The linearly independent solution of the non-homogeneous equation is y = y-c + y-p, y = c1×(x²(-1/2)cos(x)) + c2×(x²(-1/2)sin(x)) + (8/35)×x²(3/2) + (2/35)×x²(-1/2) where c1 and c2 are arbitrary constants.
The associated homogeneous equation is: x²2y'' + xy' + (x²2 - 1/4)y = 0
The complementary solution can be found by assuming y has the form y-c = c1y1 + c2y2, where c1 and c2 are constants, and y1 and y2 are the given linearly independent solutions.
y-c = c1×(x²(-1/2)cos(x)) + c2×(x²(-1/2)sin(x))
Now, the particular solution, denoted as y-p, of the non-homogeneous equation.
y-p has the form:
y-p = Ax²(3/2) + Bx²(-1/2)
where A and B are constants to be determined.
The first and second derivatives of y-p:
y-p' = A×(3/2)x²(1/2) - (1/2)Bx²(-3/2)
y-p'' = A(3/4)×x²(-1/2) + (3/4)Bx²(-5/2)
Substituting these into the non-homogeneous equation:
x²2y_-p'' + xy-p' + (x²2 - 1/4)×y-p = x²(3/2)
x²2×(A×(3/4)x²(-1/2) + (3/4)Bx²(-5/2)) + x(A×(3/2)x²(1/2) - (1/2)Bx²(-3/2)) + (x^2 - 1/4)(Ax²(3/2) + Bx²(-1/2)) = x²(3/2)
Simplifying and collecting like terms:
(3A/4)x²(3/2) + (3B/4)x²-1/2) + (3A/2)x²(3/2) - (1/2)Bx²(3/2) + (A - (1/4))x²(5/2) + (B/4)x²(1/2) - (A/4)x²(-1/2) + Bx²(-3/2) = x²(3/2)
Matching the coefficients of like powers of x:
[(3A/4) + (3A/2) - (1/2)B]x²(3/2) + [(3B/4) + (B/4)]x²(-1/2) + [(A - (1/4))]x²(5/2) + [(-A/4) + B]x²(-1/2) + [B/4]x²(-3/2) = x²(3/2)
Equating the coefficients of x²(3/2) on both sides:
(3A/4) + (3A/2) - (1/2)B = 1
(9A/4) - (1/2)B = 1
Equating the coefficients of x²(-1/2) on both sides:
[(3B/4) + (B/4)] - (A/4) = 0
(4B/4) - (A/4) = 0
Simplifying the equations:
(9A - 2B) = 4
4B - A = 0
Solving these equations simultaneously ,A = 8/35 and B = 2/35.
Therefore, the particular solution is: y-p = (8/35)×x²(3/2) + (2/35)×x²(-1/2)
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2x+3y=1470 changed to slope intercept form, write a description which is clear precise and correct of how to graph the line using the slope intercept method,changes equation to to function notation and explains clearly what the graph of the equation represents. graph the equation and labels the intercept correctly. Write at least 3 sentences explaining how the graphs of the two equations are the same and how they are different.
Answer:
y= 490 - 2x
Step-by-step explanation:
Answer: Do I get brainliest if I try? 7 = 490 - 2x
Step-by-step explanation:
Can someone help me with this problem! I WILL GIVE A BRAINIEST!!! I need it asap PLEASE.
Answer:
(
−
1
)
(
3
2
+
−
6
)
Step-by-step explanation:
it says priya's family exchanged 250 dollars for 4,250 pesos. Riya bought a sweater for 510 pesos. how many did the sweater cost?
Please help please help please URGENT PLEASE NEED HELP PLEASE FAST RESPONSE PLEASE
Answer:
x = -4, x = 4
Step-by-step explanation:
A denominator cannot equal zero since division by zero is undefined.
Set the denominator equal to zero and solve for x. That will give you the values of x that would cause the denominator to be equal to zero and must be excluded from the domain.
x^2 - 16 = 0
(x + 4)(x - 4) = 0
x + 4 = 0 or x - 4 = 0
x = -4 or x = 4
Answer: x = -4, x = 4
What is m/3= -1.5 what is m???
Answer:
-4.5
Step-by-step explanation:
M would be -4.5 because if you multiply -1.5 by 3 you get -4.5. Therefore the equation would be -4.5/3= -1.5 .
