle is shown.

From the right-angled triangle,

The angle Ф = 60°

We know that the trigonometric ratio

tan Ф = opposite / adjacent

  • opposite = 4
  • adjacent = n

Thus,

tan 60 = 4 / n

√3 = 4/n

n = 4/√3

Thus,

n = 4/√3

  = (4 × √3) / (√3 × √3)

  = 4√3 / 3

Thus,

n  = 4√3 / 3

Using Pythagorean theorem

m = √n²+4²

m=\sqrt{\left(4\cdot \frac{\sqrt{3}}{3}\right)^2+4^2}

m=\sqrt{\frac{4^2}{3}+4^2}

m=\sqrt{\frac{64}{3}}

m=\frac{8}{\sqrt{3}}

m=\frac{8\sqrt{3}}{3}

Thus,

  • m=\frac{8\sqrt{3}}{3}
  • n  = 4√3 / 3

Therefore, option D is true.

3 0
3 years ago
Simplify this radical <br> 3√12<br> and this one <br> 2√(48x^3 )
MakcuM [25]
For number one you should get 6√3





4 0
3 years ago
Need help It is working with functions and I need assistance
Ainat [17]

Answer: its 4. Look at the graph, x is horizontal and y is vertical (first go sideways then go up.) if coordinates are x,y then first go sideways when looking for x. they give you x. 7. then we go up. the graph intersects 7 at 4, therefore the coords are 7, 4 and your y coordinate is 4.

Step-by-step explanation:

5 0
3 years ago
The mean number of words per minute (WPM) typed by a speed typist is 149 with a standard deviation of 14 WPM. What is the probab
Troyanec [42]

Answer:

78.81%

Step-by-step explanation:

We are given;

Population mean; μ = 149

Sample mean; x¯ = 147.8

Sample size; n = 88

standard deviation; σ = 14

Z-score is;

z = (x¯ - μ)/(σ/√n)

Plugging in the relevant values;

z = (147.8 - 149)/(14/√88)

z = -0.804

From z-distribution table attached, we have; p = 0.21186

P(X > 147.8) = 1 - 0.21186 = 0.78814

In percentage gives; p = 78.81%

6 0
2 years ago
What are the real and imaginary parts of the complex number?
Licemer1 [7]

Answer:

The real part is 2

The imaginary part is -5

Step-by-step explanation:

A complex number consists of a real part and an imaginary part. For example given the complex number z = x+it

x is the real part of the complex number z i.e Re(z) = x

Imaginary part of the complex number z is y i.e Im(z) = y.

Note that the real part are on the x axis of a graph while the y axis is the imaginary axis attached to the complex notation i

Given the complex number 2-5i

Comparing 2-5i to x+iy

x= 2 and y = -5

The real part is 2 (value that is not attached to the complex notation)

The imaginary part is 5(value attached to the complex notation)

8 0
3 years ago
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