A rectangular board is 1100 millimeters long and 800 millimeters wide. What is the area of the board in square meters? Do not round

Answer:

8/25.

Step-by-step explanation:

As a fraction it is 32/100 but simplified is 8/25 :)

1. The given equation is probably supposed to read

y'' - 2y' - 3y = 64x exp(-x)

First consider the homogeneous equation,

y'' - 2y' - 3y = 0

which has characteristic equation

r² - 2r - 3 = (r - 3) (r + 1) = 0

with roots r = 3 and r = -1. Then the characteristic solution is

[tex]y = C_1 e^{3x} + C_2 e^{-x}[/tex]

and we let y₁ = exp(3x) and y₂ = exp(-x), our fundamental solutions.

Now we use variation of parameters, which gives a particular solution of the form

[tex]y_p = u_1y_1 + u_2y_2[/tex]

where

[tex]\displaystyle u_1 = -\int \frac{64xe^{-x}y_2}{W(y_1,y_2)} \, dx[/tex]

[tex]\displaystyle u_2 = \int \frac{64xe^{-x}y_1}{W(y_1,y_2)} \, dx[/tex]

and W(y₁, y₂) is the Wronskian determinant of the two fundamental solutions. This is

[tex]W(y_1,y_2) = \begin{vmatrix}e^{3x} & e^{-x} \\ (e^{3x})' & (e^{-x})'\end{vmatrix} = \begin{vmatrix}e^{3x} & e^{-x} \\ 3e^{3x} & -e^{-x}\end{vmatrix} = -e^{2x} - 3e^{2x} = -4e^{2x}[/tex]

Then we find

[tex]\displaystyle u_1 = -\int \frac{64xe^{-x} \cdot e^{-x}}{-4e^{2x}} \, dx = 16 \int xe^{-4x} \, dx = -(4x + 1) e^{-4x}[/tex]

[tex]\displaystyle u_2 = \int \frac{64xe^{-x} \cdot e^{3x}}{-4e^{2x}} \, dx = -16 \int x \, dx = -8x^2[/tex]

so it follows that the particular solution is

[tex]y_p = -(4x+1)e^{-4x} \cdot e^{3x} - 8x^2\cdot e^{-x} = -(8x^2+4x+1)e^{-x}[/tex]

and so the general solution is

[tex]\boxed{y(x) = C_1 e^{3x} + C_2e^{-x} - (8x^2+4x+1) e^{-x}}[/tex]

2. I'll again assume there's typo in the equation, and that it should read

y''' - 6y'' + 11y' - 6y = 2x exp(-x)

Again, we consider the homogeneous equation,

y''' - 6y'' + 11y' - 6y = 0

and observe that the characteristic polynomial,

r³ - 6r² + 11r - 6

has coefficients that sum to 1 - 6 + 11 - 6 = 0, which immediately tells us that r = 1 is a root. Polynomial division and subsequent factoring yields

r³ - 6r² + 11r - 6 = (r - 1) (r² - 5r + 6) = (r - 1) (r - 2) (r - 3)

and from this we see the characteristic solution is

[tex]y_c = C_1 e^x + C_2 e^{2x} + C_3 e^{3x}[/tex]

For the particular solution, I'll use undetermined coefficients. We look for a solution of the form

[tex]y_p = (ax+b)e^{-x}[/tex]

whose first three derivatives are

[tex]{y_p}' = ae^{-x} - (ax+b)e^{-x} = (-ax+a-b)e^{-x}[/tex]

[tex]{y_p}'' = -ae^{-x} - (-ax+a-b)e^{-x} = (ax-2a+b)e^{-x}[/tex]

[tex]{y_p}''' = ae^{-x} - (ax-2a+b)e^{-x} = (-ax+3a-b)e^{-x}[/tex]

Substituting these into the equation gives

[tex](-ax+3a-b)e^{-x} - 6(ax-2a+b)e^{-x} + 11(-ax+a-b)e^{-x} - 6(ax+b)e^{-x} = 2xe^{-x}[/tex]

[tex](-ax+3a-b) - 6(ax-2a+b) + 11(-ax+a-b) - 6(ax+b) = 2x[/tex]

[tex]-24ax+26a-24b = 2x[/tex]

