In each of Problems 9 and 10, solve the given initial value problem and determine at least approximately where the solution is valid. (2x - y) + (2y - x)y' = 0, y(1) = 3
Answers
The initial value problem (2x - y) + (2y - x)y' = 0, y(1) = 3 has the particular solution y = -x²/2 + 2x + 1/2, and is valid for all x except for x = 2y.
An initial value problem is a differential equation that is given with an initial condition, which is a specific value for the solution of the equation at a particular point.
Problem 9 and 10 involve solving the same initial value problem: (2x - y) + (2y - x)y' = 0, y(1) = 3. To solve this initial value problem, we must find the general solution to the differential equation and then use the initial condition to determine the particular solution.
First, we must find the general solution to the differential equation (2x - y) + (2y - x)y' = 0. We can rearrange the equation to get (2y - x)y' + (2x - y) = 0. This is a separable differential equation, so we can separate the variables and integrate both sides to get:
y' = -(2x - y)/(2y - x)
∫(y')dy = -∫(2x - y)/(2y - x)dx
y = -x²/2 + 2x + C
Where C is an arbitrary constant of integration. To find the particular solution, we can use the initial condition y(1) = 3. We can substitute this into the general solution to find the value of C:
3 = -1/2 + 2 + C
C = 3 + 1/2 - 2 = 1/2
So the particular solution is y = -x²/2 + 2x + 1/2. This solution is valid for all values of x such that 2y - x ≠ 0, which means that the solution cannot be evaluated for x = 2y. This is because the denominator in the differential equation would be zero, which would make the equation undefined.
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Related Questions
A cruise cost £4500 and you have to pay a 30% deposit. What is the deposit and what is the balance.
Answers
Answer:
$5350
Step-by-step explanation:
I need help solving please
Answers
The value of slope of line is,
⇒ m = - 1
We have to given that,
Two points on the line are (- 4, 5) and (- 7, 8).
Now, We know that,
Slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is,
m = (y₂ - y₁) / (x₂ - x₁)
Here, Two points on the line are (- 4, 5) and (- 7, 8).
Hence, Slope is,
m = (8 - 5) / (- 7 + 4)
m = 3 / - 3
m = - 1
Therefore, The value of slope of line is,
⇒ m = - 1
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2/5 of employees in a company drive to work, 1/3 travel by bus and the rest walk. 1. Find the fraction of who walk.
Answers
Answer:
4/15
Step-by-step explanation:
2/5 drive
1/3 bus
and rest walk
fraction of those who walk is 1-(2/5+1/3)
2/5+1/3=(6+5)/15=11/15
15/15-11/15=4/15
The extended warranty on a ceiling fan is 18% of the purchase price. If the price of the fan is $140, how much is the warranty?
The extended warranty on a ceiling fan is 18% of the purchase price. If the price of the fan is $140, how much is the warranty?
a.
$7.78
b.
$25.20
c.
$18.72
d.
$12.86
Answers
Answer:
b.$25.20
Step-by-step explanation:
Calculation for how much is the warranty
Using this formula
Warranty cost=Extended warranty purchase d price percentage*Purchased Price
Let plug in the formula
Warranty cost =18%*$140
Warranty cost =$25.20
Therefore the warranty cost will be $25.20
Answer:
B
Step-by-step explanation:
hi please help
anyone can help?
Answers
The two expressions in the second row and one expression in the first row will be 11t - 2u & 10t + 2u and 21t, respectively.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The three expressions in the third row are given below.
4t - 6u, 7t + 4u, and 3t - 2u
The two expressions in the second row are given as,
4t - 6u + 7t + 4u = 11t - 2u
7t + 4u + 3t - 2u = 10t + 2u
The one expression in the first row is calculated as,
11t - 2u + 10t + 2u = 21t
The two expressions in the second row and one expression in the first row will be 11t - 2u & 10t + 2u and 21t, respectively.
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860.89 is what percent of 437?
Answers
Answer:
197
Step-by-step explanation:
1.97 = 437/860.89
1.97=197%
Step by step explanation :
To k this we can set up an equation.
860.89 = x(437)
To get x we must divide 860.89 by 437.
That’s 1.97, or 197 percent. There you have it, 860.89 is 197 percent of 437.
Pls mark brainliest if possible and have a nice day!
Question 2: Leilamade a one-time investment of $12 000.00 in a
registered retirement savings plan (RRSP) at 2.65%, compounded
semi-annually. She plans to withdraw the money when she retires in 30
years.
a) Determine the value of the investment when she retires. Show your
work.
