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3 years ago

You are going to play mini golf. A ball machine that contains

Mathematics

1 answer:

mariarad [96]3 years ago

6 0

There is a 24.71% chance of getting a blue golf ball

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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

What is −29.9 ÷ 4=

lisabon 2012 [21]

Answer:

Step-by-step explanation:

5 0

3 years ago

A line has the equation 3x ? 4y = 1. Choose the equation of a line that is parallel to the given line.

cupoosta [38]

Answer:

Find a line which also has 3/4 as the slope or 3x - 4y in standard form.

Step-by-step explanation:

If the line is 3x - 4y = 1 then the line which is parallel will have the same coefficients of x and y. Parallel lines never cross and to ensure this have the same slope. The slope is a ratio which can be solved for in an equation using the coefficients of x and y. Here the slope is:

3x - 4y = 1

-4y = -3x + 1

y = 3/4x - 1/4.

Find a line which also has 3/4 as the slope or 3x - 4y in standard form.

7 0

3 years ago

Read 2 more answers

Simplest form of the expression -2x2(x – 5) + x(2x2 – 10x) + x is

Andrei [34K]

You first simplify the expression using PEMDAS
-2x^3-10x^2+2x^3-10x^2+x
then combine like terms,
(-2x^3+2x^3), (-10x^2-10x^2), x
cancels out^
so the answer would be -20x^2+x

3 0

3 years ago

(_____)^2= (cscx-1)(cscx+1)

Lady bird [3.3K]

$(csc(x)-1)(csc(x)+1)=csc^2(x)-1=cot^2(x)$

We know that $csc^2(x)-1=cot^2(x)$ because of the Pythagorean trig identity $1+cot^2(x)=csc^2(x)$ .

4 0

3 years ago