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3 years ago

Please help me :)))))

Mathematics

1 answer:

maria [59]3 years ago

3 0

Median: 10

lower quartile: 8

upper quartile: 11.5

range: 6

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Please help me with the below question.

VMariaS [17]

By letting

$y = \displaystyle \sum_{n=0}^\infty c_n x^{n+r}$

we get derivatives

$y' = \displaystyle \sum_{n=0}^\infty (n+r) c_n x^{n+r-1}$

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

a) Substitute these into the differential equation. After a lot of simplification, the equation reduces to

$5r(r-1) c_0 x^{r-1} + \displaystyle \sum_{n=1}^\infty \bigg( (n+r+1) c_n + (n + r + 1) (5n + 5r + 1) c_{n+1} \bigg) x^{n+r} = 0$

Examine the lowest degree term $\left(x^{r-1}\right)$ , which gives rise to the indicial equation,

$5r (r - 1) + r = 0 \implies 5r^2 - 4r = r (5r - 4) = 0$

with roots at r = 0 and r = 4/5.

b) The recurrence for the coefficients $c_k$ is

$(k+r+1) c_k + (k + r + 1) (5k + 5r + 1) c_{k+1} = 0 \implies c_{k+1} = -\dfrac{c_k}{5k+5r+1}$

so that with r = 4/5, the coefficients are governed by

$c_{k+1} = -\dfrac{c_k}{5k+5} \implies \boxed{g(k) = -\dfrac1{5k+5}}$

c) Starting with $c_0=1$ , we find

$c_1 = -\dfrac{c_0}5 = -\dfrac15$

$c_2 = -\dfrac{c_1}{10} = \dfrac1{50}$

so that the first three terms of the solution are

$\displaystyle \sum_{n=0}^2 c_n x^{n + 4/5} = \boxed{x^{4/5} - \dfrac15 x^{9/5} + \frac1{50} x^{13/5}}$

4 0

2 years ago

Find the side of a cube if its volume is 1331 cm³.

SSSSS [86.1K]

answe= aprox 11

Using the formula

V=a3

Solving fora

a=V⅓=1331⅓≈11

4 0

3 years ago

(4x+8)+(2x+20)=90 help me solve this and draw a diagram

Lemur [1.5K]

Answer:

x = 31/3

Step-by-step explanation:

4x+8+2x+20=90

4x+2x+8+20=90

6x+28=90

6x+28-28=90-28

6x=62

x = 31/3

5 0

3 years ago

Hello help please i’ll mark brainliest!!!

Wittaler [7]

Answer:

The moon has moved past the full moon and is moving toward the third quarter.

Step-by-step explanation:

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3 years ago

Add. Write fractions in simplest form.<br> 4-12 EVENS

Virty [35]

4. 1/3 6.-0.9 or -9/10 8. 2 1/3 10. -3.45 12.4.54 or 4 27/50

7 0

3 years ago