y'+y=y^2; y(0)=-1/3
Giải phương trình trên

Answers

Answer 1

Step-by-step explanation:

[tex]y' + y = y^2[/tex]

We can rewrite the differential equation above as

[tex]\dfrac{dy}{dx} + y = y^2[/tex]

[tex]dy = (y^2 - y)dx[/tex]

or

[tex]\dfrac{dy}{y^2 -y} = dx[/tex]

We can rewrite the left side of the equation above as

[tex]\dfrac{dy}{y^2-y}=\dfrac{dy}{y(y-1)}= \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy[/tex]

We can the easily integrate this as

[tex]\displaystyle \int \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy = \int dx[/tex]

or

[tex]\displaystyle \int \dfrac{dy}{y-1} - \int \dfrac{dy}{y} = \int dx[/tex]

This will then give us

[tex]\ln |y-1| - \ln |y| + \ln |k| = x[/tex]

where k is the constant of integration. Combining the terms on the left hand side, we get

[tex]\ln \left|\dfrac{k(y-1)}{y} \right| = x[/tex]

or

[tex]\dfrac{y-1}{y} = \frac{1}{k}e^x[/tex]

Solving for y, we get

[tex]y= \dfrac{1}{1- \frac{1}{k} e^x}=\dfrac{k}{k-e^x}[/tex]

We know that [tex]y(0)= \frac{1}{3}[/tex], so when we substitute [tex]x=0[/tex], we find that [tex]k = -\frac{1}{2}[/tex].

Therefore, the final form of the solution to the differential equation above is

[tex]y = \dfrac{1}{1+2e^x}[/tex]


Related Questions

anyone know the answer to this question ?

Answers

Question:

c=3x+80  

R=12x- 0.02x^2

R= revenue  

C=cost  

X=items sold  

A) 9x-(0.2x^2+80)

B) x(9-0.2x)-80  

C) x(9-0.02x)

D) 9x-0.02x^2+80

Answer:

c) x(9-0.2x)

is the correct answer

PLZ MARK BRAINLIEST

Express it in slop-intercept form​

Answers

Answer:

y = ½x -3

Step-by-step explanation:

_____________________

Find the value of angle x to the nearest degree:
COS X = 0.5505

Answers

Answer:

x = 57°

Step-by-step explanation:

Cos(x) = 0.5505

x = Cos⁻¹(0.5505)

x = 56.59

Rounding to the nearest degree;

x = 57°

Hope this helps!

Which is the solution to the equation below? 4n+5=25-3n

Answers

Answer:

[tex]n = \frac{20}{7}[/tex]

Step-by-step explanation:

[tex]4n + 5 = 25 - 3n\\4n + 3n = 25 - 5 \\7n = 20\\\\n = \frac{20}{7}[/tex]

Answer:

n = 20/7

Step-by-step explanation:

4n+5=25-3n

Add 3n to each side

4n+3n+5=25-3n+3n

7n +5 = 25

Subtract 5 from each side

7n+5-5=25-5

7n = 20

Divide by 7

7n/7 = 20/7

n = 20/7

Which ordered pairs are solutions to the equation 5x+12y=12?

Answers

I found 3 order pair. I hope this helps let me know if you have any questions:)

which expression is equivalent to 13 - 4.5 +(-8)

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{13 - 4.5 + (-8)}\\\\\large\textsf{= 13 - 4.5 - 8}\\\\\large\textsf{13 - 4.5 = \boxed{\bf 8.5}}\large\checkmark\\\\\large\textsf{8.5 - 8}\\\\\boxed{\large\textsf{= \bf 0.5}}\large\checkmark\\\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 0.5}}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

please help me

if don't know don't answer, if you answer i will report ​

Answers

Answer:

A.) m = 1.5 | B.) p = -1 | C.) t = 2

Step-by-step explanation:

A.)

[tex]4(m+3)=18\\4m+12=18\\4m=6\\m=3/2=1.5[/tex]

B.)

[tex]-2(p+5)+8=0\\-2p-10+8=0\\-2p-2=0\\-2p=2\\p=-1[/tex]

C.)