I
b) Calculate the rate of return [note:] over the 30 years. Show your work.
Answers
the value of the investment when she retires is $26434.92.
What is the compound interest?Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Formula:
A = P(1 + {r}/{n})^{n.t}
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
here, we have,
given that,
Leilamade a one-time investment of $12 000.00 in a
registered retirement savings plan (RRSP) at 2.65%, compounded
semi-annually.
She plans to withdraw the money when she retires in 30
years.
So, she get finally is,
using the formula we get,
$26434.92
hence, the value of the investment when she retires is $26434.92.
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5. 5(x + 10) + x
A. 6x + 15
B.5x + 15
C.6x + 50
D.4x – 50
Answers
Answer: C
Step-by-step explanation:
first step is distributive prop. so times five by everything in parentheses
5x + 50 + x
then add common variables together
6x + 50
so your answer is C
(could you please mark this brainiest)
What is the value of
0 4,194,304
020
O 1,024
O 625
Answers
Answer: 20
Step-by-step explanation:
if 4x4=16 then 16 divided by 2 =8 witch is diviseble by 20
2) Eileen wants to borrow $40,000 to buy a new car. I She is willing to make monthly payments for 5 years. The Metro Bank offers her a loan of $40,000 for five years; the rate of interest is 6% compounded monthly. If Eileen chooses to borrow the money,
a) how much total interest will she pay?
b) how much simple interest will she pay?
c) how much compound interest will she pay?
Answers
Answer:
BLM
Step-by-step explanation:
-4x -3y =9 and 5x=15 solve by substitution. SHOW WORK PLS
Answers
Answer:
\(\sf{\boxed{\sf{x=3, \quad y=-7}}}\)
Step-by-step explanation:
In order to solve the problem, all you have to do is substitute the left to right numbers in the equation.
-4x-3y=9 and 5x=15
Solve with 5x=15.
First, divide by 5 from both sides.
5x/5=15/5
Solve.
15/5=3
x=3
Substitute of x=3.
-4*3-3y=9
Solve.
-4*3=-12
Then rewrite the problem down.
-12-3y=9
You have to isolate by the y.
-12-3y=9
Add by 12 from both sides.
-12-3y+12=9+12
Solve.
9+12=21
-3y=21
Then, divide by -3 from both sides.
-3y/-3=21/-3
Solve.
21/-3=-7
y=-7
As a result, the solution is x=3, and y=-7, which is our answer.
Write down the value of the 5 in each of these
numbers.
8.154
751 602
1 567 324 896
Answers
Answer:
8.154 - 0.05
751 602 - 50 000
1 567 324 896 - 500 000 000
Morganton Company makes one product and it provided the following information to help prepare the master budget:
The budgeted selling price per unit is $60. Budgeted unit sales for June, July, August, and September are 8,600, 17,000, 19,000, and 20,000 units, respectively. All sales are on credit.
Thirty percent of credit sales are collected in the month of the sale and 70% in the following month.
The ending finished goods inventory equals 25% of the following month’s unit sales.
The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Each unit of finished goods requires 5 pounds of raw materials. The raw materials cost $2.40 per pound.
Thirty five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.
The direct labor wage rate is $14 per hour. Each unit of finished goods requires two direct labor-hours.
The variable selling and administrative expense per unit sold is $1.80. The fixed selling and administrative expense per month is $67,000.
5. If 96,250 pounds of raw materials are needed to meet production in August, how many pounds of raw materials should be purchased in July?
Answers
Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July
X pounds - 0.35 * X pounds = 9,500 pounds
Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.
To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.
Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.
The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.
To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.
Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.
The payment for raw materials purchases in July (35% of X pounds) will be:
0.35 * X pounds
The payment for raw materials purchases in August (65% of X pounds) will be:
0.65 * X pounds
Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:
Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July
X pounds - 0.35 * X pounds = 9,500 pounds
Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.
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how do i check 5p +2 = 4p - 1
Answers
Answer:-3
Step-by-step explanation:
Answer:
p = -3
Step-by-step explanation:
5p + 2 = 4p - 1
-4p -2 -4p -2
p = -3
6th grade math, help me please:)
Answers
Answer:
A. 3/5
Step-by-step explanation:
Simple math, 9/15. Divide both by 3.
3*3=9 and 3*5=15 so answer is 3/5!
