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disa [49]
2 years ago
10

Please help me with the below question.

Mathematics
1 answer:
VMariaS [17]2 years ago
4 0

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}}

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4. A triangle has angle measures of 72º and 3°. What is the measure of the third angle?
8090 [49]

Answer:

105

the whole triangle adds up to 180

72+3=75

180-75=105

7 0
3 years ago
Given the recursive function f(n) = f(n - 1) - 3 ; f(1) = 9 , what would be the first three terms of the sequence ?
Ann [662]

The first three terms of sequence are 9 , 6 , 3

<em><u>Solution:</u></em>

Given the recursive function f(n) = f(n - 1) - 3

Where f(1) = 9

To find: First three terms of sequence

Substitute n = 2 , n = 3 and n = 4 in given recursive function

When n = 2

f(n) = f(n - 1) - 3

f(2) = f(2 - 1) - 3

f(2) = f(1) - 3

f(2) = 9 - 3 = 6

f(2) = 6

Thus second term is 6

When n = 3

f(3) = f( 3 - 1) - 3

f(3) = f(2) - 3

f(3) = 6 - 3 = 3

f(3) = 3

Thus the third term is 3

When n = 4

f(4) = f( 4 - 1) - 3

f(4) = f(3) - 3

f(4) = 3 - 3

f(4) = 0

Thus the fourth term is 0

Thus first three terms of sequence are 9 , 6 , 3

6 0
3 years ago
A carpenter makes wooden chairs.
monitta

Answer:

Is there supposed to be a graph somewhere?

8 0
3 years ago
6. Select all values of x for which f(x) = g(x).<br> A.0<br> B. 1<br> C.-3<br> D.4
Sati [7]
The answer would be A
6 0
3 years ago
Solve this system of equations by
Goshia [24]
Answer: x = 12 and y = -8

Explanation:
x + y = 4
4x + 3y = 24
———————
-3(x + y = 4)
4x + 3y = 24
———————-
-3x - 3y = -12
4x + 3y = 24
———————
x = 12

If x = 12
x + y = 4
12 + y = 4
y = -8
6 0
2 years ago
Read 2 more answers
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