Solve the given differential equation by using an appropriate substitution. The DE is of the form dy/dx = f(Ax + By + C), which is given in (5) of Section 2.5. dy/dx = 4 + (y − 4x + 6)^1/2

Answers

Answer 1

dy/dx = 4 + √(y - 4x + 6)

Make a substitution of v(x) = y(x) - 4x + 6, so that dv/dx = dy/dx - 4. Then the DE becomes

dv/dx + 4 = 4 + √v

dv/dx = √v

which is separable as

dv/√v = dx

Integrating both sides gives

2√v = x + C

Get the solution back in terms of y :

2√(y - 4x + 6) = x + C

You can go on to solve for y explicitly if you want.

√(y - 4x + 6) = x/2 + C

y - 4x + 6 = (x/2 + C

y = 4x - 6 + (x/2 + C


Related Questions

b Draw a picture to show 3:5= 6:10. Explain how your picture show equivalerit ratios.​

Answers

Answer:

3:5 = 6:10

3x2 : 5x2

= 6:10

Answer:

Step-by-step explanation:

Draw 3:5 balls shaded, and draw 6:10 balls shaded. Then, divide the 10 balls into two, with three shaded balls and 5 total balls on one side.

if 12 +2 =2 orderly what is 6 +3 orderly​

Answers

Answer:

3

Step-by-step explanation:

Please Mark me brainliest

Answer:

aren't one of the numbers in the equations supposed to be negative?

(03.04) Use the graph below for this question: What is the average rate of change from x = −3 to x = 5? (1 point)
A.−1
B.0
C.1
D.8

Answers

Answer:

B. 0

Step-by-step explanation:

Rate of change from x = -3 to x = 5

Rate of change = [tex] \frac{f(b) - f(a)}{b - a} [/tex]

where, from the graph, we have:

a = -3, f(a) = -1,

b = 5, f(b) = -1,

Plug in the values

Rate of change = [tex] \frac{-1 -(-1)}{5 - (-3)} [/tex]

Rate of change = [tex] \frac{0}{8} [/tex]

Rate of change = 0

(ii). nth term of: 10+4-2...​

Answers

9514 1404 393

Answer:

  an = 10 -6(n -1)

Step-by-step explanation:

The series is an arithmetic series with a first term of 10, and a common difference of 4-10 = -6. The n-th term of an arithmetic series is given by ...

  an = a1 +d(n -1) . . . . . for first term a1 and common difference d

__

For the parameters this series has, the n-th term is ...

  an = 10 -6(n -1)

Melinda takes out a loan to purchase a car. The balance on her loan after x months is represented by the equation y = 10,000 – 250x and the value of the car after x months is represented by y = 8,000 – 50x. Which statement describes when Melinda’s loan will be equal to the value of the car?

After 10 months, the loan and value of the car will both be equal to $7,500.
After 12 months, the loan and value of the car will both be equal to $7,000.
After 14 months, the loan and value of the car will both be equal to $6,500.
After 16 months, the loan and value of the car will both be equal to $6,000.

Answers

Answer:

Step-by-step explanation:

12 months

Answer:

12 months b on edg

Step-by-step explanation:

edg 2022


A 7-foot board is cut into two pieces. If one piece is x feet long, express the other length in terms of X

Answers

Step-by-step explanation:

According to the question,

Total length the board = 7 feetIt has been cut into two pieces.Length of one piece = x feet

Basically,

[tex]\longrightarrow[/tex] Total length of the board = Sum of the length of the two pieces

[tex]\longrightarrow[/tex] Total length of the board = Length of 1st piece + Length of the 2nd piece

[tex]\longrightarrow[/tex] 7 feet = x feet + Length of the 2nd piece

[tex]\longrightarrow[/tex] (7 – x) feet + Length of the 2nd piece

Hence, we got the required answer!

what is the answer for this question?
1. Dayne has three investment portfolios: A, B and C. Portfolios A, B and C together are worth a total of $175000, portfolios A and B together are worth a total of $143000, while portfolios A and C together are worth a total of $139000.
Use Cramer’s Rule to find the value of each portfolio.

