Giải phương trình vi phân sau
Y"=2y'+y=e^x
You likely mean to write the differential equation,
y'' - 2y' + y = exp(x)
The homogeneous part
y'' - 2y' + y = 0
has characteristic equation
r² - 2r + 1 = (r - 1)² = 0
with a root at r = 1 with multiplicity 2, so the characteristic solution is
y = C₁ exp(x) + C₂ x exp(x)
For the particular solution, we assume an ansatz
y = ax² exp(x)
where a is an unknown constant. Differentiating the ansatz twice:
y' = ax² exp(x) + 2ax exp(x) = (ax² + 2ax) exp(x)
y'' = (ax² + 2ax) exp(x) + (2ax + 2a) exp(x) = (ax² + 4ax + 2a) exp(x)
Substitute y and its derivatives into the DE:
(ax² + 4ax + 2a) exp(x) - 2 (ax² + 2ax) exp(x) + ax² exp(x) = exp(x)
Solve for a :
(ax² + 4ax + 2a) - 2 (ax² + 2ax) + ax² = 1
2a = 1
a = 1/2
Then the particular solution is
y = 1/2 x² exp(x)
The general solution is then
y = C₁ exp(x) + C₂ x exp(x) + 1/2 x² exp(x)
whats 5+5? please help quick quick quick
Answer:
It's 10 lol
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Because it is
Write an equation of the line passes through (4,1) and is parallel to y=-2x+7 .
Answer:
y= -2x+9
Step-by-step explanation:
First of all, since they need to be parallel, they must have the same slope to never intercept. Next, you can use a graphing calculator to test y-intercepts like desmos. You will find that 9 works, as it goes through (4,1) and never intercepts with the 1st line.
A Biology test has 20 questions and is worth a total of 100 points. The test
consists of True/False questions worth 2 points each and multiple choice questions
worth 7 points each. How many of the test questions
are multiple choice and how
many of the test questions are True/ False?
# of true/false questions =
# of multiple choice questions =
THIS IS ALGEBRA PLEASE
Answer:
I've done alot of calculations on this but I cant get a definite answer I hope you got it I'm sorry I couldn't help you I tried but only got into a dead end
On a number line, where would 2/10 be located? Choose all answers that make
a true statement.
a box contains 4 red balls and 6 purple balls. Ezra takes out a ball, puts it back and then takes out another ball. what is the probability that both balls were red
Answer:
16/100 = 4/25
Step-by-step explanation:
4/10 * 4/10 = 16/100
what is the unit rate if there are 1,760 in 8 servings
Answer:
Unit rate = 220 calories
Step-by-step explanation:
In order to find the unit rate, you simply have to divide the total number of calories (1760) by the number of servings (8).
1760/8=220.
Therefore, the unit rate is 220 calories.
Multiply the numerator and the denominator of the given fraction by the following factor to find an equivalent fraction
Fraction: 8/15
Factor: 4x
Answer:
32/60
Step-by-step explanation:
because you are multiplying both the numerator and denominator by the same factor, you will get the same ratio (producing an equivalent fraction)
numerator: 8*4=32
denominator: 15*4=60
final equivalent fraction: 32/60
help plssssssssssssssssssssssssssssssssssssss
combine like terms (3x-2y+z)+(5z-8x-5y)+(-15x+8z)
Answer:
−20−7+14
Step-by-step explanation:
WILL MARK BRAINLIEST The width of a table is 2 feet less than the length. The area is 20 square feet. Find the dimensions. Show and
explain all work using mathematical concepts in this module.
Answer:
length ≈ 5.583 ft
width ≈ 3.583 ft
Step-by-step explanation:
If we let x represent the length of the table in feet, then the width is (x-2). The area is ...
