The given differential equation has the answer C₁ +C₂ 1/81 -x⁹ +1/9 x⁹ln(x). It has been solved using the variation of parameters method below.
We have the differential equation xy'' − 8y' = x^8. In order to solve any differential equation using the variation of parameters method, we first write the equation as and solve -
= xy'' − 8y' = 0
After solving this, we get the Auxiliary equation-
so CF is y = 1/9 x⁹ + C₁ +C₂
Now, we write -
y1 (x) = 1/9 x⁹
y2 (x) = 1
y1'(x) = x^8
y2'(x) = 0
now, using wronskian formula
= W = -x^8
Now, applying the formulas -
= u = [tex]- \int{\frac{f(x)y2(x)}{W(x)} } \, dx[/tex] and v = [tex]\int{\frac{f(x)y1(x)}{W(x)} } \, dx[/tex]
= u = log(x) and v = -x⁹/81
now particular integrals are
PI = 1/81 -x⁹ +1/9 x⁹ln(x)
total solution
y = C.F+P.I
y = C₁ +C₂ 1/81 -x⁹ +1/9 x⁹ln(x)
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A rectangle has vertices A(1, 6), B(6, 6), C(6, 3) and D(1, 3). What is the "Area" of the rectangle?
Answer:
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
Length times width. 3 is length and width is 5
30. Which reason justifies the statement below?
A. Definition of Congruence
B. Angle Addition Postulate
C. Supplement Theorem
D. Definition of Vertical Angles
The correct reason for the statement ∠1 ≅ ∠2 will be;
⇒ Definition of Vertical Angles.
Option D is true.
What is Vertical angles?
When the two lines are crosses to each other at a point then the vertical angles are formed.
Given that;
∠1 and ∠2 are formed between two lines which crosses at a point.
Now,
The two lines are vertical lines which passes through a point and ∠1 and ∠2 are formed between them.
So, By definition of Vertical Angles;
∠1 ≅ ∠2
Therefore,
The correct reason for the statement ∠1 ≅ ∠2 will be;
⇒ Definition of Vertical Angles.
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El triple del mayor de tres números pares consecutivos, más 6 es igual al doble del menor. Encuentra el número mayor. Porfaaaa :(
Answer:
-14. Aunque podría estar equivocado. Espero poder ayudar
Step-by-step explanation:
prove that Sn=n(n+1) for the sequence an=2n,where n is any positive integers
Answer:
Proved
Step-by-step explanation:
Given
[tex]a_n = 2n[/tex]
Required
Prove that [tex]S_n = n(n+1)[/tex]
The given sequence is an arithmetic sequence.
The Sn of this sequence is:
[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]
Calculate a1
[tex]a_n =2n[/tex]
[tex]a_1 =2*1[/tex]
[tex]a_1 =2[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(a_1 + a_n)[/tex]
[tex]S_n = \frac{n}{2}(2 + 2n)[/tex]
Factor out 2
[tex]S_n = \frac{n*2}{2}(1 + n)[/tex]
[tex]S_n = n(1 + n)[/tex]
[tex]S_n = n(n + 1)[/tex] --- Proved
Ms. Halloween works in a factory. She receives a salary of $9.10 per hour and piecework pay of 15 cents per unit produced. Last week she worked 40 hours and produced 988 units. a. What was her piecework pay? What was her total hourly pay for the week? What was her total pay for the week? b. If her boss offered to pay her a straight $13 per hour and no piecework pay for the week, would she earn more or less than under the piecework pay system? c. What would her total weekly salary have been if she produced 0 units?
Answer:
1065.1
Step-by-step explanation:
Part a:
1. Halloween's piecework pay = $148.20
2. Halloween's total hourly pay for the week = $364
3. Halloween's total pay for the week = $512.20
Part b:
Total amount received for the week = $520 and she earns more when she get the straight salary on hourly basis.
Part c:
Halloween's hourly pay for 0 units production = $364
What is a salary?
Salary is a compensation or fixed amount of money paid to an employee by an employer in return for work performed.
For the given situation,
Halloween's salary received per hour = $9.10
Halloween's piecework pay per unit = 15 cents
Total work per week = 40 hours
Total unit produced per week = 988 units.
Part a:
1. Halloween's piecework pay = [tex](988)(15)[/tex]
⇒ [tex]14820 cents[/tex]
we know that $1 = 100 cents
⇒ [tex]\$148.20[/tex]
2. Halloween's total hourly pay for the week = [tex](40)(9.10)[/tex]
⇒ [tex]\$364[/tex]
3. Halloween's total pay for the week = [tex]364+148.20[/tex]
⇒ [tex]\$512.20[/tex]
Part b:
Halloween's boss offered to pay her a straight $13 per hour and no piecework pay for the week.