Hope this helps :))
does anyone know what this is ?
9514 1404 393
Answer:
x = 2
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relations between trig functions and angle.
Tan = Opposite/Adjacent
tan(θ) = y/x
Sin = Opposite/Hypotenuse
sin(θ) = y/4
The given relation is ...
tan(θ) = 2·sin(θ)
y/x = 2(y/4)
2 = x . . . . . . . multiply by (2x/y)
_____
Additional comment
Then the angle can be found from the relation ...
Cos = Adjacent/Hypotenuse
cos(θ) = x/4 = 2/4 = 1/2
θ = arccos(1/2) = 60°
and the value of y is ...
y = 4·sin(60°) = 2√3
Find the GCF 36, 22.
Answer:
The greatest common factor (GCF) of 36 and 22 is 2.
Answer:
2 is the GCF of 36 and 22.
A random sample of 1000 people who signed a card saying they intend to quit smoking were contacted 9 months later. Turned out that 210 (21%) of the sampled individuals had not smoked in the past 6 months. What is the population, parameter, sample and statistic?
Answer:
Population is the total number of people that fall into the description of those that the research concerns.
In this case, Population is: Everyone who signed a card saying that they intend to quit smoking.
Sample. This is a subset of the population that the research is based on.
Sample = 1,000 people surveyed.
Parameter and Statistic are both descriptive measures but parameter is for the population and statistic is for the sample.
Parameter = Percentage of total population who have not smoked in 6 months.
Statistic = 21% of sample who have not smoked in 3 months.
What is 38 times 4 plus the square root of 30
Answer:157.47722557
Step-by-step explanation:
Quadrilateral ABCD is a rectangle. The measure of angle CBE is equal to 32°, find the
measure of angle BEC.
Answer:
116 degrees
Step-by-step explanation:
well from the picture we know this is a 45 45 90 style triangle therefore in if CBE is equal to 32 then ECB should also be equal to 32 leaving you with a total number of 64 degrees within the triangle. and in every triangle you must add up the degrees to 180 so if we subtract 64 from 180 we get 116 degrees for BEC
Answer: 116
Step-by-step explanation:
32 + 32 (because the angles are complementary) + 116 = 180!
A wooden plank is 424cm long.
50% of it is cut off.
How long is the plank now?
Answer:
214cm long of wooden plank
a, b ve c birbirinden farklı pozitif tam sayılardır.
Buna göre,
a.b.c = 12
eşitliğini sağlayan kaç değişik (a, b, c) üçlüsü vardır?
A) 6
B) 9
C) 12
D) 18
E) 24
A.6 would be the answer
f(x)=x^3-6x^2+11x-6 is (x-4)
Answer: 10
Step-by-step explanation:
Answer:
x-4
Step-by-step explanation:
trust me!!
Jaden is saving money to buy a bike that costs $290. He has saved $140 so far. He plans on saving $25 each week. Write and solve an equation to determine in how many weeks (identify the question) Jaden will have enough money to buy the bike.
What does the variable in question 4a represent?
Answer:
25w+140=290
He will have enough money in 6 weeks
w represents the amount of weeks
Step-by-step explanation:
25w+140=290
$25 every week + the original $140 = the total needed $290
Answer:
140 + 25w = 290
w = 6
Step-by-step explanation:
Goal: $290
Currently have $140
Saving $25 each week (variable)
Start with your given amounts :
(base) 140 + 25w (variable solving for) = 290 (goal you want equation to equal)
w stands for the amount of weeks for the goal to be reached
Solve:
140 + 25w = 290
subtract 140
25w = 150
divide 25
w=6
Double check (optional but suggested)
140 + 25 (6) = 290
140 + 150 = 290
290 = 290
correct
What is a venn diagram
Answer:
A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things
Venn diagrams help to visually represent the similarities and differences between two concepts.
Find the value of x.
2x
fi
80
27
60
x = [?]
Enter
the answer is x=18
hope that helped^^
Mariana gets $15 per hour working at McDonald's and Jayvon gets $15 per hour as well. Jayvon had $50 in the
bank to start. After how many weeks will Jayvon and Mariana have the same amount of money in their bank
accounts?
Answer:
What r the options?
Step-by-step explanation:
50.0 divided by 100 equals??