A = LW
20 = x(x -2)
Writing this in standard form gives ...
x^2 -2x -20 = 0
The coefficients used in the quadratic formula are a=1, b=-2, c=-20. The solutions are ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-2)\pm\sqrt{(-2)^2-4(1)(-20)}}{2(1)}\\\\=\dfrac{2\pm\sqrt{4+80}}{2}=1\pm\sqrt{21}[/tex]
Of these values, the only one that makes sense is ...
length = 1+√21 ≈ 5.583 ft
width = length -2 ≈ 3.583 ft
Let width is x
length be x+2
Area=Length ×Breadthx(x+2)=20x²+2x=20x²+2x-20=0On solving
we get
x is around 3.58 or 3.6ft
Width=3.6ftLength=3.6+2=5.6ftRobin is making floral arrangements for a party. Each arrangement has 8 roses and 10 carnations. Each carnation costs $0.75 and each rose costs $1.85. Which expression represents the total cost for one arrangement? A 8 + 10 + (0.75 + 1.85) B (8 + 0.75)(10 + 1.85) C 10(0.75) + 8(1.85) D 8(0.75) + 10(1.85)
QUESTION 18 PLEASE HELP ME ASAPP
Answer:
constant over time
Step-by-step explanation: for every 3 cookies the cost goes up 2 dollars
1plss help, it time.............................
Answer:
24 in
Step-by-step explanation:
Compare "like" things:
Big/small = Big/small
30/L = 10/8
Crossmultiply
240 = 10L
Divide by 10
240/10 = 10L/10
24 = L
Help help bell help be math ASAP
Answer:
2x + 2 = 28
2x = 26
x = 13
Step-by-step explanation:
In circle L with mZKLM 74 and KL = 10 units, find the length of arc KM.
Round to the nearest hundredth.
happy to you are you happy
A factory wants to fill a conical storage tank with sand. The tank has a height of 23.7 meters and a diameter of 21.4 meters.
Calculate the volume of the storage tank to the nearest hundredth.
Answer:
ur mom
Step-by-step explanation:
ur mom + 3= 69
The volume of the storage tank to the nearest hundredth is 2840.04 m³.
Given that, the conical tank has a height of 23.7 meters and a diameter of 21.4 meters.
What is the volume of a cone?The volume of a cone is the amount of space occupied by a cone in a three-dimensional plane. A cone has a circular base, which means the base is made of a radius and diameter.
The volume of a cone formula is 1/3 πr²h.
Put h=23.7 meters and radius = 21.4/2 = 10.7 meters in the volume of a cone formula
That is, 1/3 × 3.14 × (10.7)² × 23.7
= 2840.0389 m³
≈ 2840.04 m³
Therefore, the volume of the storage tank to the nearest hundredth is 2840.04 m³.
To learn more about the volume of a cone visit:
https://brainly.com/question/1984638.
#SPJ6
help me please please
Answer:
i think its D or 14/16
Step-by-step explanation:
Answer:
[tex]\frac{14}{16}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}[/tex] + [tex]\frac{10}{16}[/tex]
Before adding we require the denominators of both fractions to be common
Multiply numerator/ denominator of first fraction by 4
= [tex]\frac{1(4)}{4(4)}[/tex] + [tex]\frac{10}{16}[/tex]
= [tex]\frac{4}{16}[/tex] + [tex]\frac{10}{16}[/tex] ( now add the numerators leaving the common denominator )
= [tex]\frac{4+10}{16}[/tex]
= [tex]\frac{14}{16}[/tex]
The fraction can be simplified by dividing the numerator/ denominator by 2 to
[tex]\frac{7}{8}[/tex]
How many terms does the expression 14 + 9 have? What are they? Explain how you know.
Answer:
23, so 1. i know because i added 14+9 and got 23. im sorry if you meant like a definition term, please comment if thats what you meant. because i'll help you then.
Step-by-step explanation:
A statistics teacher was interested in the relationship between the number of days students waited to start a project
and the score that project received (out of 100 points). Information was collected on several students and was used
to obtain the regression equation ý= -3.64x + 96.5, where x represents the number of procrastination days and ý is
the predicted grade. What is the predicted grade of a student who procrastinated for 1 week?
O24.59
71.02
O 92.86
O. 96.5
Answer:
71.02
Step-by-step explanation:
x is the number of days
1 week = 7 days
-3.64 (7) + 96.5 = 71.02
A sequence begins with-3. Each term is calculated by multiplying the previous term by -4, then subtracting 1.
Which option correctly represents the sequence described?
A -3, 11, -45, 179, ...
B {-3, -13, -53, -213, ...}
C. {-3, 11, -45, 179, ...}
D -3, -13, -53, -213,...
