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3 years ago

Simplify -7x - (15y) + 3x - 2y

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

3 0

Answer:

Step-by-step explanation:

combine like terms

-7x + 3x - 15y - 2y

-4x - 17y

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Find two power series solutions of the given differential equation about the ordinary point x = 0. compare the series solutions

monitta

I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take $z=y'$ , so that $z'=y''$ and we're left with the ODE linear in $z$ :

$y''-y'=0\implies z'-z=0\implies z=C_1e^x\implies y=C_1e^x+C_2$

Now suppose $y$ has a power series expansion

$y=\displaystyle\sum_{n\ge0}a_nx^n$
$\implies y'=\displaystyle\sum_{n\ge1}na_nx^{n-1}$
$\implies y''=\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}$

Then the ODE can be written as

$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge1}na_nx^{n-1}=0$

$\displaystyle\sum_{n\ge2}n(n-1)a_nx^{n-2}-\sum_{n\ge2}(n-1)a_{n-1}x^{n-2}=0$

$\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0$

All the coefficients of the series vanish, and setting $x=0$ in the power series forms for $y$ and $y'$ tell us that $y(0)=a_0$ and $y'(0)=a_1$ , so we get the recurrence

$\begin{cases}a_0=a_0\\\\a_1=a_1\\\\a_n=\dfrac{a_{n-1}}n&\text{for }n\ge2\end{cases}$

We can solve explicitly for $a_n$ quite easily:

$a_n=\dfrac{a_{n-1}}n\implies a_{n-1}=\dfrac{a_{n-2}}{n-1}\implies a_n=\dfrac{a_{n-2}}{n(n-1)}$

and so on. Continuing in this way we end up with

$a_n=\dfrac{a_1}{n!}$

so that the solution to the ODE is

$y(x)=\displaystyle\sum_{n\ge0}\dfrac{a_1}{n!}x^n=a_1+a_1x+\dfrac{a_1}2x^2+\cdots=a_1e^x$

We also require the solution to satisfy $y(0)=a_0$ , which we can do easily by adding and subtracting a constant as needed:

$y(x)=a_0-a_1+a_1+\displaystyle\sum_{n\ge1}\dfrac{a_1}{n!}x^n=\underbrace{a_0-a_1}_{C_2}+\underbrace{a_1}_{C_1}\displaystyle\sum_{n\ge0}\frac{x^n}{n!}$

4 0

3 years ago

A rectangle has a length of 2 m and a width of 40 cm what is the perimeter of the rectangle ( show your work)

sweet [91]

Answer:

0.05 im pretty sure to my calcutor

Step-by-step explanation:

4 0

3 years ago

What is the square root of 8 rounded to the nearest tenth?

frozen [14]

Square Root of 8 to the nearest tenth, means to calculate the square root of 8 where the answer should only have one number after the decimal point.

Here are step-by-step instructions for how to get the square root of 8 to the nearest tenth:

Step 1: Calculate

We calculate the square root of 8 to be:

√8 = 2.82842712474619

Step 2: Reduce

Reduce the tail of the answer above to two numbers after the decimal point:

2.82

Step 3: Round

Round 2.82 so you only have one digit after the decimal point to get the answer:

2.8

To check that the answer is correct, use your calculator to confirm that 2.82 is about 8.

8 0

3 years ago

Find the length of the segment that joins the points (-5, 4) and (6,-3).

Helen [10]

Answer:

$\boxed {\boxed {\sf d=\sqrt{170} \ or \ d\approx 13.04}}}$

Step-by-step explanation:

We are asked to find the length of a segment or the distance between the 2 points. The formula for distance is:

$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

x₁= -5
y₁= 4
x₂= 6
y₂ = -3

Substitute the values into the formula.

$d= \sqrt{(6--5)^2+(-3-4)^2$

Solve inside the parentheses.

6--5 (Back to back negative signs become a positive)= 6+5 =11
-3-4= -7

$d= \sqrt{(11)^2+(-7)^2$

Solve the exponents.

(11)²= 11*11= 121
(-7)²= -7*-7= 49

$d= \sqrt {(121)+(49)$

Add.

$d= \sqrt {170}$

$d=13.0384048104$

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

13.0384048104

$d\approx 13.04$

The length of the segment is √170 or approximately 13.04.

7 0

3 years ago

I need help with this questions, please help ill mark brainliest..

Natasha_Volkova [10]

Answer:

Options (1), (3) and (5)

Step-by-step explanation:

Equation that represents the relationship between the three sides of a triangle is,

a² + b² = c²

Where c = longest side of the triangle

If the length of the given sides satisfy the equation, triangle formed by the sides will be a right triangle.

Option A.

27 in, 36 in, 45 in

(45)² = (27)² + (36)²

2025 = 729 + 1296

2025 = 2025

True.

Option 2.

18 in, 22 in, 28 in

(28)² = (18)² + (22)²

784 = 324 + 484

784 = 808

False.

Option 3

10 in, 24 in, 26 in

(26)² = (10)² + (24)²

676 = 100 + 576

676 = 676

True.

Option 4

20 in, 21 in, 31 in

(31)² = (20)² + (21)²

961 = 400 + 441

961 = 841

False.

Option 5

28 in, 45 in, 53 in

(53)² = (28)² + (45)²

2809 = 784 + 2025

2809 = 2809

True.

Therefore, Options (1), (3) and (5) will be the correct options.

6 0

3 years ago