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Amiraneli [1.4K]
3 years ago
5

The indicated function y1(x) is a solution of the associated homogeneous equation. Use the method of reduction of order to find

a second solution y2(x) of the homogeneous equation and a particular solution yp(x) of the given nonhomogeneous equation. y'' + y' = 1; y1 = 1
Mathematics
1 answer:
Serga [27]3 years ago
6 0

Answer:

Required solution is y(x)=1+A\cos x+B\sin x where A and B are constants.

Step-by-step explanation:

Given nonhomogenous differential equation is,

y''(x)+y'(x)=1\hfill (1)   with y_1(x)=1

To find another solution, consider m=\frac{\partial}{\partial x} be such that,

m^2+1=0\implies m=\pm i

Hence,

C.F=A\cos x+B\sin x   where A and B are constants.

Let  D=\frac{\partial}{\partial x}

P.I=\frac{1}{1+D^2}(1)

=(1+D^2)^{-1}(1)

=(1-D^2+.....)(1)=1

Hence,

y(x)=1+A\cos x+B\sin x where A and B are constants.

which is required solution.

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A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness L and index of refraction n=1.5
boyakko [2]

Additional information to complete the question:

How long does it take for a short pulse of light to travel from one end of the glass to the other?

Express your answer in terms of some or all of the variables f and L. Use the numeric value given for n in the introduction.

T = ___________ s

Answer:

 T = \frac{15}{f}

Step-by-step explanation:

Given:

Thickness og glass = L

Index of refraction n=1.5

Frequency = f

Wavelength = \frac{L}{10}

λ(air) = \frac{L}{10}

λ(glass) = λ(air) / n

             = \frac{\frac{L}{10}}{1.5}

             = \frac{L}{10} * \frac{1}{1.5}

             = \frac{L}{15}

V(glass) = fλ(glass)

              = f * \frac{L}{15}

          T = \frac{L}{V_{glass}} = \frac{15}{f}

     

7 0
3 years ago
A factory produces 90 packages of mixed nuts in 1 min. A quality control manager selected 10 of these 90 packages at random and
valentina_108 [34]
Answer:

34

explanation:

First of all, put the numbers in order

30, 31, 31, 32, 33, 35, 35, 35, 36, 36

Then, find the middle number.
In this case, there is an even amount of numbers so, we have to pick the 2 middle numbers which is 33 and 35.

Now all you have to do is add these two numbers together then divide by 2 which will give you 34.

or, in simpler questions like this one, you can just say 34 as you know it is between 33 and 35.


In other questions, it might have and odd amount of numbers, for example:

3, 3, 5, 8, 10

so all you would do here is pick the middle number which would be 5. (it has 2 numbers on each side of it)
7 0
2 years ago
What’s the answer to this problem?
Vinil7 [7]

×=23

:) :) :) :) :););) ;););)

5 0
3 years ago
How can I solve 30x-18-5-4x=55
Elden [556K]

\text{Solver for x:}\\\\30x-18-5-4x=55\\\\\text{Combine like terms}\\\\26x-18-5=55\\\\26x-23=55\\\\\text{Add 23 to both sides}\\\\26x=78\\\\\text{Divide both sides by 26}\\\\\boxed{\text{x = 3}}

3 0
3 years ago
Please help I literally don’t understand this at all
mel-nik [20]

Answer:

x=13 y=10 z=3 d) 260

Step-by-step explanation:

vertex angles are congruent so you can set them equal to each other and solve

and then a straight like adds up to 180 so 180-(7(x-3)+5y)= your missing angle and then that angles is congruent to its opposite so 2(5z+15)=60

8 0
2 years ago
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