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rewona [7]
1 year ago
12

Find a linear differential operator that annihilates the given function. (Use D for the differential operator.) 4 ex cos 3x

Mathematics
1 answer:
Keith_Richards [23]1 year ago
4 0

If the function is

y = 4 e^x \cos(3x)

then we have derivatives

Dy = 4 e^x \cos(3x) - 12 e^x \sin(3x)

D^2y = -32 e^x \cos(3x) - 24 e^x \sin(3x)

Now consider the linear ODE

aD^2y + bDy + cy = 0

Substituting y and its derivatives reduces the equation to

(-32a + 4b + 4c) \cos(3x) + (-24a - 12b) \sin(3x) = 0

Now,

-24a - 12b = 0 \implies b = -2a

-32a + 4b + 4c = 0 \implies c = 10a

Then the minimal ODE with the given solution is

aD^2y -2a Dy + 10ay = 0

or

\boxed{D^2y  -2 Dy + 10y = 0}

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Convert 0.00425 into scientific notation 
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Step-by-step explanation:

4.25 \times  {10}^{ - 3}

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Which equation is a direct variation function? A) y = x B) y = (1/4)x + 2 C) y = x^2 D) y = 4
Ivanshal [37]
I think the answer is 16
4 0
3 years ago
Three solutions for 5x+7y=19
ddd [48]
Just sub in ANY number for x and solve for y

5x + 7y = 19.....lets say x = 0
5(0) + 7y = 19
7y = 19
y = 19/7...so when x = 0, y = 19/7.....(0,19/7)

5x + 7y = 19....lets say x = 1
5(1) + 7y = 19
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7 0
3 years ago
Jackie runs and dances for a total of 55 minutes every day. She dances for 25 minutes longer than she runs.
AlladinOne [14]

9514 1404 393

Answer:

  A: x + y = 55; y - x = 25

  B: 15 minutes running

  C: no

Step-by-step explanation:

<h3>Part A:</h3>

The two equations relate to the total number of minutes, and to the difference specified in the problem statement.

  x + y = 55 . . . . . . total time is 55 minutes

  y = x + 25 . . . . . . dances 25 minutes longer

__

<h3>Part B:</h3>

We can substitute for y in the first equation to find the value of x, the time spent running.

  x + (x +25) = 55

  2x = 30 . . . . subtract 25

  x = 15 . . . . . . divide by 2

Jackie spends 15 minutes running each day.

__

<h3>Part C:</h3>

The value of y from is found using the second equation:

  y = x +25 = 15 +25 = 40

Jackie <u>will not spend 45 minutes dancing</u> if she meets the requirements on times.

5 0
2 years ago
It cost $35 for one adult and two children to attend a show.it cost $60 for two adults and three children to attend the same sho
yarga [219]

Answer:

i got 2100

Step-by-step explanation:

i got that by multiplying 60 x 35 = 2100


hope this helps

let me know if it is right


4 0
3 years ago
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