Answer:
answer is A
Step-by-step explanation:
this is a probability question
divide the number of baskets made by the total number of attempts
9/15 = 3/5
Sphenathi stated that the distance from Bloemfontein to upington is 16.3 show all calculations whether his claim is correct
Answers
The distance between Bloemfontein and Upington is a distance of 582 kilometers. The distance between two cities may vary depending on the route taken, traffic, and other factors. The distance between these two cities is measured in a straight line, which may not be the actual road distance.
To determine the distance between Bloemfontein and Upington, we used the Haversine formula, which computes the shortest distance between two points on the surface of a sphere. We first begin by finding the latitude and longitude of the two cities.Bloemfontein is located at -29.1211° latitude and 26.2140° longitude.Upington is located at -28.4478° latitude and 21.2561° longitude.Using the Haversine formula, we can determine that the distance between the two cities is about 582 kilometers.Sphenathi's statement that the distance from Bloemfontein to Upington is 16.3 kilometers is incorrect. Perhaps they mistakenly calculated the distance between two points within the cities. They could also have made a typographical mistake while writing their statement. Therefore, the statement is false, and the actual distance between Bloemfontein and Upington is 582 kilometers.For such more question on longitude
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What is the mean (average) of
a, a, b, b, b,c
Answers
Answer:
Ans might be a+b+c
Step-by-step explanation:
Hope the picture will help
Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots. The test scores of 40 students are listed below. Construct a boxplot for the data set.
25 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
Answers
Answer:
Minimum = 25
First quartile = 58
Second quartile = 72
Third quartile = 80
Maximum = 98
Step-by-step explanation:
Suppose you have a jar with 380 marbles that are either red or green. You want to estimate how may marbles in the jar are red without counting all of them. You take four random samples of 16 marbles. After each sample, the marbles are returned to the jar. Choose the best conclusion you can make.
Answers
Simply count the number of red marbles in each sample and divide by the total number of marbles in the sample (16). Then, take the average of those proportions to estimate the proportion of red marbles in the jar as a whole
Based on the information provided, the best conclusion we can make is an estimate of the proportion of red marbles in the jar. We can use the four random samples of 16 marbles to calculate the proportion of red marbles in each sample, and then take the average of those proportions to estimate the overall proportion of red marbles in the jar.
It's important to note that this estimate may not be perfectly accurate, since the samples are small and may not perfectly represent the entire jar. However, it's a useful way to get an idea of how many red marbles are in the jar without having to count all of them.
To calculate the proportion of red marbles in each sample
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10.8.8 Check Your Understanding
Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to
park her car. Each night, the hotel charged d dollars and $17.20 for parking. Which equation represents the total
amount, in dollars, Allison paid for the three nights?
A) d+3(17.20) = 782.07
(B) 3d+17.20 = 782.07
C) 3(d-17.20) = 782.07
D) 3(d+17.20) = 782.07
Answers
We can see that the correct equation that can depict the problem is 3(d+17.20) = 782.07. Option D
Which equation shows the total charge?We have to look at the problem that we have here. In the case of the question that we have been asked, we can see that for the problem that has been given here, it is clear that; Allison went on a business trip and stayed at a hotel for three nights. She paid a total of $782.07 for the room and to park her car.
If it is known that Each night, the hotel charged d dollars and $17.20 for parking. We can say that let the amount that is charged for the lodging be d and we have the equation as; 3(d+17.20) = 782.07.
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Stephanie has a spinner with sections labelled 1, 2 and 3.
She spun it 100 times and recorded how many times it landed on each section in
the table below.
Work out the relative frequency of landing on an odd number, giving your answer
as
a) a fraction in its simplest form.
b) a decimal.
Section
1
Frequency 17
2
20
3
63
Answers
Answer:
\(\frac{4}{5}\)
0.8
Step-by-step explanation:
Happy to help:)
15-9x 1/2
I’ll give Brainiest
Answers
Answer:
-9x/2 + 15/2
Step-by-step explanation:
(15-9x)* 1/2
15(1/2)-9x 1/2
15/2 -9x *1/2
15/2-9x/2
-9x/2 + 15/2
Answer:
21/2 ( SEE IMAGE BELOW)
Step-by-step explanation:
Calculate the product
15- 9/2
Calculate the Differnce
21/2
so the answer is 21/2
The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
Answers
The statements that will be true about parallelogram ABCD are: A, B, D, and E.
Properties of a Parallelogram -
Diagonals of a parallelogram bisect each other into congruent segments.
Opposite angles and sides of a parallelogram are always congruent.