Answers

Answer:

The correct answer is:

Portfolio A = $107,000

Portfolio B = $36,000

Portfolio C = $32,000

Step-by-step explanation:

According to the question,

[tex]A+B+C=175000[/tex]...(1)

[tex]A+B = 143000[/tex]...(2)

[tex]A+C=139000[/tex]...(3)

Now,

From (1) and (2), we get

⇒ [tex]Portfolio \ C = (1)-(2)[/tex]

                        [tex]=175000-143000[/tex]

                        [tex]=32000[/tex]...(4)

From (1) and (3), we get

⇒ [tex]Portfolio \ B =(1)-(3)[/tex]

                        [tex]=175000-139000[/tex]

                        [tex]=36000[/tex]...(5)

From (1), (4) and (5), we get

⇒ [tex]Portfolio \ A = (1)-(4+5)[/tex]

                        [tex]=175000-(36000+32000)[/tex]

                        [tex]=175000-68000[/tex]

                        [tex]=107000[/tex]  

                 

Thus the above is the correct answer.

Did any one know this?

Answers

Answer:

x sqrt(2)

Step-by-step explanation:

sqrt(a) / sqrt(b) = sqrt(a/b)

sqrt( 14 x^3) / sqrt(7x)

sqrt(14x^3/7x)

sqrt(2x^2)

sqrt(ab) = sqrt(a)sqrt(b)

sqrt(x^2) sqrt(2)

x sqrt(2)

Find the area of a triangle with the given description. (Round your answer to one decimal place.)
a triangle with sides of length 14 and 28 and included angle 20°

Answers

9514 1404 393

Answer:

  67.0 square units

Step-by-step explanation:

The formula for the area is ...

  Area = 1/2ab·sin(C)

  Area = (1/2)(14)(28)sin(20°) ≈ 67.036 . . . . square units

The area of the triangle is about 67.0 square units.

Question 4 of 16
If the probability of rain today is 35%, what is the probability that it will not rain
today?
A. 100%
B. 65%
C. 35%
D. 50%

Answers

Answer:

I think the answer is B. 65%

7. Solve for x: x/6 - y/3 = 1

Please give steps!

Answers

x/6 - y/3 = 1
<=> x/6 = 1+ y/3
<=> x/6 = (3+y)/3
<=> x = (3+y)/3 x 6
<=> x = 2(3+y)
So the answer is x = 2(3+y)

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.4 inches, and standard deviation of 4.1 inches.

A) What is the probability that a randomly chosen child has a height of less than 61.25 inches?

Answer= (Round your answer to 4 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 46.5 inches?

Answer= (Round your answer to 4 decimal places.)

Answers

(A)

P(X < 61.25) = P((X - 55.4)/4.1 < (61.25 - 55.4)/4.1)

… ≈ P(Z ≤ 0.1427)

… ≈ 0.5567

(B)

P(X > 46.5) = P((X - 55.4)/4.1 > (46.5 - 55.4)/4.1)

… ≈ P(Z > -2.1707)

… ≈ 1 - P(Z ≤ -2.1707)

… ≈ 0.9850

32% adults favor the use of unmanned drones by police agencies. Twelve u.s. adults are randomly selected. Find the probability that the number of u.s. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight

Answers

Answer:

C

Step-by-step explanation:

32% of 12 =

32/100 x 12

= 3.84

So, C would be the correct choice

I wasn't sure about my answer so used the Gauthmath App

Can someone help me find the answer?

Answers

Answer: B. This function has no intercept. I think B is the correct answer.

I need to know the answer ASAP

Answers

Answer:

Step-by-step explanation:

6. The perimeter of a square room is 48 m, how much square metre carpet required it cover it ?

Answers

Answer:

144

Step-by-step explanation:

Answer:

first you have to now each side length ,since it is square so all sides are equal so 48/4=12 i.e perimeter =4 so our qoustion is area so the area of square is side square

Step-by-step explanation:

so side =12 , 12square is 144 that set.

