Giải phương trình vi phân
a. dy/dx
b. y' + 2xy = 4x

Answers

Answer 1

Your first differential equation is incomplete, so I'll just look at the second one.

y' + 2xy = 4x

Multiply both sides by exp(x ²):

exp(x ²) y' + 2x exp(x ²) y = 4x exp(x ²)

The left side is the derivative of a product:

(exp(x ²) y )' = 4x exp(x ²)

Integrate both sides:

exp(x ²) y = ∫ 4x exp(x ²) dx

For the integral, substitute u = x ² and du = 2x dx :

exp(x ²) y = 2 ∫ exp(u) du

Solve for y :

exp(x ²) y = 2 exp(u) + C

exp(x ²) y = 2 exp(x ²) + C

y = 2 + C exp(-x ²)


Related Questions

PLEASE HELP! WILL MARK BRAINLIEST!

Answers

Answer:

at first put the value of X

after that do the equation.

Step-by-step explanation:

hope it will help you

Answer:

a = 2

Step-by-step explanation:

substitute x with the number 5.

5+8a=25+5a-7a

subtract 5a from both sides

5+3a=25-7a

add 7a to both sides

5+10a = 25

subtract 5 from both sides

10a=20

divide both sides by 10

a = 2

Use logarithmic differentiation to differentiate the question below
[tex]y = x \sqrt[3]{1 + {x}^{2} } [/tex]

Answers

Answer:

[tex] \orange{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Step-by-step explanation:

[tex]y = x \sqrt[3]{1 + {x}^{2} } \\ assuming \: log \: both \: sides \\log y = log(x \sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + log(\sqrt[3]{1 + {x}^{2} } ) \\ \therefore log y = logx + \frac{1}{3} log({1 + {x}^{2} } ) \\ differentiating \: both \: sides \: w.r.t.x \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{1}{3} . \frac{1}{(1 + {x}^{2}) } (0 + 2x) \\ \frac{1}{y} \frac{dy}{dx} = \frac{1}{x} + \frac{2x}{3(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3(1 + {x}^{2}) + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 3{x}^{2} + 2 {x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{1}{y} \frac{dy}{dx} =\frac{3 + 5{x}^{2} }{3x(1 + {x}^{2}) }\\ \frac{dy}{dx} =\frac{y(3 + 5{x}^{2} )}{3x(1 + {x}^{2}) } \\ \\ \frac{dy}{dx} =\frac{x \sqrt[3]{1 + {x}^{2} } (3 + 5{x}^{2} )}{3x(1 + {x}^{2}) }\\ \\ \frac{dy}{dx} =\frac{(3 + 5{x}^{2} )\sqrt[3]{1 + {x}^{2} } }{3(1 + {x}^{2}) }\\ \\ \purple{ \bold{\frac{dy}{dx} =\frac{ 5{x}^{2} + 3 }{3\sqrt[3]{(1 + {x}^{2})^{2} } }}}[/tex]

Only answer if you're very good at Math.

What is the sum of 7x/x^2 - 4 and 2/x + 2?

A: 7x + 2/x^2 - 4

B: 9x - 4/x^2 - 4

C: 7x + 2/ x^2 + x - 2

D: 9/x

Answers

Answer:

Solution given:

B: 9x - 4/x^2 - 4

Step-by-step explanation:

.k

There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.03 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
What is the probability that the first machine produces an acceptable cork? (Round your answer to four decimal places.)
What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)
Please explain the math behind your answer so I am able to understand!(:

Answers

Answer:

0.7888 = 78.88% probability that the first machine produces an acceptable cork.

0.9772 = 97.72% probability that the second machine produces an acceptable cork.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

First machine:

Mean 3 cm and standard deviation 0.08 cm, which means that [tex]\mu = 3, \sigma = 0.08[/tex]

What is the probability that the first machine produces an acceptable cork?

This is the p-value of Z when X = 3.1 subtracted by the p-value of Z when X = 2.9. So

X = 3.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.1 - 3}{0.08}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a p-value of 0.8944

X = 2.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.9 - 3}{0.08}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a p-value of 0.1056

0.8944 - 0.1056 = 0.7888

0.7888 = 78.88% probability that the first machine produces an acceptable cork.

