Help help math help help help math

Answer:

You told me to resolve this question

Let

[tex]\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots[/tex]

Differentiating twice gives

[tex]\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots[/tex]

[tex]\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n[/tex]

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

[tex]\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0[/tex]

Then the coefficients in the power series solution are governed by the recurrence relation,

[tex]\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}[/tex]

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

[tex]k=0 \implies n=0 \implies a_0 = a_0[/tex]

[tex]k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}[/tex]

[tex]k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}[/tex]

[tex]k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}[/tex]

It should be easy enough to see that

[tex]a_{n=2k} = \dfrac{a_0}{(2k)!}[/tex]

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

[tex]k = 0 \implies n=1 \implies a_1 = a_1[/tex]

[tex]k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}[/tex]

[tex]k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}[/tex]

[tex]k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}[/tex]

so that

[tex]a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}[/tex]

So, the overall series solution is

[tex]\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)[/tex]

[tex]\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}[/tex]

Answer:

0.09

Step-by-step explanation:

Answer:

LJ< JK<LK

Step-by-step explanation:

for a theorem, the order of the side of the triangle is the same as the order of the opposite angles since for the angles it's K<L<J, you replace each with the opposite side (quick trick, it's the one not containing the letter!)

Answer:

6^3

Step-by-step explanation:

3 × 3 × 3 × 3 × 3 × 3=729

6^3=216

3 × 3 × 3 × 3 × 3 × 3=729

3^6=729

Hope this helps :)

3 × 3 × 3 × 3 × 3 × 3

63

9 × 9 × 9

36

Answer:

Step-by-step explanation:

5 / 6 = 0.83333333...

0.833333...•100 = 83.333333...

83.3%

Answer:

You can do this type of questions with inverse proportion.

_

%83,3

Answer:

0.00706666666

Step-by-step explanation:

Answer:

Answer# 1: A. 26

Answer# 2: A. 25

1. What is m + 5n where m = 1 and n = 5?

Substitute 1 for "m" and 5 for "n":

[tex]\sf (1)+5(5)[/tex]

Multiply 5*5 =25

[tex](1)+25[/tex]

Add :

[tex]\sf 26[/tex]

____________________

2. What is 5m + 5n where m = 10 and n = -5?

Substitute 10 for "m" and -5 for "n".

[tex]\sf 5\left(10\right)\:+\:5\left(-5\right)[/tex]

Multiply 5 * 10= 50

[tex]\sf 50+5\left(-5\right)[/tex]

Multiply 5 * -5 = -25

[tex]\sf 50-25[/tex]

Subtract:

[tex]\sf 25[/tex]

___________________________________

Answer:

6 cm for both sides

Step-by-step explanation:

Answer/Step-by-step explanation:

[tex]\frac{1-\cos \left(x\right)}{\sin \left(x\right)}=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}[/tex]

When you have an equation like this, you can start from either side. So, let us start from the left side.

[tex]\underline{\mathrm{Left\:side:}} \quad\frac{1-\cos \left(x\right)}{\sin \left(x\right)}[/tex]

[tex]\sf{Rewrite\: using \:Trig \:identities=\frac{\sin \left(x\right)}{1+\cos \left(x\right)}}\\\\\mathrm{Therefore,\: it \:is \:true}[/tex]

Answer:

proportion of ratio will be used

Answer:

C. 1 4/10 + 9/10 + 6/10

got it right

Answer:

B: (-2,-3)

Step-by-step explanation:

The problem basically wants you to find the vertex because that is the turning point of an absolute value graph where the slope goes from negative to positive immediately. B is the best choice because the vertex is translated 2 to the left and 3 down.

Answer:

Step-by-step explanation:

Answer:

Working out 20% of 30

If you are using a calculator, simply enter 20÷100×30 which will give you 6 as the answer.

Step-by-step explanation:

Answer:

Step-by-step explanation:

what is 20% of 30? how would you calculate it?

30 : 100 * 20 = 6

or

30 * 0.20 = 6

Answer: the answer is in the attachment.

Answer:

Hope this helps :)

Step-by-step explanation:

Answer:

It is b

Step-by-step explanation: Because only one that makes sense

Answer:

A child psychologist is interested in the number of times a newborn baby’s crying wakes its mother after midnight. For a random sample of 50 mothers, the following information was obtained. Let X = the number of times per week a newborn baby’s crying wakes its mother after midnight. For this example, x = 0, 1, 2, 3, 4, 5.

P(x) = probability that X takes on a value x.

x P(x)0 P(x = 0) = 250

1 P(x = 1) = 1150

2 P(x = 2) = 2350

3 P(x = 3) = 950

4 P(x = 4) = 450

5 P(x = 5) = 150

Step-by-step explanation:

pa follow po pls.

1. 3/7 = 72/x

By cross multiplication we get :

➟ 3x = 72 × 7

➟ x = 72 × 7/3

➟ x = 24 × 7

➟ x = 168

2. m/8 = 8/20

By cross multiplication we get :

➟ 20m = 8 × 8

➟ 20m = 64

➟ m = 64/20

➟ m = 16/5

Answer:

20 three-point scores

61/3=20 R1

Answer:

7

Step-by-step explanation:

61 divided by 8 = 7 remainder 5

you can do 7 3's and 7 5's which would make 7x3 = 21  +  7 x 5 = 35  21 + 35 = 56

61 - 56  = 5 (add 1 to the amount of 5's)

7 3's and 8 5's

Answer:

50 in²

Step-by-step explanation:

The area of the rectangle = 8 × 4 = 32 in²

area of Δ NPO = [tex]\frac{1}{2}[/tex] × PO × PN = [tex]\frac{1}{2}[/tex] × 3 × 4 = 6 in² ( PN = RM )

area of Δ PQR = [tex]\frac{1}{2}[/tex] × RP × 3 = [tex]\frac{1}{2}[/tex] × 8 × 3 = 12 in² ( RP = MN )

area of MNOPQR = 32 + 6 + 12 = 50 in²

Answer:

13 more should be purchased.

40-27=13

Answer:

The only way she was able to use it if she knew your email and linked you to the account or she had some sort of permissions to get brainly on her device.

Answer:

-3

Step-by-step explanation:

a. Simply put (x+h) wherever you have x.

[tex]f(x+h) = -3(x+h)+7 = -3x +7 -3h[/tex]

b. We have the first part, just subtract

[tex]f(x+h) = -3(x+h)+7 = -3x +7 -3h - (-3x+7) = -3x+7-3h +3x -7 = -3h[/tex]

c. Finally, we divide by h[tex]\frac{-3h}h = -3[/tex]

Answer:

Number 4

Step-by-step explanation:

Side-Angle-Side, it has to be between the two sides.

Answer:

what answer

Step-by-step explanation:

?????????????

Answer:

four times a number less 10 is equall to 16 ia not

Answer:

No

No

Yes

Yes

No

Step-by-step explanation:

In this case we are looking at substitution, so any where you find x put three(3) in replace of it.

And remember the answer should be 36,

I find it difficult to type the answer so I will take a picture instead.