[tex]3+5(t-1)=8\\3+5t-5=8\\5t-2=8\\5t=10\\t=2[/tex]

Answer:

(a)=

4(m+3)=18

4m+12=18

4m=18-12

4m=6

m=

[tex] \frac{6}{4} [/tex]

(b)=

-2(p+5)+8=0

-2p-10+8=0

-2p=0+10-8

-2p=2

p=

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

(c)=

3+5(t-1)=8

3+5t-5=8

5t=8-3+5

5t=10

t=

[tex] \frac{10}{5} = 2[/tex]

[tex]please \: mark \: as \: brainliest \: because \: i \: spent \: much \: time \: on \: this \: question[/tex]

Suppose a 90% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$38,737, $50,463]. The population standard deviation used for the analysis is known to be $14,300.
a. What is the point estimate of the mean salary for all college graduates in this town?
Point estimate
b. Determine the sample size used for the analysis.
Sample size

Answers

Answer:

a. The point estimate was of $44,600.

b. The sample size was of 16.

Step-by-step explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

a. What is the point estimate of the mean salary for all college graduates in this town?

Mean of the bounds, so:

(38737+50463)/2 = 44600.

The point estimate was of $44,600.

b. Determine the sample size used for the analysis.

First we need to find the margin of error, so:

[tex]M = \frac{50463-38737}{2} = 5863[/tex]

Relating the margin of error with the sample size:

We have that 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 - 0.9}{2} = 0.05[/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 pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.64.

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.

For this problem, we have that [tex]\sigma = 14300, M = 5863[/tex]. So

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

[tex]5863 = 1.645\frac{14300}{\sqrt{n}}[/tex]

[tex]5863\sqrt{n} = 1.645*14300[/tex]

[tex]\sqrt{n} = \frac{1.645*14300}{5863}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645*14300}{5863})^2[/tex]

[tex]n = 16[/tex]

The sample size was of 16.

Find the center and radius of x^2 + y^2 +6x - 7=0

Answers

Answer:

The center (-3, 0)

9514 1404 393

Answer:

center: (-3, 0)radius: 4

Step-by-step explanation:

The desired parameters can be found by putting the equation into the standard form for the equation of a circle:

  (x -h)^2 +(y -k)^2 = r^2 . . . . . circle centered at (h, k) with radius r

The values of h and k will be half the coefficients of the linear x- and y-terms, respectively.

  x^2 +6x +9 +y^2 -7 = 9 . . . . . add 9 to complete the square

  (x +3)^2 +y^2 = 16 . . . . . . . . . add 7 to get the desired form

This equation shows us (h, k) = (-3, 0) and r = 4.

The center is (-3, 0), and the radius is 4.

...help please I would appreciate it
No link please

Answers

Answer:

B

Step-by-step explanation:

Answer:

it's B. pa brainliest nalang po thanks

Step-by-step explanation:

B.

What is the surface area of a dome ( 1/2 sphere) with a radius of 12 meters?
A.

Answers

Answer:

[tex]Area = 1357.344m^2[/tex]

Step-by-step explanation:

Given

Shape: dome

[tex]r = 12[/tex]

Required

The surface area

This is calculated as:

[tex]Area = 3\pi r^2[/tex]

So, we have:

[tex]Area = 3*3.142* 12^2[/tex]

[tex]Area = 1357.344m^2[/tex]

Round 263.492 to the nearest tenth.

Answers

Answer:

260.

because 263 is below 265 so it wont change to 270.

A quantity P is an exponential function of time t. Use the given information about the function P = P0e^{kt} to find values for the parameters k and P0.
​P=40 when t=4 and P=50 when t=3.

Answers

Answer:

P = 40 x 4

= 160

P = 50 x 3

= 150

This circle is centered at the origin, and the length of its radius is 8. What is the circle's equation? 5 A. X+ y = 8 B. x2 + y2 = 64 O c. x2 + y2 = 8 D. X8+ y = 64​

Answers

Answer:

Step-by-step explanation:

A circle centered in [tex]P(x_o,y_o)[/tex] an radius [tex]r[/tex] has a equation:

[tex](x-x_o)^2+(y-y_o)^2=r^2[/tex]

So, your equation wold be:

[tex](x-0)^2+(y-0)^2=8^2\Rightarrow x^2+y^2=64[/tex]

The correct circle's equation with radius 8 is,

⇒ x² + y² = 64

What is mean by Circle?

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

This circle is centered at the origin, and the length of its radius is 8.

Since, The general equation of circle with center (h, k) and radius r is,

⇒ (x - h)² + (y - k)² = r²

Here, Center = (0, 0)

Radius = 8

Hence, The correct circle's equation with radius 8 is,

⇒ (x - h)² + (y - k)² = r²

⇒ (x - 0)² + (y - 0)² = 8²

⇒ x² + y² = 64

Thus, The correct circle's equation with radius 8 is,

⇒ x² + y² = 64

Learn more about the circle visit:

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3. A bicycle has wheels with a diameter of 622 mm. The

bicycle rolls forward and the wheel turns 5 radians.