Answer:
A
Step-by-step explanation:
We know that to find the next term we have to do
-3(-4)-1, which is equal to 11.
There are only to solutions with the '11' as the second term, A and C.
It can't be C as curly brackets state a set of numbers.
10 miles per hour is an example of an objects what?
Step-by-step explanation:
Speed is the correct answer
Look at the graph below. What is the slope of the line?
A. - 1/2
B - 2
C. 1/2
D. 2
Answer:
1/2
Step-by-step explanation:
We know two points on the line
(-1,1) and (3,3)
The slope of a line is given by
m = (y2-y1)/ (x2-x1)
= ( 3-1)/(3- -1)
= (3-1) /(3+1)
= ( 2/4
= 1/2
Recently, your parents read in the newspaper that American factory worker jobs have the lowest income ra
What is the best explanation for this fact?
A A factory worker does not need a lot of education
B Companies are relocating factories to other parts of the world.
C Factories are always in poor areas.
D A computer can do the work a factory worker currently does
Answer:
A. A factory worker does not need a lot of education.
Step-by-step explanation:
The answer is " A " which is a factory worker does not need a lot of education. since most people don't have a PHD degree or anything higher education, it results in a lot of people joining due to the benefit of the factory worker doesn't need a lot of worker which makes it low in demand too.
What is the LCD/LCM of this equation
-12.2 + 2.8W - 8.8 = 1.05w
Answer: 2.8 W. 2.6 W. 2.4 W. 2.2 W. 2.0 W. 1.9 W. 1.7 W
Step-by-step explanation:
Answer:
LCD/ LCM = 100
Step-by-step explanation:
- 12.2 + 2.8W - 8.8 = 1.05W
- 12 [tex]\frac{2}{10}[/tex] + 2 [tex]\frac{8}{10}[/tex] W - 8 [tex]\frac{8}{10}[/tex] = 1 [tex]\frac{5}{100}[/tex] W
- [tex]\frac{122}{10}[/tex] + [tex]\frac{28}{10}[/tex] W - [tex]\frac{88}{10}[/tex] = [tex]\frac{105}{100}[/tex] W
the LCM/ LCD is 100
r less than one-eighth
Answer:
what did you mean
Step-by-step explanation:
is not a question
What is the vertex of the absolute value function below?
(will give brainliest)!!!
(–3, –2)
(–3, 2)
(2, –3)
(2, 3)
Answer:
(-3,2)
Step-by-step explanation:
Go where the two coordinates match, you'll see that it's (-3,2).
I see that that's Edge2021, I know how that feels. :/
Hope this helped! :)
Answer:
(-3, 2)
Step-by-step explanation:
You start at your school, 10 miles from your house and walk home at a rate of 2 miles per hour **negative slope since you are walking toward your house so the distance to home is DECREASING Distance from Home In Miles Distance from Home (Miles) TO 5 Time (Hours)
Answer:
Step-by-step explanation:
If you're supposed to plot that, it would be a line from (0, 10) to (5, 0)
slope would be -2 mi/hr
A rectangle has a perimeter of 270cm and its length is 2½cm times its width find its width
Answer:
Width = 38.57cm
Step-by-step explanation:
Perimeter = 270cm
Let x be the width, so
Length = 2 1/2 x = 5x/2
Perimeter of Rectangle = 2(length + width)
270cm = 2(5x/2 + x)
270 = 5x + 2x
7x = 270
x = 38.571 cm
Therefore, the width is 38.57cm (rounded to 2nd decimal place)
Answer:
width = 38.6 cm (approx.)
Step-by-step explanation:
let the width be x cm, so that the length is 2.5x cm.
Perimeter = 2 (length + width)
2 (length + width) = 270 cm
or, 2 (2½x cm + x cm) = 270 cm
or, 3½x cm = 270/2 = 135 cm
or, x = 270/7 cm = 38.6 cm (approx.)
helpp anyone?? :(
No linkssss porfavorr plaesaaje cjkq
Answer:
127/100 = 1.27
1.4
1 whole and 1/3 = 1.5
Step-by-step explanation:
Hope this helps
May I get Braineist pls