Find the length of the missing side

Answers

9514 1404 393

Answer:

short leg: x; long leg: 12; hypotenuse: y

Step-by-step explanation:

The sides of the triangle can be read from the figure:

short leg: xlong leg: 12hypotenuse: y

The ratios tell you ...

  long leg = x√3 = 12

  x = 12/√3 = 4√3 . . . . . divide by √3. (same as multiply by (√3)/3)

  2x = 2·4√3 = 8√3

Then the missing sides are ...

short leg: 4√3long leg: 12hypotenuse: 8√3

The sume of the reciprocals of two consecutive integers is 3/2. Find the two integers

Answers

Answer:

1 and 2

Step-by-step explanation:

Let's say our first number is x. Our second number is the number after that, or x+1. A reciprocal of a number is 1/that number. Therefore, the reciprocal of x is 1/x and the reciprocal of x+1 is 1/(x+1). The question states the sum of the reciprocals of the two numbers is equal to 3/2. Therefore,

1/x + 1/(x+1) = 3/2

multiply both sides by 2 to remove a denominator

2/x + 2/(x+1) = 3

multiply both sides by x to remove a denominator

2 + (2*x)/(x+1) = 3x

multiply both sides by (x+1) to remove the other denominator

2*(x+1) + 2*x = 3x*(x+1)

expand

2*x+2 + 2*x = 3x²+3

combine like terms

4x + 2 = 3x²+3

subtract (4x+2) from both sides to make everything equal to 0 and to form a quadratic

3x² - 4x + 1 = 0

To factor this, we need to find two numbers that add up to b and multiply to a*c in an equation of form ax²+bx + c. Here, a=3, c=1, and b = -4

Two numbers that add to -4 and multiply to 3*1=3 are -3 and -1. We can thus factor this out to get

3x²-3x-x+1 = 0

3x(x-1) -1 ( x-1) = 0

(3x-1)(x-1) = 0

Therefore, solving for 0, we get

3x-1=0

x = 1/3

x-1 = 0

x=1

The only integer solution possible is x=1

To confirm, 1/1 + 1/(1+1) = 3/2, so x=1 is correct, with 1+1=2 being the second integer

Researchers studied symptom distress and palliative care designation among a sample of 710 hospitalized patients. Controlling for age, they used a t-test to compare average distress from nausea scores in men and women. Lower scores indicated less distress from nausea. They report men had an average score of 1.02 and woman had an average score of 1.79. Which statement is correct?
(2pts)
Select Men had significantly less distress from nausea. as your answer
Men had significantly less distress from nausea.
Select Men had half as much distress from nausea as woman but we can not determine if this is a significant difference. as your answer
Men had half as much distress from nausea as woman but we can not determine if this is a significant difference.
Select Men had less distress from nausea on average than women but we can not determine if this is a significant difference. as your answer
Men had less distress from nausea on average than women but we can not determine if this is a significant difference.
Select There is a positive correlation between distress from nausea and gender. as your answer
There is a positive correlation between distress from nausea and gender.

Answers

Answer:

A. Men had less distress from nausea on average than women but we can not determine if this is a significant difference.

Step-by-step explanation:

Working based on the information given, the mean values of each group with with men having an average score of 1.02 and women have an average of 1.79 this reveals that distressing nausea on average is higher in women than in men . However, to test if there is a significant difference would be challenging as the information given isn't enough to make proceed with the test as the standard deviations of the two groups aren't given and no accompanying sample data is given.

If the cube root parent function is horizontally stretched by a factor of 4, then translated 5 units right and 3 units up, write an equation to represent the new function?

Answers

Answer:

The cube root parent function:

f(x) = [tex]\sqrt[3]{x}[/tex]

Horizontally stretched by a factor of 4:

g(x) → f(1/4x) = [tex]\sqrt[3]{1/4x}[/tex]

Translated 5 units right:

h(x) → g(x - 5) = [tex]\sqrt[3]{1/4x - 5}[/tex]

Translated 3 units up:

k(x) → h(x) + 3 = [tex]\sqrt[3]{1/4x - 5} + 3[/tex]

Find the measure of the incanted angle to the nearest degree

Answers

Answer:

34⁰

Step-by-step explanation:

let unknown angle be x

cos x=19/23

cos x=0.826

x=cos inverse of 0.826

x=34.3⁰

Place the labels in the chart
If you can draw this out for me or describe were they are that will be very helpful:)

Answers

Answer:

Check the image

A group of high school students were surveyed about their handedness and their favorite sport. The results are displayed below.