How many millimeters forward did the bicycle move?

Distance = ( ) (622) = (15.708) ()

= (2.618)

וחתן

Answers

Answer:

1553.6mm

Step-by-step explanation:

Given data

Diameter = 622mm

Radius= 622/2= 311mm

Circumference= 2πr

Circumference= 2*3.142*311

Circumference= 1954.32

Each revolution the wheels will turn 1954.32mm

Now let us convert radian to turns

1 radian= 0.159155 turns

5 radians=  x turns

cross multiply

x= 5*0.159155

x=0.795 turns

If 1 turn will give 1954.32mm

0.795 turn will give  x

cross multiply

x= 0.795*1954.32

x=1553.6mm

The Coordinate Plane
BRE
-2
В
The midpoint of AB = ([?],[ ])

Answers

Answer:

0,0

Step-by-step explanation:

prove by factorization √16×81=√16×√81

Answers

Answer:

√16×81 = 4×9 or √1296 = 36

√16×√81 = 4×9 = 36

Step-by-step explanation:

√81×16

We simplify 81 and 16 by prime factorisation (expressing a number as a product of its prime factors).

√81 = √3×3×3×3 = √9×9 = √9² = 9

√16 = √2×2×2×2 = √4×4 = √4² = 4

(y-4)^0 - 3y^0 for y = 1

Answers

Answer:

(1-4)^0-3y^0

( -3)^0 -3^0

1 -1

0

Answer:

-2

Step-by-step explanation:

(y -4)^0 - 3y^0

substitute the value of y

(3-4)^0 - 3*1^0

(-1)^0 - 3*1

1 - 3

-2

Let Q(x, y) be the predicate "If x < y then x2 < y2," with domain for both x and y being R, the set of all real numbers.
a) When x = −2 and y = 1, is Q(x, y).
a. true
b. false
The hypothesis of Q(−2, 1) is__, which is___. The conclusion is___, which is____. Thus Q(−2, 1) is a conditional statement with a____hypothesis and a_____conclusion. So Q(−2, 1) is____.
b) Give values different from those in part (a) for which Q(x, y) has the same truth value as in part.
c) Give values different from those in part (c) for which Q(x, y) has the same truth values as in part.

Answers

Answer:

a) Q(-2,1) is false

b) Q(-5,2) is false

c)Q(3,8) is true

d)Q(9,10) is true

Step-by-step explanation:

Given data is [tex]Q(x,y)[/tex] is predicate that [tex]x<y[/tex] then [tex]x^{2} <y^{2}[/tex]. where [tex]x,y[/tex] are rational numbers.

a)

when [tex]x=-2, y=1[/tex]

Here [tex]-2<1[/tex] that is [tex]x<y[/tex]  satisfied. Then

[tex](-2)^{2}<1^{2}[/tex]

[tex]4<1[/tex] this is wrong. since [tex]4>1[/tex]

That is [tex]x^{2}[/tex][tex]>y^{2}[/tex] Thus [tex]Q(x,y)[/tex] [tex]=Q(-2,1)[/tex]is false.

b)

Assume [tex]Q(x,y)=Q(-5,2)[/tex].

That is [tex]x=-5, y=2[/tex]

Here [tex]-5<2[/tex] that is [tex]x<y[/tex] this condition is satisfied.

Then

[tex](-5)^{2}<2^{2}[/tex]

[tex]25<4[/tex] this is not true. since [tex]25>4[/tex].

This is similar to the truth value of part (a).

Since in both [tex]x<y[/tex] satisfied and [tex]x^{2} >y^{2}[/tex] for both the points.

c)

if [tex]Q(x,y)=Q(3,8)[/tex] that is [tex]x=3[/tex] and [tex]y=8[/tex]

Here [tex]3<8[/tex] this satisfies the condition [tex]x<y[/tex].

Then [tex]3^{2} <8^{2}[/tex]

[tex]9<64[/tex] This also satisfies the condition [tex]x^{2} <y^{2}[/tex].

Hence [tex]Q(3,8)[/tex] exists and it is true.

d)

Assume [tex]Q(x,y)=Q(9,10)[/tex]

Here [tex]9<10[/tex] satisfies the condition [tex]x<y[/tex]

Then [tex]9^{2}<10^{2}[/tex]

[tex]81<100[/tex] satisfies the condition [tex]x^{2} <y^{2}[/tex].