It follows that -24a = 2 and 26a - 24b = 0, so that a = -1/12 = -12/144 and b = -13/144, so the particular solution is

[tex]y_p = -\dfrac{12x+13}{144}e^{-x}[/tex]

and the general solution is

[tex]\boxed{y = C_1 e^x + C_2 e^{2x} + C_3 e^{3x} - \dfrac{12x+13}{144} e^{-x}}[/tex]

Answer:

a = -x + 2

Step-by-step explanation:

First, you must distribute to get 2x + 2 and adding in the -3x it equals 2x + 2 - 3x = a

Combine the like terms to get -x + 2 = a

Since there is 2 variables then the answer will stay a = -x + 2 because x or a must be substituted in order to find the other variable

100 francs = 50 dollars

Exchange rate = 50/100

= 1/2

= 0.50 dollars per franc (C)

Note :-

It's dollars per franc because here the dollar has more value.

______

RainbowSalt2222 ☔

Answer:

Im pretty sure it is c

Step-by-step explanation:

9514 1404 393

Answer:

  D. choosing first second-, and third-place winners in a cooking contest​

Step-by-step explanation:

Permutations are involved when order matters. The order of people surveyed, sundae flavors, and flowers are irrelevant. The order of first-second-third is entirely relevant.

Cooking contest winners involve permutations.

Answer:

All closed.

Addition, subtraction as well as multiplication of polynomials result into another polynomial. Therefore, the set of polynomials is closed under addition, subtraction and multiplication.

Open polynomial set is (x² + x - 4) - (x² + x + 8)

Closed polynomial sets are (2 - x)(1 + 3x) and (5b - 3c)(7b - 3c)

A polynomial is an expression consisting of variables and their coefficients, operations of addition, subtraction, multiplication, and positive-integer powers of variables are involved in polynomial. If the result of a polynomial set applying different operations is polynomial then it is closed under that operation.

Given, polynomial sets

(x² + x - 4) - (x² + x + 8)

Applying subtraction operation

x² + x - 4 - x² - x - 8

Subtracting like terms

-12

The result is integer, it is open polynomial set

(2 - x)(1 + 3x)

Applying multiplication operation

2 - x - x - 3x²

= 2 - 2x - 3x²

The result is polynomial, it is closed polynomial set

(5b - 3c)(7b - 3c)

Applying multiplication operation

35b² - 15bc - 21bc + 9c²

= 35b² - 36bc + 9c²

The result is polynomial, it is closed polynomial set

Hence, (x² + x - 4) - (x² + x + 8) is an open polynomial set

(2 - x)(1 + 3x) and (5b - 3c)(7b - 3c) are closed polynomial sets.

Learn more about polynomials here:

https://brainly.com/question/11536910

#SPJ2

Answer: (3c+4)

Step-by-step explanation:

Answer:

0.005

Step-by-step explanation:

Answer:

Below:

Step-by-step explanation:-

The answer is in the comment!! someone answered your question!!

Answer:

false this is because the answer would contain all the values in both sets

Answer:

42.20

Step-by-step explanation:

132 ×0.32

=42.24

rounded off it give 42.20

Step-by-step explanation:

each department has 3 options for their representative.

and each of these options can be associated with the 3 options of the next department. and so on.

so, we have

3×3×3×3 = 3⁴ = 81

possibilities to firm that committee overall.

Answer:

slope = - [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 7 ) and (x₂, y₂ ) = (7, 1 )

m = [tex]\frac{1-7}{7-2}[/tex] = [tex]\frac{-6}{5}[/tex] = - [tex]\frac{6}{5}[/tex]

Hello there! :)

To find the slope of the line when we are given 2 points, we use the following formula:

m=[tex]\frac{y2-y1}{x2-x1}[/tex]

m=[tex]\frac{1-7}{7-2} \\\frac{-6}{5}[/tex]

So the slope is -6/5. Hope this helps!

