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never [62]
2 years ago
15

Which operation is NOT closed for polynomials?

Mathematics
1 answer:
lesya692 [45]2 years ago
5 0
Answer: All of the operations that you have listed will produce a polynomial. Therefore, they are all closed for polynomials. (Did you have a typo?)

When we say an operation is closed for a particular problem, we mean that the resulting answer is of the same type as at the beginning.

In these cases, we are starting with polynomials in each problem. After performing the operations, we still have polynomials. Therefore, they are all closed.

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3y''-6y'+6y=e*x sexcx
Simora [160]
From the homogeneous part of the ODE, we can get two fundamental solutions. The characteristic equation is

3r^2-6r+6=0\iff r^2-2r+2=0

which has roots at r=1\pm i. This admits the two fundamental solutions

y_1=e^x\cos x
y_2=e^x\sin x

The particular solution is easiest to obtain via variation of parameters. We're looking for a solution of the form

y_p=u_1y_1+u_2y_2

where

u_1=-\displaystyle\frac13\int\frac{y_2e^x\sec x}{W(y_1,y_2)}\,\mathrm dx
u_2=\displaystyle\frac13\int\frac{y_1e^x\sec x}{W(y_1,y_2)}\,\mathrm dx

and W(y_1,y_2) is the Wronskian of the fundamental solutions. We have

W(e^x\cos x,e^x\sin x)=\begin{vmatrix}e^x\cos x&e^x\sin x\\e^x(\cos x-\sin x)&e^x(\cos x+\sin x)\end{vmatrix}=e^{2x}

and so

u_1=-\displaystyle\frac13\int\frac{e^{2x}\sin x\sec x}{e^{2x}}\,\mathrm dx=-\int\tan x\,\mathrm dx
u_1=\dfrac13\ln|\cos x|

u_2=\displaystyle\frac13\int\frac{e^{2x}\cos x\sec x}{e^{2x}}\,\mathrm dx=\int\mathrm dx
u_2=\dfrac13x

Therefore the particular solution is

y_p=\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x

so that the general solution to the ODE is

y=C_1e^x\cos x+C_2e^x\sin x+\dfrac13e^x\cos x\ln|\cos x|+\dfrac13xe^x\sin x
7 0
3 years ago
Help I need nhelp on this question and no links please
Naddik [55]

Image of answer

I hope that helps

- 4018669

3 0
2 years ago
Use the function below to find F(4)
Ne4ueva [31]

Answer:

A 256/3

Step-by-step explanation:

1/3 * 4^4 =

1/3 * (4*4*4*4) =

1/3 * 256 = 256/3

4 0
1 year ago
Read 2 more answers
Ashley earns money at a constant rate. Ashley earns $15 in 2.5 hours. We want to know how much money, m, Ashely will earn after
bogdanovich [222]

Answer:

Step-by-step explanation:

$15/2.5hr=$6 so if earnings are y and hours worked is x then

y=6x

6 0
3 years ago
6x-9=y ; y=-3x linear equations solution for x and y I need help can someone explain
snow_lady [41]
The answer is
 x = 1 and y = -3
<span>[1] 6x-9=y [2] y=-3x</span>
7 0
3 years ago
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