What is the probability that the second machine produces an acceptable cork?

For the second machine, [tex]\mu = 3.04, \sigma = 0.03[/tex]. Now to find the probability, same procedure.

X = 3.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.1 - 3.04}{0.03}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

X = 2.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.9 - 3.04}{0.03}[/tex]

[tex]Z = -4.67[/tex]

[tex]Z = -4.67[/tex] has a p-value of 0

0.9772 - 0 = 0.9772

0.9772 = 97.72% probability that the second machine produces an acceptable cork.

What is the value........

Answers

Answer:

[tex]a_5 = 120[/tex]

Step-by-step explanation:

Given

[tex]a_1 = 1[/tex]

[tex]a_n = n(a_{n-1})[/tex]

Required

[tex]a_5[/tex]

This is calculated as:

[tex]a_5 = 5(a_{5-1})[/tex]

[tex]a_5 = 5*a_4[/tex]

Calculate [tex]a_4[/tex]

[tex]a_4 =4(a_{4-1})[/tex]

[tex]a_4 =4*a_3[/tex]

Calculate [tex]a_3[/tex]

[tex]a_3 =3*a_2[/tex]

Calculate [tex]a_2[/tex]

[tex]a_2 = 2 * a_1[/tex]

[tex]a_2 = 2 * 1[/tex]

[tex]a_2 = 2[/tex]

So:

[tex]a_3 =3*a_2[/tex]

[tex]a_3 = 3 * 2 = 6[/tex]

So:

[tex]a_4 =4*a_3[/tex]

[tex]a_4 = 4 * 6 =24[/tex]

Lastly;

[tex]a_5 = 5*a_4[/tex]

[tex]a_5 = 5 * 24[/tex]

[tex]a_5 = 120[/tex]

5x + 3y = 17
-8x - 3y = 9

Answers

Answer:

1)x=−3/5y+17/5  

2)x=−3/8y+−9/8

Step-by-step explanation:

Let's solve for x.

5x+3y=17

Step 1: Add -3y to both sides.

5x+3y+−3y=17+−3y

5x=−3y+17

Step 2: Divide both sides by 5.

5x/5=−3y+17/5

x=−3/5y+17/5

Answer:

x=−3/5y+17/5  

Let's solve for x.

−8x−3y=9

Step 1: Add 3y to both sides.

−8x−3y+3y=9+3y

−8x=3y+9

Step 2: Divide both sides by -8.

−8x/−8=3y+9/−8

x=−3/8y+−9/8

Answer:

x=−3/8y+−9/8

I HOPE THIS IS CORRECT IF NOT TELL ME AND ILL FIX IT.

The salaries of professional baseball players are heavily skewed right with a mean of $3.2 million and a standard
deviation of $2 million. A baseball analyst randomly selects 40 athletes and records the mean salary. What is the shape
of the distribution of the sample mean for all possible random samples of size 40 from this population?
skewed left
skewed right
approximately Normal
approximately uniform

Answers

Answer:

approximately Normal with a mean of 3.2 million and a standard deviation of 0.32 million

Step-by-step explanation:

For normal distribution conditions

1) Sample size is greater than 30

2) Population standard deviation is known

3) population is normal distributed

Above any condition given problem if satisfied than it's distribution will approximately normal.

n = 40 > 30

Sample size(n) greater than 30 and population standard deviation is known.

So the distribution will approximately be normal

Hope this helps!

The shape  of the distribution of the sample mean for all possible random samples of size 40 from this population is approximately Normal

The following any or all conditions should be there for normal distribution:

The Sample size is more than 30 .Population standard deviation is known .The Population is normal distributed

Now  

n = 40 > 30

Here  

Sample size(n) more than 30 and population standard deviation is known.

Learn more: brainly.com/question/17429689

Find the surface area of the regular pyramid.