Total amount received for the week = [tex](40)(13)[/tex]
⇒ [tex]\$520[/tex]
Difference in pay = [tex]520-512.20[/tex]
⇒ [tex]\$7.80[/tex]
Thus, she earns more when she get the straight salary on hourly basis.
Part c:
If her production is 0 units, then she might get her hourly pay only.
⇒ [tex](40)(9.10)[/tex]
⇒ [tex]\$364[/tex]Hence we can conclude that
Part a:
1. Halloween's piecework pay = $148.20
2. Halloween's total hourly pay for the week = $364
3. Halloween's total pay for the week = $512.20
Part b:
Total amount received for the week = $520 and she earns more when she get the straight salary on hourly basis.
Part c:
Halloween's hourly pay for 0 units production = $364
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Given the linear equation & its graph, what is the slope?
Answer:
Slope: 5/3
Step-by-step explanation:
Linear equation:
y = mx + b
m is the slope
so if,
y = 5/3x - 4
5/3 is the slope.
Hope this helps :)
Let me know if there are any mistakes!!
Your uncle is 2 years older than 3 times your age.
You are x years old. Write an expression to describe your uncles age.
It would be a lot helpful if you could answer this! :D
you are x
three times is 3x
2 years older is 3x + 2
Answer:
3x+2
Step-by-step explanation:
3 times x plus 2 since he's 2 years older than that
It's math,I'll send u a picture!
Answer:
suree.
Step-by-step explanation:
The area of Ms. Anderson’s office floor measures 120
square feet. She puts down a carpet that covers 40%
of the floor. What is the area of Ms. Anderson’s floor not covered by the carpet?
Answer:
72 square feet not covered
Step-by-step explanation:
100%-40% = 60%
60% of 120 = 0.6x120 = 72
Answer:
72
Step-by-step explanation:
because i know
PLEASE HURRY!
Type the correct answer in each box.
The table shows Alice's age (a) and her daughter Martha's age (m). Complete the table and the equation.
Alice’s Age in Years
(a) Martha’s Age in Years
(m)
28 6
33 _
37 15
41 19
48 _
This equation relates Alice’s and Martha's ages in years.
Alice’s age (a) = Martha’s age (m) + _
Answer:
33-11
48-26
Alice’s age (a) = Martha’s age (m) + 22
Step-by-step explanation:
In order to find the blank spots you would need to find the difference in the filled spots. We are trying to figure out the difference which is subtraction.
28 - 6 = 22
To make sure we are correct we would do another problem.
37 - 15 = 22
So in order to find Martha's age when Alice was 33, we would subract 22.
33 - 22 = 11
Same when Alice was 48.
48 - 22 = 26
And the last equation is asking the difference between them, which would be 22.
Answer: 11 and 26
Step-by-step explanation:
hope this helps :)
Please help with this area assignment
Answer:
375
Step-by-step explanation:
15 times 25 equals 375
a que numero micro corresponde 7/2
Answer:
31/2 d nada xdddddddddddddddddddddddddddd
I need help with this question
Answer:
2,540 miles
Step-by-step explanation:
The computation of the fewer miles is given below;
For Space explorer B
= 15,000 miles ÷ 5 hours
= 3,000 miles per hour
For space explorer A
y = 4,600 x
That means in one hour it covered 460 miles
So, the fewer miles would be
= 3,000 - 460
= 2,540 miles
1. A house cost $112,000 in 2010. By the year 2015, the house had a value of $132,000. What was the growth rate as a percent for that 5-year period?
Pls help
A. 6.48%
B. 3.34%
C. 5.23%
D. 2.15%
Answer:
The growth rate for the period was of 17.86%.
Step-by-step explanation:
To find the growth rate as a percent, we multiply the change by 100, and divide by the initial value.
A house cost $112,000 in 2010. By the year 2015, the house had a value of $132,000.
Change: 132 - 112 = 20
Initial value: 112
Growth rate as a percent:
20*100/112 = 17.86%
The growth rate for the period was of 17.86%.
Answer:b
Step-by-step explanation:
write a real-world problem given the equation 2/3x = 12. Then solve the equation.
Answer:
You want to buy long pieces of paper at Dollar Tree for 66 cents. You have $12. How many long pieces of paper can you buy
Step-by-step explanation:
Which professionals most directly use geometry In their work?
O A. accountants
© B. astronomers
O C. judges
© D.
pharmacists
O E. politicians
Answer:
Step-by-step explanation:
The carnival also offers two magic shows. The morning show is only 20 minutes and it costs $3.75. For the afternoon show, it is 35 minutes and costs $5.25. Which show would give you more for your money?