Which of the following statements is not true, according to the graph?

The left-handed group has a higher percentage of people who prefer baseball.
The right-handed group has a lower percentage of people who prefer basketball.
The percentage of people who prefer soccer has a lower percentage in the left-handed group.
The percentage of people who prefer football is approximately the same for the right- and left-handed groups.

Answers

Answer:

The percentage of people who prefer football is approximately the same for the right- and left-handed groups.

Step-by-step explanation:

The bar for the right-handed group representing soccer is between 10% and 20% (below 20%) while the bar for the left-handed group representing soccer is at 20%.

Percentage of left-handed group of people who prefer soccer is higher than the right-handed group who prefer soccer. Therefore, they don't have the same percentage.

Answer:

D

Step-by-step explanation:

;)

mJWL=87 degrees. Find the value of x.

Answers

JWL = JWI + IWL

87 = (2x + 24) + (3x - 12)

87 = 5x + 12

5x = 75

x = 15

Hope this helps!

The value of the variable x will be 15. Then the correct option is A.

What is an angle?

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.

The measure of the angle ∠JWL will be 87°.

The angle ∠JWI and angle ∠IWL will be the linear angle.

Then the sum of the angle ∠JWI and angle ∠IWL is equal to the angle ∠JWI.

          ∠JWI + ∠IWL = 87°

(2x + 24) + (3x – 12) = 87

                    5x + 12 = 87

                           5x = 87 – 12

                           5x = 75

                             x = 75 / 5

                             x = 15

Thus, the value of the variable x will be 15.

Then the correct option is A.

More about the angled link is given below.

https://brainly.com/question/15767203

#SPJ5

An educational psychologist wishes to know the mean number of words a third grader can read per minute. She wants to make an estimate at the 95% level of confidence. For a sample of 582 third graders, the mean words per minute read was 24.1. Assume a population standard deviation of 3.7. Construct the confidence interval for the mean number of words a third grader can read per minute.

Answers

Answer:

The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{3.7}{\sqrt{582}} = 0.3[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 24.1 - 0.3 = 23.8

The upper end of the interval is the sample mean added to M. So it is 24.1 + 0.3 = 24.4.

The 95% confidence interval for the mean number of words a third grader can read per minute is (23.8, 24.4).

The domain for all variables in the expressions below is the set of real numbers. Determine whether each statement is true or false.(i)∀x ∃y(x+y≥0)

Answers

The domain of a set is the possible input values the set can take.

It is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers

Given that: ∀x ∃y(x+y≥0)

Considering x+y ≥ 0, it means that the values of x + y are at least 0.

Make y the subject in x+y ≥ 0

So, we have:

[tex]\mathbf{y \le -x}[/tex]

There is no restriction as to the possible values of x.

This means that x can take any real number.

Hence, it is true that the domain of ∀x ∃y(x+y≥0) is the set of real numbers.

Read more about domain at:

https://brainly.com/question/15110684

Can someone help me out

Answers

Answer:

π×64×4=804.25

Step-by-step explanation:

Formula of cylinder is π×square of radius×height

Answer:

803.8

Step-by-step explanation:

it's 3.14×8×8×4 which would give you 803.84 and then you round which would give you 803.8

0.5 kilograms (kg) is equal to how many ounces? Round your answer to the

Answers

Answer:

17.637 ounces

Step-by-step explanation:

35.274 ounces is 1 kilogram so divide 35.274 by 2

Might want to keep the other guy Brainly

Write a quadratic equation with integer coefficients having the given numbers as solutions.

Answers

9514 1404 393

Answer:

  x² -22 = 0

Step-by-step explanation:

The roots are opposites, so the equation is pretty simple.

  x = ±√22

  x² = 22 . . . . . square both sides

  x² -22 = 0 . . . . your quadratic equation in standard form

What is 21 1/8 minus 14 1/8

Answers

Answer:

8.75

Step-by-step explanation:

211/8 = 26.375

141/8 = 17.625

now,

211/8-141/8

26.375-17.625

8.75

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