Thus, [tex]Q(9,10)[/tex] point exists and it is true. This satisfies the same values as in part (c)

6x+2y=
6x+2y=
\,\,16
16
2x-2y=
2x−2y=
\,\,32
32

Answers

Answer:

x = 6, y = -8

Step-by-step explanation:

First we take the equations side by side and put them like this:

 6x + 2y = 16

+ 2x - 2y = 32

8x = 48

Then solve for x.

x = 6

Then insert x back into either equation

2(5) - 2y = 32

10 - 2y = 32

solve for y,

y = -10

Which expression can be used to convert 22 Australian dollars to US dollars? Assume 1.2 Australian dollars equals 1 US dollar

Answers

Answer: 26.4

Step-by-step explanation: 1.2x22=

there are 750 spectator in the stadium of which 420 are women and the rest are men​

Answers

Complete Question:

There are 750 spectator in the stadium of which 420 are women and the rest are men. What percent of the spectators are women?

Answer:

Percentage = 56%

Step-by-step explanation:

Given the following data;

Total number of people = 750

Number of women = 420

To find the percentage of women;

First of all, we would determine the number of male spectators (men);

Number of men = Total number of people - Number of women

Number of men = 750 - 420

Number of men = 330

Next, we find the percentage of women;

[tex] Percentage = \frac {420}{750} * 100 [/tex]

[tex] Percentage = \frac {42}{75} * 100 [/tex]

[tex] Percentage = 0.56 * 100 [/tex]

Percentage = 56%

Therefore, the percentage of the spectators that are women is 56%.

find the measure of one interior angle in a regular 23-gon

Answers

Answer: A polygon with 23 sides has a total of 3780 degrees. total interior angles = (n - 2)180°, where n is the number of sides.

The measure of one interior angle of the given regular polygon with 23 sides is 164.3 degrees

How to calculate the sum of the interior angle of a regular polygon?

The formula which is used to calculate the sum of the angle of regular polygon is given by

sum of the interior angles = ( n - 2 ) × 180 degrees

Where,

n is the number of sides

According to the given question.

We have a regular polygon with 23 sides.

⇒ n = 23

Therefore,

The sum of the interior angles of the given regular polygon

= (23-2) × 180

= 3,780 degrees

So, the measure of one interior angle = [tex]\frac{3780}{23} = 164.3 degrees[/tex]

Hence, the measure of one interior angle of the given regular polygon with 23 sides is 164.3 degrees.

Find out more information about interior angle of a regular polygon here:

https://brainly.com/question/22408868

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One side of a REGULAR OCTAGON is 19 ft.
What is the PERIMETER of this octagon?
feet.
I

Answers

Perimeter: 19ft x 8 sides = 152ft

Explanation: Regular octagon means equivalent sides and more.

Answer:

152 ft.

Step-by-step explanation:

19*8 = 152

what are the domain and range of this function?

Answers

Answer:

domain: all real numbers

range: {y | y ≥ 0}

Write the missing power of 10 in each equation.

0.80 × [ ] = 8
[ ] × 0.002 = 20
0.04 × [ ]= 4
[ ]× 0.5 = 500

Answers

1. 10 or 10 to the first power
2. 10000 or 10 to the fourth power
3. 100 or 10 to the second power
4. 1000 or 10 to the third power

Mary has three baking pans. Each pan is 8" × 8" × 3". Which expression will give her the total volume of the pans?

Answers

Answer: An expression [tex]3 \times (8 \times 8 \times 3)[/tex] will give her the total volume of the pans.

Step-by-step explanation:

Given: Length = 8 inch

Width = 8 inch

Height = 8 inch

Formula to calculate the volume of rectangular pans is as follows.

[tex]Volume = length \times width \times height\\[/tex]

Substitute the values into above formula as follows.

[tex]Volume = length \times width \times height\\= 8 \times 8 \times 3 in^{3}\\= 192 in^{3}[/tex]

Therefore, volume of each pan is 192 cubic inch. As there are three baking pans so total volume of the pans is as follows.

[tex]3 \times 192 in^{3}\\= 576 in^{3}[/tex]

Thus, we can conclude that an expression [tex]3 \times (8 \times 8 \times 3)[/tex] will give her the total volume of the pans.


2. What is the best estimate of the value of In 16?

Answers

Answer:

Hey your question is in incomplete

Step-by-step explanation:

k66jntynnu.uk8 677nunni.i7k78mi

which number represents 4%​

Answers

Answer:

4

Step-by-step explanation:

In the video, you saw that Michael used a budget to make sure he pays bills when they’re due. What are some other reasons someone would want to create a budget?

Answers

Someone might want to create a budget to treat themselves later with their saved money. Another reason it is good to have a budget is to not max out your credit card.
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