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Andrews [41]
4 years ago
12

Find the general solution of y''' + 6y'' + y' − 34y = 0 if it is known that y1 = e−4x cos(x) is one solution.

Mathematics
1 answer:
SashulF [63]4 years ago
3 0

Answer:

Step-by-step explanation:

Given is a differential equation of III order,

y''' + 6y'' + y' - 34y = 0

The characteristic equation would be cubic as

m^3+6m^2+m-34=0

By trial and error, we find that

f(2) = 2^3+6(2^2)+2-34 =0\\

Thus m=2 is one solution

Since given that e^{-4x} cos xis one solution we get

m = -4+i and hence other root is conjugate m=-4-i

Hence general solution would be

y=Ae^{2x} +e^{-4x} (Bcosx +C sinx)

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The volume of a rectangular prism is 270 cubic centimeters the height of the prism is 5 centimeters. What could the length and w
kotegsom [21]

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Volume = 270 cm³

height = 5 cm

length = ?

width = ?

Formula

Volume of a rectangular prism = height x length x width

- Solve for Area of the base (height x length)

Area of the base = Volume / height

-Substitution

Area of the base = 270 / 5

-Result

Area of the base = 54 m²

2.- Find the prime factors of 54

                    54   2

                    27   3

                      9   3

                      3   3

                       1

3.- The possible values of the sidas of the rectangle are:

Combining the prime factor of 54.

              Length                        Width

              2 x 3 = 6           and    3 x 3 = 9

or            2 x 3 x 3 = 18   and    3 x 1 = 3

or            3 x 3 x 3 = 27  and     2 x 1 = 2

6 0
3 years ago
The mean weight 20 students in a room is 65 kg one student one student who weight is 88kg went into the room what is the new mea
umka2103 [35]

The new mean is 66.09

<u>Explanation:</u>

Mean weight of 20 students = 65kg

One student with 88kg entered the room.

New mean = ?

\frac{x_1+x_2+....+x_2_0}{20} = 65

\frac{x_1+x_2+....+x_2_0 + 88}{21} = ?

The above equation can further be written as:

x_1 + x_2 +....+x_2_0 = 65 X 20\\\\x_1 + x_2 +....+x_2_0 = 1300

New mean = \frac{1300 + 88}{21}

                 = 66.09

Therefore, the new mean is 66.09

6 0
3 years ago
The two triangles below are similar. What is the similarity ratio of AABC to ADEF?
Dominik [7]

Answer:

2 : 1

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

AC : DF = 8 : 4 = 2 : 1

6 0
3 years ago
Please solve from A thru D. Thanks
Mashutka [201]
The unkown side legnth is 9 centimeteres long all you had to do was subtract all the numbers from 44 and what your left with is the unknown side.
6 0
3 years ago
At the local bakery, Ariel bought 2 oatmeal cookies for $1.50. Mei bought 1/2 dozen oatmeal cookies for $4.50. Becky bought 8 oa
elena55 [62]

Answer: Yes. The cookies are $ .75 each. The total cost is proportional to the number of cookies purchased.

T = $.75 × c

Step-by-step explanation:

4 0
2 years ago
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