determine the slope and y intercept and write the equation in slope intercept form

Answer:

[tex]-6\leq x\leq 6[/tex]

Step-by-step explanation:

This is answer for the last question.

Answer:

with what

Step-by-step explanation:

Answer:

help with? there's nothing there

Answer:

20

Step-by-step explanation:

A common denominator is a number that is a multiple of both denominators.

To find it just write the multiplication table of the numbers and find a number that appears in both of them.

In this case, we have 4 and 5:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40

5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Since it only asks for a common denominator, it can be 20, 40, 60, 80... Although it's usually smarter to pick the lower number.

[tex]1\dfrac 34 =1+ \dfrac 34 =\dfrac 74 = \dfrac{35}{20}\\\\\\1\dfrac 45 = 1+ \dfrac 45 = \dfrac 95 =\dfrac{36}{20}\\\\\text{The answer is 20}[/tex]

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:

42.20

Step-by-step explanation:

132 ×0.32

=42.24

rounded off it give 42.20

To answer this question, you would need to divide the total amount of cereal in the box by the serving size.

This would be 12 2/3 divided by 1 1/3.

We can write each mixed number as an improper fraction first before we divide:12 2/3 = 38/3 and 1 1/3 = 4/3

Now divide 38/3 by 4/3. Recall that dividing by a fraction is accomplished by multiplying by the reciprocal of the divisor: 38/3 * 3/4 = 114/12 = 38/4 OR 19/2

Also, 19/2 is equivalent to 9 and 1/2. There would be 9 and 1/2 servings in the box of cereal.

Hope this helps

9514 1404 393

Answer:

  10.49

Step-by-step explanation:

Since we know 110 = 10² +10, we can make a first approximation to the root as ...

  √10 ≈ 10 +10/21 . . . . . where 21 = 1 + 2×integer portion of root

This is a little outside the desired approximation accuracy, so we need to refine the estimate. There are a couple of simple ways to do this.

One of the best is to use the Babylonian method: average this value with the value obtained by dividing 110 by it.

  ((220/21) + (110/(220/21)))/2 = 110/21 +21/4 = 881/84 ≈ 10.49

An approximation of √110 accurate to hundredths is 10.49.

__

The other simple way to refine the root estimate is to carry the continued fraction approximation to one more level.

For n = s² +r, the first approximation is ...

  √n = s +r/(2s+1)

An iterated approximation is ...

  s + r/(s +(s +r/(2s+1)))

The adds 's' to the approximate root to make the new fraction denominator.

For this root, the refined approximation is ...

  √110 ≈ 10 + 10/(10 +(10 +10/21)) = 10 +10/(430/21) = 10 +21/43 ≈ 10.49

_____

Additional comment

Any square root can be represented as a repeating continued fraction.

  [tex]\displaystyle\sqrt{n}=\sqrt{s^2+r}\approx s+\cfrac{r}{2s+\cfrac{r}{2s+\dots}}[/tex]

If "f" represents the fractional part of the root, it can be refined by the iteration ...

  [tex]f'=\dfrac{r}{2s+f}[/tex]

__

The above continued fraction iteration adds 1+ good decimal places to the root with each iteration. The Babylonian method described above doubles the number of good decimal places with each iteration. It very quickly converges to a root limited only by the precision available in your calculator.

Answer:

The angle value 433.54 π rad (pi radian) in words is "four hundred and thirty-three point five four π rad (pi radian)".

Step-by-step explanation:

got the information from the internet

Answer:

-6.4 is GREATER.

The number closest to 0 is greater.

Answer

f= 1

step by step explanation

Answer:

1/98

Step-by-step explanation:

Step 1: Translate statement into equation.

Step 2: Multiply both sides by 7x.

Step 3: Divide both sides by 98.

Step 4: Check if solution is correct.

Therefore, the answer is 1/98.

Answer:

1/24

Step-by-step explanation:

8x + 1/3 = 2/3

    - 1/3   - 1/3

8x = 1/3

8x/8 = (1/3)/8

x = 1/24

Answer:

i need the question

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

Answer:

95% of 80 is 76 and 85% of 60 is 51.

Step-by-step explanation:

Answer:

a. 76,  b. 60.

Step-by-step explanation:

a)  80 * 0.95 = 76.

b)   0.85 x = 51

x = 51/0.85 = 60.

- BRAINLIEST answerer

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:

15:8=15/8

Step-by-step explanation:

45:24=45/24

15/8=15:8

Answer:

x = 42

Step-by-step explanation:

2x + 8 + 2x + 4 = 180

4x + 12 = 180

4x = 168

x = 42

Answer:

250

Step-by-step explanation:

You can take the explicit formula and simply substitute the n value with 64:

-2 + 4 * (64 - 1)

-2 + 4 * (63)

-2 + 252

250

Answer:

d because your taking away 6 from the 275

Step-by-step explanation:

Answer:

This is indeed a function

Answer:

AED 9118.80

Step-by-step explanation:

to find out how much he earns for 1 car, multiply 75990 by 0.03 (3%). so the salesman earns 2279.70 per car sold. next, multiply this number by 4 to get the amount he earned for 4 cars: 9118.80

Answer:

answer is 746.

have a nice day and do good in math

Answer:

.25

Step-by-step explanation:

there you go the answer is in the picture

Answer:

2:1  or  2

Step-by-step explanation:

*** (Ratios can be written as " a : b", or can be written as a fraction " a / b".

 >> therefore 10/5 can be simplified to 2/1 )***

    For every 10 notebooks, there are 5 ballpens.

    Therefore, for every 2 notebooks there is 1 ballpen (The simplification).

EXTRA:  

**Also remember that the ratio of notebooks to ballpens cannot be reversed into ballpen to notebook ratio, because this would change the meaning.

  2/1 is not the same as 1/2 **

Answer:

Uuuuh thats kind of suspicious, maybe you could post your question without  a link? But links are usually scams, so dont do that :)

Answer:

Just go to the 6 on the bottom line, and add a point

Answer:

see below

Step-by-step explanation:

(6,0)

 The first coordinate is the x coordinate.  Since it is positive we go to the right 6 units.  The second coordinate is the y coordinate.  We go up zero units