Answer:
35 minutes
Step-by-step explanation:
The carnival offers two magic shows
The morning show is for 20 mintes at $3.75
= 3.75/20
= 0.1875
The afternoon show is for 35 minutes at $5.25
= 5.25/35
= 0.15
Hence you pay a lesser amount for 35 minutes
how do you write this number 0.1709 in words?
Answer:
0.1709 in words-
Point one seven zero nine
Find the quotient. Answer as a decimal.
–6 ÷ 1
1
3
3
1
Answer:
≈ -0.0005
Step-by-step explanation:
simplify the expression 4x+2-1/2x
answer 41x
Step-by-step
The sum of two numbers is 15. Twice the large
number plus 4 times the smaller number is 24.
Find the large number.
Hellllllllppppp meeeee
Answer:
x=18°
Step-by-step explanation:
5x-18=4x
subtract 4x from both sides
x-18=0
add 18 to both sides
x=18°
ayudaa para mañana !!
Answer:
ok bueno dejamr haber que ago
Answer:
2/5 > 1/3
9/20 > 13/30
17/12 < 22/15
Step-by-step explanation:
Encuentra un denominador común. por ejemplo, 2/5 y 1/3 tienen un denominador común de 15. 2/5 se convierte en 6/15 y 1/3 se convierte en 5/15. 6 es mayor que 5. ¡Espero que esto ayude y buena suerte!
If 5 hours is 25% of the time a trip will take, how long will it take?
Answer:
20 hours
Step-by-step explanation:
Answer:
20
Step-by-step explanation:
We know that 25% is 1/4 of the time. So 5 hours would be multiplied by 4, which is the reciprocal of 1/4.
5 x 4 = 20, so that's your answer. I hope I helped :)
A pair of shoes that normally sells for $74.88 goes on sale for 25% off. What is the sale price?
Answer:
$56.16
Step-by-step explanation:
74.88 times 0.75 =56.16
Answer:
$56.16
Step-by-step explanation:
To find the sale price, multiply the original price by 0.75:
74.88(0.75)
= 56.16
So, the sale price is $56.16
PLEASEEEEEEEEEEEEE ANSWER THIS FASTTTTTTTTTTTTTTTT
Answer:
B 2:1
Step-by-step explanation:
Given two points (-3, 1) and (4, -1) are on a line. Write an equation in slope-
intercept form of the line.
y=____x+____
Answer:
y=-2/7x+1/7
Step-by-step explanation:
Find the slope first
-1-1/4+3
-2/7
m=-2/7
y=-2/7x+b
1=-2/7(-3)+b
b=1/7
14000.00 rate 8% 60 days simple interest
Answer:186.66is answer
p=14000
r=8%
time=60days=2month/12=1/6year
Step-by-step explanation:
simple interest=ptr/100=14000×8×1/600=186.666
For each statement, write what would be assumed and what would be proven in a proof by contrapositive of the statement. Then write what would be assumed and what would be proven in a proof by contradiction of the statement.
a. If x and y are a pair of consecutive integers, then x and y have opposite parity.
b. For all integers n, if n² is odd, then n is also odd.
Answer:
a)
Given Statement - If x and y are a pair of consecutive integers, then x and y have opposite parity.
Proof by Contrapositive:
Assumed statement: Suppose that integers x and y do not have opposite parity.
Proven Statement: x and y are not a pair of consecutive integers.
Proof -
x = 2u₁ , y = 2u₂
Then
(x, x+1) = (2u₁ , 2u₁ + 1) = (Even, odd)
If y = 2u₁ + 1
Not possible
⇒x and y are not a pair of consecutive integers.
Hence proved.
Proof by Contradiction:
Assumed statement: Suppose x and y are not a pair of consecutive integers.
Proven Statement: Suppose x and y do not have opposite parity.
Proof -
If x and y are not a pair of consecutive integers.
⇒ either x and y are odd or even
If x and y are odd
⇒x and y have same parity
Contradiction
If x and y are even
⇒x and y have same parity
Contradiction
(b)
Proof by Contrapositive:
Assumed statement: Let n be an integer such that n is not odd (i.e. n is an even integer)
Proven Statement: n² is not odd (i.e n² is even)
Proof -
Let n is even
⇒n = 2m
⇒n² = (2m)² = 4m²
⇒n² is even
Hence proved.
Proof by Contradiction:
Assumed statement: Let n be an integer such that n² be odd.
Proven Statement: suppose that n is not odd (i.e n is even)
Proof -
Let n² is odd
⇒n² is even
⇒n² = 2m
⇒2 | n²
⇒2 | n
⇒n = 2x
⇒ n is even
Contradiction
Fine the area of this figure.what two shapes can you decompose.