~Just a cheerful gal

#CarryOnLearning

[tex]MysteriousNature :)[/tex]

Answer:

Step-by-step explanation:

if 50 AED= 12 Euro

for 1 AED ? Euro

50AED/1AED= 12Euro/x

cross multiplication:

50*x=12*1

50*x=12

x=12/50

x=0.24 Euro

so for 1AED you will get 0.26 Euro

Answer:

65 cows

Step-by-step explanation:

Inverse rule of three

[tex]45-------13\\x -------- 9[/tex]

[tex]x=\frac{(45)(13)}{9}=585/9=65[/tex]

Hope this helps

Answer:

10 units

Step-by-step explanation:

Area of smaller ∆ ,

= 1/2 * 2 * 2 = 2 u

Area of larger ∆ ,

= 1/2 * 4 * 4 = 8u

Total area = 8u + 2u = 10 units

Answer:

$28

Step-by-step explanation:

5.5% is $1.54 of what number? (%/100= is/of)

5.5/100 = 1.54/X

X = (1.54 * 100) / 5.5 = $28

Answer:

sus

Step-by-step explanation:

O_O

Answer:

Step-by-step explanation:

Assuming the string is straight (it will not be so due to gravity and wind load)

θ arcsin(354 / (200(3)) = 36°

Answer:

0 hours.

Step-by-step explanation:

He finished at the same time than Kenrick finished last week. So, he/she did not delay in mowing the lawn. Hoped this helped.

Given that

In a Parallelogram CARS ,∠C = (5x-20)°

∠A = (3x+20)°

angle C and angle A are adjacent angles

We know that

In a Parallelogram the adjacent angles are supplementary.

⇛∠C + ∠A = 180°

⇛ (5x-20)°+(3x+20)° = 180°

⇛5x°-20°+3x°+20° = 180°

⇛(5x°+3x°)+(20°-20°) = 180°

⇛8x°+0 = 180°

⇛8x° = 180°

⇛ x° = 180°/8

⇛ x° = 22.5°

Answer:-The value of x = 22.5°

also read similar questions: In parallelogram MATH, m= (3x+ 20) and t= (5x-4) find A

https://brainly.com/question/11578604?referrer

find the value of x (5x+12) (3x+8) a 10 b 15 c 20 d 25

https://brainly.com/question/6950381?referrer

Answer:

12 this is da a answer

12 twelve

Answer:

.25

Step-by-step explanation:

Answer:

15:8=15/8

Step-by-step explanation:

45:24=45/24

15/8=15:8

Answer:

5

Step-by-step explanation:

First subtract 6 from 16 to find how many cucumbers she has,

16 - 6 = 10

Now we know she has 10 cucumbers.

Subtract 5 from the 10 cucumbers to find out how many she has after giving away 5.

10 - 5 = 5

After subtracting the 5 cucumbers she gave away, we are left with 5

This means Maya has 5 cucumbers now

Answer:8x-40

Step-by-step explanation:

Because when we simply 4(x-5)/2

We multiply both sides by 2 because the inverse operations of division is multiplication. 2*4(x-5)*2/2 we cancel two by two then it leave us 4*2(x-5).

Next four times two is eight. So 8(x-5) we distribe eight that means eight times x and 5, 8x-40thos is the answer. Hope this help

[tex]\begin{cases} x = -4\implies &x+4=0\\ x=-5\implies &x+5=0\\ x = 0\implies &x=0\\ x=\frac{1}{3}\implies &x -\frac{1}{3}=0\\ &3\left( x -\frac{1}{3} \right)=3(0)\\ &3x-1=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x+4)(x+5)(x)(3x-1)=\stackrel{\textit{original equation}}{0} \\\\\\ (x^2+9x+20)(x)(3x-1)=y\implies (x^3+9x^2+20x)(3x-1)=y \\\\\\ (3x^4+27x^3+60x^2)+(-x^3-9x^2-20x)=y[/tex]

[tex]3x^4+27x^3+60x^2-x^3-9x^2-20x=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 3x^4+26x^3+51x^2-20x=y~\hfill[/tex]

Answer:

p=0.4

Step-by-step explanation:

6(p+2.25)=15.9

6p+13.5=15.9

6p=2.4

p=0.4

Answer:

5 hours

Step-by-step explanation:

Answer:

Yes, because (-1,2) is a solution to both inequalities

Step-by-step explanation:

2>-1 so the first inequality is correct

-1+2>0 so the second inequality is correct