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3 years ago

Please need help on this

Mathematics

1 answer:

ivanzaharov [21]3 years ago

4 0

It would be able to turn 180

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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

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

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2 years ago

Tracy uses 1.5 cups of flour to make 1 loaf of banana bread. How many cups of flour does she need for 100 loaves of banana bread

Westkost [7]

Tracy will need 150 cups.

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4 years ago

Read 2 more answers

Easy answer!!!! Will give brainliest

pochemuha

Answer:

A and B

Step-by-step explanation:

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3 years ago

How far can a caterpillar; traveling at 0.06m/s, move in 60 seconds?

nignag [31]

Answer:

3.6 meters in 60 seconds

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3 years ago

Dwayne is walking on a straight sidewalk. He spots

Anastasy [175]

Answer:

Skew lines

Step-by-step explanation:

Skew lines are two straight lines in three dimensional space that are neither parallel nor do they intersect Examples of skew lines are the front sidewalk and a line that goes along one of the top edges of the house, or lines that connecting opposite edges of a regular tetrahedron

Other examples of skew lines can be found in non co-planar non parallel, parts of a bridge.

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3 years ago