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3 years ago

(X^-4)(x^10)=x^p Help:(

Mathematics

1 answer:

kkurt [141]3 years ago

6 0

Answer:

Step-by-step explanation:

$(x^{-4})*(x^{10})=x^{p}\\\\x^{-4+10}=x^{p}\\\\x^{6}=x^{p}\\$

Compare the powers, p = 6

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y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence

sukhopar [10]

Let

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

Differentiating twice gives

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

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

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:

$\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0$

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

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

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

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

$k=0 \implies n=0 \implies a_0 = a_0$

$k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}$

$k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}$

$k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}$

It should be easy enough to see that

$a_{n=2k} = \dfrac{a_0}{(2k)!}$

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

$k = 0 \implies n=1 \implies a_1 = a_1$

$k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}$

$k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}$

$k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}$

so that

$a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}$

So, the overall series solution is

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

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

4 0

3 years ago

The table shows how many males and females attended two different movies. How would you find the joint relative frequency of bei

kirza4 [7]

Answer:

B. Divide 124 by 229.

Step-by-step explanation:

Given the table

$\begin{array}{cccc}&\text{Action}&\text{Drama}&\text{Total}\\ \\\text{Male}&105&124&229\\ \\\text{Female}&99&151&250\\ \\\text{Total}&204&275&479\end{array}$

The <u>joint relative frequency</u> is the ratio of the frequency in a particular category and the total number of data values.

The total number of males $=229$

The number of males that like drama $=124$

So, to find the joint relative frequency of being male and attending a drama movie, you should divide 124 by 229.

8 0

3 years ago

Read 2 more answers

A straight line has a slope of 2.08. Calculate the angle that the line makes with the x (horizontal) axis.

zubka84 [21]

Answer:

The angle that the line makes with x-axis of of 64.3º.

Step-by-step explanation:

Equation of a line, and angle with the x axis:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope.

The angle that the line makes with the x axis is given by the angle which has tangent m, that is, $a = \tan^{-1}{m}$ .

In this question:

We have that $m = 2.08$ . So

$a = \tan^{-1}{2.08} = 64.3$

The angle that the line makes with x-axis of of 64.3º.

4 0

3 years ago

Jim bought 3 cds at a cost of $14.99 each what will he pay including 6% sales tax

Charra [1.4K]

14.99 *3 = 44.97

44.97*1.06 =47.6682, round off to $47.67 with tax

3 0

3 years ago

Need help please !!!

blsea [12.9K]

Answer:

option C is the correct answer

Step-by-step explanation:

The trigonometric equation you are using has a general form

y = A* tan w*(x - r)

Where

A is the amplitude of the function

w is the frequency rad/s

r is the phase shift

In your case

A = -2

The frequency is

w = (2*pi)/period

period = pi/4

w = 8

r = -pi/2

y = -2* cos 8*(x + pi/2)

7 0

3 years ago