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3 years ago

I'm smart just giving point...whats 9 time 3

Mathematics

2 answers:

OLEGan [10]3 years ago

8 0

Answer:

um it's 27

Step-by-step explanation:

hope this helps :)

Andre45 [30]3 years ago

7 0

Answer:

It is 27

Step-by-step explanation:

hope this helps

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(D^2 - 1) y = x^2 sinx

Oduvanchick [21]

$(D^2-1)y=x^2\sin x$

First consider the homogeneous part,

$(D^2-1)y=\dfrac{\mathrm d^2y}{\mathrm dx^2}-y=0$

which has characteristic equation

$r^2-1=(r-1)(r+1)=0$

This has roots $r=\pm1$ , so the characteristic solution is

$y_c=C_1e^x+C_2e^{-x}$

For the nonhomogeneous part, consider a solution of the form

$y_p=(a_2x^2+a_1x+a_0)\sin x+(b_2x^2+b_1x+b_0)\cos x$

which has second derivative

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=(-b_2x^2+(4a_2x-b_1)x+2a_1-b_0+2b_2)\cos x+(a_2x^2+(a_1+4b_2)x+a_0-2a_2+2b_1)\sin x$

Substituting into the ODE gives

$(-2b_2x^2+(4a_2-2b_1)x+2a_1-2b_0+2b_2)\cos x+(-2a_2x^2+(-2a_2-4b_2)x-2a_0-2b_1+2a_2)\sin x=x^2\sin x$

Matching up coefficients gives the system

$\begin{cases}-2b_2=0\\4a_2-2b_1=0\\2a_1-2b_0+2b_2=0\\-2a_2=1\\-2a_1-4b_2=0\\-2a_0-2b_1+2a_2=0\end{cases}$

which has solutions

$a_2=-\dfrac12,a_1=0,a_0=\dfrac12,b_2=0,b_1=-1,b_0=0$

So the particular solution is

$y_p=\left(-\dfrac12x^2+\dfrac12\right)\sin x-x\cos x$

Therefore the general solution is

$y=y_c+y_p$
$y=C_1e^x+C_2e^{-x}+\left(-\dfrac12x^2+\dfrac12\right)\sin x-x\cos x$

5 0

3 years ago

For an end of the year party, Ms. Dean purchased 96

Elodia [21]

Answer: 15

Step-by-step explanation:

7 0

2 years ago

Adam solved this equation and identified the number of solutions.

Vikentia [17]

Answer:

The mistake is he said"The equation has infinitely many solutions."

But based on what he was solving for, this equation does not have any solutions, so that's his mistake.

4 0

3 years ago

Read 2 more answers

Forty-four students go on a field trip. The students are divided into groups of 7 students. How many groups of 7 will there be?.

strojnjashka [21]

To solve this problem, you need to divide the total number of students going on the field trips with the number of students in each group.

44/7

= 6 R 2

Since, I assume there can <em>only</em> be groups of 7, the answer is 6.

4 0

3 years ago

While I was jogging I was able to run 5 miles in 30 minutes from this information we can determine my?

Vikentia [17]

You can determine your speed that is Speed = (distance/Time). Mind you in this cast time should be in hour, so 30 min - 1/2 hour or 0.5 Hour

Your speed is 5/0.5 = 10 mi/hour

6 0

3 years ago