Answer:
0.5
Step-by-step explanation:
Hopefully u got it right
Step-by-step explanation:
If you meant 50 divided by 100
[tex]\frac{50}{100} = \frac{1}{2}[/tex]
or just .5
If you meant 500 divided by 100
[tex]\frac{500}{100} = 5\\[/tex]
A man walks 10 miles in x hours. How far does he walk in one hour?
Which expression represents this?
10 + x miles
10x miles
miles
Answer:
10/x represents how far he walks in one hour
Step-by-step explanation:
PLEASE HELPP MEEE!!
I will give brainliest
Answer:
The 3rd one
Step-by-step explanation:
Let find angle z
Using law of sines
[tex] \frac{xy}{ \sin(z) } = \frac{xz}{ \sin(y) } [/tex]
Plug in the numbers
[tex] \frac{43}{ \sin(x) } = \frac{40}{ \sin(68) } [/tex]
Flip both equations
[tex] \frac{ \sin(x) }{43} = \frac{ \sin(68) }{40} [/tex]
where z=85.4 or 94.6
Using the triangle interior sun theorem,
if z=85.4 let add up all so The first 2 are rules out angles to make sure they add up to 180.
[tex]if \: z = 85.4[/tex]
[tex]85.4 + 68 + x = 180[/tex]
[tex]x = 153.4[/tex]
[tex]x = 26.6[/tex]
The fourth one doesnt have 26.6 as a angle so it cant be that
Let try if z=94.6
[tex]68 + 94.6 + x = 180[/tex]
[tex]162.6 + x = 180[/tex]
[tex]x = 17.4[/tex]
The third one has that.
Also we reuse law of sines YZ=12.9 so it is the third one.
4x=-20 solve for x show your work
Answer: x = 5
Step-by-step explanation:
Answer:
x = -5
Step-by-step explanation:
We have the expression 4x = -20 and are asked to solve x.
To solve, we need to isolate x.
4x = -20
Divide 4 :
x = -5
this from usatestprep
Answer:
either b or a
Step-by-step explanation:
Answer:
A I believe
Step-by-step explanation:
witch of the following statements are true
In this figure, angles R and S are complementary. Find the measure of angle S.
S
62°
R
PLEASE HELP ASAP
Answer:
Angle S is 28 degrees.
Step-by-step explanation:
You know angle R is 62 degrees and that angle Q is 90 degrees because the angle is marked by a teeny square (as I like to call it). You ten can add these two angles together and you will get the angle of 152 degrees. And as you should know that all angles of a triangle added together are 180 degrees you just take 180 degrees and subtract it with the two known angles added together. Thus you know that the final answer to S is 28 degrees.
The mid point of ab is m(-2,-6) if the coordinates of a are (-1,4) what are the coordinates of B
Answer:
i hate thsi coordinate chapter its very difficult chapter u know
help!!!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
it is how many more
Simplify (2/3 + 1/6).
Write the sum in the simplest form.
if you could answer this that would be so appreciated :).
Given are the lengths of two sides of a triangle. Find the range of the lengths for the third side. this is triangle inequality theorem.
1. 3.6, 10.8
2. 6.9, 3.2
3. 6, 4
I’m sorry for spam but I really need help
Only answer is you know the answer plz!
Answer:Triangle Inequality Theorem
The Triangle Inequality theorem states that
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The Converse of the Triangle Inequality theorem states that
It is not possible to construct a triangle from three line segments if any of them is longer than the sum of the other two.
The length of s is greater than 3 and less than 11
Step-by-step explanation:
To solve this equation we must first -
2x - 4= 10
O subtract 4 from both sides
O add 4 to both sides
divide by 4
O multiply by 4
Answer:
divide by 4
Step-by-step explanation:
2x - 4 = 10
10 ÷ 4 = 2.5
2.5 ÷ 2 = 1.25
x = 1.25
Answer:
ADD 4 to both sides
Step-by-step explanation:
2x-4=10
2x+4=10+4
2x=10+4
2x=14
2x/14
x=7
Hope this helps:)
Solve for p.
16p = 160
Answer
160 divided by 16 = 10
Answer: 16p=160:
P = 10Step-by-step explanation:
If you times by ten at any time then just add a zero to the end. So just add a zero to 16 to make it 160
In this case your going to solve it like this:
160 / 16 = 10