Can I get help please....
Sara bought 3/4 of a pound of bananas and 3/5 of a pound of pears. How much fruit did Sara buy?

Answer:

33/44 = 0.75

0.75*44 = 33

Answer:

44% of 75 = 33

Step-by-step explanation:

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:

x=11/5

Step-by-step explanation:

isolate x

22/10 = 10x/10

22/10 = x

simplify

11/5 = x

Answer:

y = (x - 1)(x - 3)

y = (x + 2)^2

Step-by-step explanation:

3)

Has roots at x = {1, 3}

y = (x - 1)(x - 3)

4)

Has double root at x = -2

y = (x + 2)^2

Answer:

k=2.117

Step-by-step explanation:

Answer:

3.017 + k = 5.134

So, k = 5.134 - 3.017

So, k = 2.117

Answer:

300°

Step-by-step explanation:

what is 5/6 of a full rotation?

A full rotation is 360°

360 * 5/6 = 300°

Answer:

The answer is 125.6

Step-by-step explanation:

C= 2x3.14x20

C=6.28x 20

C= 125.6

Answer:

the set of side lengths will be d

Answer: 52.3 seconds

Step-by-step explanation:

209.2 divided by 4

which is 52.3 seconds

Answer: x=80

Let that be x

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\begin{cases} h= 0\\ k = 4 \end{cases}\implies y=a(x-0)^2+4~\hfill \textit{we also know that} \begin{cases} x = 1\\ y = 3 \end{cases} \\\\\\ 3=a(1-0)^2+4\implies 3=1a+4\implies \boxed{-1=a} \\\\\\ y=-1(x-0)^2+4\implies \blacktriangleright y = -x^2+4\blacktriangleleft[/tex]

Answer:

A.    y = –(x – 1)2 + 3    = Rewrite in vertex form and use this form to find the vertex  (h,k).    (1,3)=  Already in vertex form.  y=−(x−1)2+3

OR

D.    y = –x^2 + 4    = Rewrite in vertex form and use this form to find the vertex  (h,k).    (0,4)=  Find the vertex form.     y=−(x+0)2+4

Step-by-step explanation:

A.    y = –(x – 1)2 + 3    = Rewrite in vertex form and use this form to find the vertex  (h,k).    (1,3)=  Already in vertex form.  y=−(x−1)2+3

B.    y = –x^2 – 4    = Rewrite in vertex form and use this form to find the vertex  (h,k).    (0,−4)=   Find the vertex form.     y=−(x+0)2−4

C.    y = –x^2 + 3     = Rewrite in vertex form and use this form to find the vertex  (h,k).    (0,3)=  Find the vertex form.     y=−(x+0)2+3

D.    y = –x^2 + 4    = Rewrite in vertex form and use this form to find the vertex  (h,k).    (0,4)=  Find the vertex form.     y=−(x+0)2+4

Answer:

40 students earned a B on this paper.

40%×80=32 people who chose action as their fav.

Answer:

c po is the correct aswer

Step-by-step explanation:

correct me if im wrong hope it's help

thanks

Answer:

B. Insurance ensures that losses are not passed on to society

Hope this helps :)

Answer:

4

Step-by-step explanation:

2+2=4

Answer:

240oz.

Step-by-step explanation:

15oz=1batch

She needs 16 batches.

15oz. x 16batches = 240oz.

Hope this helps :)

Answer:

He should change 3.6 to 36

and

he should change 8.42 to 84.2

He should also move the decimal up when dividing like in the picture I posted.

Step-by-step explanation:

I other words, he should shift the decimal points to the right one

I hope that I could help!

He should also move the decimal up when dividing in the picture that is posted.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

We need to find 8.42 divided by 3.6 longhand.

8.42 / 3.6

= 2.33

He should change 3.6 to 36 and he should change 8.42 to 84.2

He should also move the decimal up when dividing in the picture that is posted.

Learn more about division here:

https://brainly.com/question/26411682

#SPJ2

Answer:

n = 1

Step-by-step explanation:

"The sum of" is addition

"2 times a number" is 2n

"and 5" is + 5

equals 7 is =7

2n + 5 = 7

     - 5   - 5

2n = 2

2n/2 = 2/2

n = 1

Step-by-step explanation:

brand a is better option why because we have paint and paint roller

If you buy 1 gallon can of paint both brands will cost $30 and brand B paint is a better option because it costs less.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

Suppose y is the total cost and x is the gallons cases,

The equations according to the given condition are,

y = 27 x + 3

y = 2x +5

The values obtained after solving the above equation will be (1,30). As a result, 1 gallon of paint cost you $ 30.

For condition 2 Juanita needs 15 gallons of paint, x =15

For A, y = 408

For B, y = 380

The brands A and B cost $408 and $380.So the brand costs Juanita more.

Thus, if you buy 1 gallon can of paint both brands will cost $30 and brand B paint is a better option because it costs less.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ5

Answer:

319973/400

Step-by-step explanation:

800 - 27/4%

800 - ( 27/4 × 1/100)

800 - 27/400

= 319973/400

Answer:

m=1

Step-by-step explanation:

[tex]m=\frac{8-6}{2-0} =\frac{2}{2} =1[/tex]

I hope this help you

Answer:

(2)

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

1 dozen=12 eggs. 12 ×5=60

Answer:

60

Step-by-step explanation:

dozen=12

5x12=60

Answer:

This is indeed a function

Answer:

Mean = 8

Variance = 22

Standard deviation = 4.6904

Step-by-step explanation:

To find out Mean the formula is : total sum of data set / number of values

(11 + 11 + 3 + 1 + 11 + 11) / 6 = 48 / 6 = 8

Mean = 8

Now for variance we will form a table

x                  11     11     3      1      11      11

(x - Mean)    3     3    -5     -7      3      3  

(x - Mean)²   9     9    25    49    9      9

Now we the formula of variance =

Variance = (9+9+25+49+9+9)/(6-1) = 110/5 = 22

Variance = 22

Now we know Standard deviation = √(variance)

Therefore standard deviation = √22 = 4.6904

Hope this helps!<3

Answer: Mean = 8

Step-by-step explanation:

Answer:

8/25.

Step-by-step explanation:

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

Answer:

Use the distributive property to multiply 2 by x−1.

l2x-2I=11

2x-2=-11

Add 2 to both sides of the equation.

2x=-9

Divide both sides by 2.

x=13/2

That's the final answer

Hope u have a great day!!

Answer:

4(2x raise to power 2-4-7x)

Answer:

the answer is slope=94, y-intercept = 2

Step-by-step explanation:

i took the test

Answer:

493/40

i tried my best on it

Answer:

493 /40

Step-by-step explanation:

(12.325 × 100) /  (1 × 1000)  =  

=12325/ 1000