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vitfil [10]
3 years ago
15

Using the power series methods solve the 1st order Lane-Emden Equation:

Mathematics
1 answer:
nikklg [1K]3 years ago
5 0

Answer:

Step-by-step explanation:

xy = 2y + xy = 0

Hence, 2y + xy = 0 ---------(1)

Differentiating equation (1) n times by Leibnitz theorem, gives:

2y(n) + xy(n) + ny(n - 1) = 0

Let x = 0: 2y(n) + ny(n - 1) = 0

2y(n) = -ny(n - 1)

∴ y(n) = -ny(n - 1)/2 for n ≥ 1

For n = 1: y = 0

For n = 2: y(1) = -y

For n = 3: -3y(2)/2

For n = 4: -2y(3)

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Sally invests £8000 in a savings account. The account pays 2.8% compound interest per year work out the value of her investment
Alborosie

Answer: the value of her investment after 4 years is £8934.3

Step-by-step explanation:

The formula for determining compound interest is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount invested.

t represents the duration of the investment in years.

From the information given,

P = 8000

r = 2.8% = 2.8/100 = 0.028

n = 1 because it was compounded once in a year.

t = 4 years

Therefore,

A = 8000(1+0.028/1)^1 × 4

A = 8000(1+0.028)^4

A = 8000(1.028)^4

A = £8934.3 to the the nearest penny

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3 years ago
The functions f(x) and g(x) are shown.
erastova [34]

The function f(x) takes on the value 2 when x =  -7 and x = -3, and thus the corresponding points are (-7,2) and (-3,2).

The points where g(x) = 0 are called "roots" or "solutions," and is (3,0).

f(x) > g(x)  on the approx. interval (-9, -3/4).

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2 years ago
What is the cube root of 8x27?
larisa86 [58]
8 = 2^3
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(2^3)*(3^3)=6^3
Cube root of 6^3 = 6
3 0
3 years ago
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Can somewon help me simplefly it i will mark u brainlist if u get it correct
krek1111 [17]

Answer:

1.25j +5.25

Step-by-step explanation:

2.75j + 2.25 - 1.5j +3

Combine like terms

2.75j -1.5j   + 2.25 +3

1.25j +5.25

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200,000 + 80,000 + 3,000 + 900 + 80
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