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2 years ago

Is -451 in the sequence below? 15,7,-1,-9,,-17..

Mathematics

2 answers:

Virty [35]2 years ago

8 0

Answer:

nope

Step-by-step explanation:

Andrews [41]2 years ago

5 0

Answer:

No, the closest to -451 in the sequence is -429

Step-by-step explanation:

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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

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

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

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2 years ago

George and Chin work as landscapers. George charges $90 for a 6-hour job. Chin charges $84 for the same job.The table shows thei

gulaghasi [49]

The equation must equal 84, so you can eliminate B and D.

Chin charges a rate for 2 hours, then charges a reduced rate for 4 hours. There are no discounts present in his rate, so you can eliminate A.

The equation for Chin's charges can be found by the equation C. 2x + 4y = 84.

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2 years ago

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Given right triangle ABC with right angle C, and sin A = ¼. Which of the following expressions are also equal to ¼?

BaLLatris [955]

Answer:

cos(A)

Step-by-step explanation:

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2 years ago

The school store sells binders for $5 and notebooks for $4. The store needs to sell $80 worth of these two items combined each w

lorasvet [3.4K]

Answer:

Step-by-step explanation:

Step one:

given

let binders be x

and notebooks be y

let the total sale be T

the cost of binder is $5 each

the cost of notebook is $4 each.

the total sales expected is $80

step two:

the linear model for the total sales is given as

T=x+y

using the given data, the situation can be represented linearly as

80=5x+4y

Therefore the linear expression for the total sale is 80=5x+4y

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3 years ago

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An olympic-size swimming pool is a rectangle that measures 50 meters in length and 25 meters in width. Make a scale drawing of a

Veronika [31]

Answer:

Length: 10 cm

Width: 5 cm

Step-by-step explanation:

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