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Alik [6]
3 years ago
12

Definition: The statement formed when an equal sign is placed between two expressions is called an

Mathematics
1 answer:
melamori03 [73]3 years ago
7 0

Answer:

equation

example=2+3=5

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sergeinik [125]
The answer would be 142<span />
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A rectangular piece of plastic has an area of 10 square millimeters and a perimeter of 22 millimeters. What are the dimensions o
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The piece of plastic have dinmensions of 1mm by 10mm
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Power Series Differential equation
KatRina [158]
The next step is to solve the recurrence, but let's back up a bit. You should have found that the ODE in terms of the power series expansion for y

\displaystyle\sum_{n\ge2}\bigg((n-3)(n-2)a_n+(n+3)(n+2)a_{n+3}\bigg)x^{n+1}+2a_2+(6a_0-6a_3)x+(6a_1-12a_4)x^2=0

which indeed gives the recurrence you found,

a_{n+3}=-\dfrac{n-3}{n+3}a_n

but in order to get anywhere with this, you need at least three initial conditions. The constant term tells you that a_2=0, and substituting this into the recurrence, you find that a_2=a_5=a_8=\cdots=a_{3k-1}=0 for all k\ge1.

Next, the linear term tells you that 6a_0+6a_3=0, or a_3=a_0.

Now, if a_0 is the first term in the sequence, then by the recurrence you have

a_3=a_0
a_6=-\dfrac{3-3}{3+3}a_3=0
a_9=-\dfrac{6-3}{6+3}a_6=0

and so on, such that a_{3k}=0 for all k\ge2.

Finally, the quadratic term gives 6a_1-12a_4=0, or a_4=\dfrac12a_1. Then by the recurrence,

a_4=\dfrac12a_1
a_7=-\dfrac{4-3}{4+3}a_4=\dfrac{(-1)^1}2\dfrac17a_1
a_{10}=-\dfrac{7-3}{7+3}a_7=\dfrac{(-1)^2}2\dfrac4{10\times7}a_1
a_{13}=-\dfrac{10-3}{10+3}a_{10}=\dfrac{(-1)^3}2\dfrac{7\times4}{13\times10\times7}a_1

and so on, such that

a_{3k-2}=\dfrac{a_1}2\displaystyle\prod_{i=1}^{k-2}(-1)^{2i-1}\frac{3i-2}{3i+4}

for all k\ge2.

Now, the solution was proposed to be

y=\displaystyle\sum_{n\ge0}a_nx^n

so the general solution would be

y=a_0+a_1x+a_2x^2+a_3x^3+a_4x^4+a_5x^5+a_6x^6+\cdots
y=a_0(1+x^3)+a_1\left(x+\dfrac12x^4-\dfrac1{14}x^7+\cdots\right)
y=a_0(1+x^3)+a_1\displaystyle\left(x+\sum_{n=2}^\infty\left(\prod_{i=1}^{n-2}(-1)^{2i-1}\frac{3i-2}{3i+4}\right)x^{3n-2}\right)
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3 years ago
Change the percent to a decimal. 0.4% =
zysi [14]
0.004 is 0.4% in decimal form
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Read 2 more answers
Anna is a teacher at an elementary school. She purchased 73 tickets to take the first-grade children and some parents on a field
Svetllana [295]

She bought 54 child tickets and 19 adult tickets.

Step-by-step explanation:

No. of tickets purchased = 73

Cost of tickets = $771

Cost of one child ticket = $9

Cost of one adult ticket = $15

Let,

Child ticket = x

Adult ticket = y

According to given statement;

x+y=73   Eqn 1

9x+15y=771   Eqn 2

Multiplying Eqn 1 by 9;

9(x+y=73)\\9x+9y=657\ \ \ Eqn\ 3\\

Subtracting Eqn 3 from Eqn 2;

(9x+15y)-(9x+9y)=771-657\\9x+15y-9x-9y=114\\6y=114\\

Dividing both sides by 6;

\frac{6y}{6}=\frac{114}{6}\\y=19

Putting y=19 in Eqn 1

x+19=73\\x=73-19\\x=54\\

She bought 54 child tickets and 19 adult tickets.

Keywords: linear equations, subtraction

Learn more about linear equations at:

  • brainly.com/question/3227215
  • brainly.com/question/3269852

#LearnwithBrainly

4 0
3 years ago
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