Alternate interior angles are always congruent in measure.
Thus, the following would be true of parallelogram ABCD:
AP ≅ CP (congruent segment's of a bisected diagonal)
BC ≅ AD (congruent opposite sides)
∠CAD ≅ ∠ACB (congruent angles)
∠BPC ≅ ∠APD (congruent angles)
Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.
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find the slope and y-intercept.
Answers
The slope and the y-intercept of the line y = 4x + 5 are given as follows:
Slope of 4.y-intercept of 4.How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:
m represents the slope of the function, which is by how much the dependent variable y increases or decreases when the independent variable x is added by one.b represents the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, the intercept is given by the value of y at which the graph crosses or touches the y-axis.The function for this problem is given as follows:
y = 4x + 5.
Hence the slope and the intercept are given as follows:
m = 4.b = 5.Missing InformationThe problem asks for the slope and the intercept of y = 4x + 5.
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the nth term of a sequence is 23-4n. Find the value of n when the nth term is - 65.
Answers
Answer:
n = 22
Step-by-step explanation:
given \(a_{n}\) = 23 - 4n and \(a_{n}\) = - 65 , then equate right sides and solve for n
23 - 4n = - 65 ( subtract 23 from both sides )
- 4n = - 88 ( divide both sides by - 4 )
n = 22
Sebastian got estimates from 7 companies for his kitchen remodel:
$27,500 $31,000 $36000 $92,000 $29,000 $30,500 and $28,500
Which measure of center best describes the data, the mean or the median?
Answers
Answer:
27.500
Step-by-step explanation:
PLZ I NEED HELP !!!! Staci works in a store that sells T-shirts. She made the graph below to show the relationship between the number of customers that come into the store each day and the number of T-shirts the store sells that day?????????
Answers
Answer:
the data points are about evenly distributed on both sides of the line
Step-by-step explanation:
hope i helped
6 divided by 1 1/8
Dont force the calcu- nvm I forgot Fractions cant be used in calculators :(
Answers
Answer:
4 and 4/11
Step-by-step explanation:
Answer:
4 4/11
Step-by-step explanation:
You start with 6/1 divided bye 11/8. You keep the 6/1, switch the division to multiplication, and flip the 11/8 to 8/11. You multiply the fractions and get 48/11. Simplifying gives 4 4/11.
Round to the nearest hundredth (2 decimal places) when necessary
Answers
Answer:
833.85 is the area of the trapezoid
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
If it's area, then:
area = 833.85 m²
Step-by-step explanation:
area = 1/2(b1 + b2)(h) = 1/2(38 + 13)(32.7) = 833.85 m²
Alice has two bags of marbles: Bag A contains 8 red and 3 blue marbles, and Bag B contains 5 red and 7 blue marbles. She randomly selects a bag and then draws one marble at random. It is blue. What is the probability that it came from Bag B?
Can you explain why the answer is 77/113? and actually answer the question if you don't know, dont post an answer
1
Answers
It might help to draw out a probability tree. Check out the diagram below. The first two branches at the top represent bags A and B. The probability of picking either bag is 1/2 assuming each bag is equally likely to be picked.
If we go with bag A, then the probability of getting blue is 3/11 since there are 3 blue out of 8+3 = 11 total. The probability of getting bag A and a blue marble is (1/2)*(3/11) = 3/22 which I've marked in the diagram as well.
If we go with bag B, then the probability of getting blue is 7/12 since there are 7 blue out of 5+7 = 12 total. The probability of getting bag B and blue is (1/2)*(7/12) = 7/24
Add up the results found getting
P(blue) = P(blue & bag A) + P(blue & bag B)
P(blue) = 3/22 + 7/24
P(blue) = 36/264 + 77/264
P(blue) = 113/264
This is shown in the diagram as well.
--------------------------------------------------
Recall that conditional probability in general is defined as follows
P(A given B) = P(A and B)/P(B)
In this problem, we'll have
P(bag B given blue) = P(bag B and blue)/P(blue)
Therefore, we can say...
P(bag B given blue) = P(bag B and blue)/P(blue)
P(bag B given blue) = (7/24)/(113/264)
P(bag B given blue) = (7/24)*(264/113)
P(bag B given blue) = (7*264)/(24*113)
P(bag B given blue) = (7*24*11)/(24*113)
P(bag B given blue) = (7*11)/(113)
P(bag B given blue) = 77/113
In short, the probability of getting bag B, given the marble is blue, is 77/113.
