Answer:
1/3 (a+b)
Step-by-step explanation:
The required solution is 1/3ab.
It is required to find the solution.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Let the 2 numbers be a and b.
According to given question we have,
Product =a× b=ab
1/3 of product =1/3ab
Therefore, the required solution is 1/3ab.
Learn more details about arithmetic here:
https://brainly.com/question/11559160
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Differential Equation
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]
Seventy-nine ÷ nine and five
Answer:
13.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
If a certian perosn has a mass of 250kg on earth, would that person's mass be on the moon, if the moon's gravity is 1.62m/s2? *
10 points
245kg x 1.62m/s2
245 x 1.62m/s2
It remains the same
The person would be weightless
Answer:
Weight On the Moon: 41.34 kilograms
Step-by-step explanation:
day!
Altea is making pumpkin spice cupcakes.
She needs 15 ounces of pureed pumpkin
for each batch. If she makes 16 batches of
the cupcakes, how many ounces of the
pureed pumpkin will she need?
o
Answer:
240oz.
Step-by-step explanation:
15oz=1batch
She needs 16 batches.
15oz. x 16batches = 240oz.
Hope this helps :)
There are 550 calories in 100 g of bacon. There are 196 calories in a fried egg. Philip has 60 g of bacon and two fried eggs for breakfast. Work out the total number of calories in this breakfast.
Answer:
509.6 calories
Step-by-step explanation:
196+196=392 calories
10g of bacon=19.6 calories
60g of bacon=19.6×6=117.6 calories
392+117.6=509.6 calories
Solve each of the following equations. Show its solution set on a number line. Check your answers. 2|2-x|=-5
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!!
How does insurance reduce social burden?
A. Insurance ensures that people don't have to pay high deductibles.
B. Insurance ensures that losses are not passed on to society.
C. Insurance ensures that lenders publicize rates and treat all
customers equally.
D. Insurance ensures that people are treated fairly in hiring and
employment decisions.
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 :)
How many eggs are 5dozens
Answer:
60
Step-by-step explanation:
1 dozen=12 eggs. 12 ×5=60
Answer:
60
Step-by-step explanation:
dozen=12
5x12=60
Which set of side lengths will form a triangle
A: 16ft, 4ft, 21ft
B: 30ft, 30ft, 60ft
C: 12ft, 12ft, 20ft
D: 3ft, 5ft, 10ft
PLS HELP
Answer:
the set of side lengths will be d
Complete the equation for the line shown in the graph. (-1,-2) (0,1) (1,4)
Factor this completely thank you
Answer:
4(2x raise to power 2-4-7x)
Solve for X. 22 = 10x Simplify your answer as much as possible. x = 음. 6 08 ?
Answer:
x=11/5
Step-by-step explanation:
isolate x
22/10 = 10x/10
22/10 = x
simplify
11/5 = x
Write the first five terms for the following recursive rule.
f(1)=7
f(n)=f(n-1)+12
Answer:
PLEASE MARK ME AS BRANLIEST!!!!!
Step-by-step explanation:
a1 = first term; an= an-1 + d a1 = the first term in the sequence an = the nth term in the sequence an-1 = the term before the nth term n = the term number d = the common difference.
{10, 15, 20, 25, 30, 35, } first term = 10, common difference = 5 recursive formula: a1= 10; an= an-1 + 5
f(n) = f(n-1) + 12
f(1) = 7
f(2) = (7-1) + 12 = 18
f(3) = (18-1) + 12 = 29
f(4) = (29-1) + 12 = 40
f(5) = (40-1) + 12 = 51
7, 18, 29, 40, 51
If xcos(x)= 2, find (-x) • cos(-x)
[tex](-x) \cos(-x)\\\\=-x \cos x \\\\=-(x \cos x)\\\\=-2[/tex]
need help with these two math problems
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
Dora opens a savings account and puts in $ 290 at the start. Every week, she deposits $ 30 in the account. Which type of function would you use to model the relationship between the number of weeks since Dora opened the account, and the amount of money in the account
Answer:
f(x)=290+30x
Step-by-step explanation:
the 290 is for the money initially put in, the 30 is for the thirty dollars, and the x represents the number of weeks.
)) Fill in the missing number.
()) 70% of
=
56
Answer: x=80
Step-by-step explanation: multiplying both sides by 100 and dividing both sides by 70 then we have x=56 x 100/70 then your answer is x=80. If you're using a calculator, simply enter 56x100 divided by 70 which will give you the answerLet that be x
70% of x=567/10 × x=56x=56×10/7x=8(10)x=80Solve the equation: 3.017 + k = 5.134
Answer:
k=2.117
Step-by-step explanation:
Answer:
3.017 + k = 5.134
So, k = 5.134 - 3.017
So, k = 2.117
what is 5 sixths of a full rotation
Answer:
300°
Step-by-step explanation:
what is 5/6 of a full rotation?
A full rotation is 360°
360 * 5/6 = 300°
Can someone help me please
Answer:
40 students earned a B on this paper.
40%×80=32 people who chose action as their fav.
please help me i’ll give brainlist and points
Answer:
Area solution
Step-by-step explanation:
A=(16+10)×12/2= 156 m^2
This table represents the number of pounds, p, a puppy grows after w, weeks.
When graphed, all of the points in the table lie on the same line.
What is the slope and y-intercept of the line?
slope=−94, y-intercept=−0.8
slope=−49, y-intercept = 2
slope=49, y-intercept=−0.8
slope=94, y-intercept = 2
Weeks, w Weight in pounds, p
0 2
2 6.5
4 11
6 15.5 help plz
Answer:
the answer is slope=94, y-intercept = 2
Step-by-step explanation:
i took the test
Is this a function or not a function?
Answer:
This is indeed a function
What is the slope of the line that has a y-intercept of (0, 6) and passes through the point (2, 8)?
m= ?
Answer:
m=1
Step-by-step explanation:
[tex]m=\frac{8-6}{2-0} =\frac{2}{2} =1[/tex]
I hope this help you
1.
Write the equation of the parabola in vertex form.
A. y = –(x – 1)2 + 3
B. y = –x2 – 4
C. y = –x2 + 3
D. y = –x2 + 4
[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
Can someone help me please I’ve been stuck for a week :(
Answer:
8/25.
Step-by-step explanation:
As a fraction it is 32/100 but simplified is 8/25 :)
What is 6 3/4 percent of 800
Answer:
319973/400
Step-by-step explanation:
800 - 27/4%
800 - ( 27/4 × 1/100)
800 - 27/400
= 319973/400
what are the mean variacne and standard deviatioon of the values? round to the nerates tenth. 11,11,3,1,11
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:
pls help the will mean the world
Answer:
A: the area of the walls that are being painted
C: the cost per gallon of different paints
F: the number of square feet that can be painted per gallon of paint
Step-by-step explanation:
Write 12.325 as a mixed number. quick I need help
Answer:
493/40
i tried my best on it
Answer:
493 /40
Step-by-step explanation:
(12.325 × 100) / (1 × 1000) =
=12325/ 1000