Answers

Answer:

B

Step-by-step explanation:

Base area = side^2 = 3^2 = 9 m^2

Base perimeter = side x 4 = 3 x 4 = 12 m

LA = (base perimeter x slant height)/2 = (12 x 5)/2 = 30 m

SA = base area + LA = 9 + 30 = 39 m^2

In science class sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes and the other two experiments required the same number of test tubes. How many test tubes were needed for each of the the other two experiments

Answers

Answer:

as we know Sara need 8 tube in 3 experiment

she will use 2 tube in 1 experiment

now she have 6 tube in other experiments

so the question said to find how many tube were used in both experiment equally so 3,3 test tube were needed for each of the other two experiment

Step-by-step explanation:

total tube=8 (3 experiment)

used =2tube (1 experiment)

remaining=8-2=6

now ,

dividing 6 into 2 equal part

so,=6/2=3

so 3 tube were used in 2nd experiment and 3in 3rd experiment

which is the graph of g(x)

Answers

Answer:

The 1st graph is the answer and matches

-x/2 + 2   -2  ≤ x < 2 because it is equal to -2

The 4th graph is incorrect slightly at = 2x - 3   x  ≥ 2

as  the graph is descending and shows x = -1/2 as the gradient 4/-2 = -1/2

m = -1/2 would be the equation.

Therefore 2 (-1/2) = -1 and  -1 - 3 = -4 and 4 is not  greater than 2 so is wrong/.

Step-by-step explanation:

why are chiken nugget rw that come from plans

Answers

Answer:

because i decided that

Step-by-step explanation:

A positive real number is 1 more than another. When -2 times the smaller is added to the square of the larger, the result is 33. Find the numbers.

Answers

Answer:

The smaller number is 4√2 and the larger number is (4√2 + 1).

Step-by-step explanation:

Let the two numbers be x and y, where y is the larger of the two numbers.

Since y is the larger number, it is one more than the smaller number. So:

[tex]y=x+1[/tex]

When negative two times the smaller is added to the square of the larger, the result is 33. In other words:

[tex]-2x+y^2=33[/tex]

Substitute:

[tex]-2x+(x+1)^2=33[/tex]

Solve for x. Square:

[tex]-2x+(x^2+2x+1)=33[/tex]

Simplify:

[tex]x^2+1=33[/tex]

Subtract one from both sides:

[tex]x^2=32[/tex]

And take the square root of both sides:

[tex]x=\pm\sqrt{32}=\pm 4\sqrt{2}[/tex]

Since y is positive, we can ignore the negative case. So, the smaller number is:

[tex]x=4\sqrt{2}\approx5.66[/tex]

And the larger number is:

[tex]y = 4\sqrt{2} + 1 \approx6.66[/tex]

Write an equation for a line perpendicular to y=3x+1 and passing through the point (6,2)

Answers

Answer:

[tex]y = -\frac{1}{3}x + 4[/tex]

Step-by-step explanation:

Required

Equation of line

passes through [tex](6,2)[/tex]

In an equation of the form [tex]y =mx + b[/tex]; the slope is [tex]m[/tex]

So, by comparison;

The slope of [tex]y = 3x + 1[/tex] is: [tex]m =3[/tex]

From the question, we understand that the required equation is perpendicular to [tex]y = 3x + 1[/tex]

This means that its slope is:

[tex]m_2 =-\frac{1}{m}[/tex]

So, we have:

[tex]m_2 =-\frac{1}{3}[/tex]

The line equation is:

[tex]y = m_2(x - x_1) + y_1[/tex]

Where:

[tex](x_1,y_1) = (6,2)[/tex]

So, we have:

[tex]y = -\frac{1}{3}(x - 6) + 2[/tex]

[tex]y = -\frac{1}{3}x + 2 + 2[/tex]

[tex]y = -\frac{1}{3}x + 4[/tex]

Teresa is playing a video game. She earns 10 points when she completes Level 1. Each time she completes a level, she earns three times as many points as the previous level.

How many points will Teresa earn when she completes Level 7?

Enter your answer in the box.

Answers

Answer: 7290

Step-by-step explanation:

Three times is asking you to multiply the points before them by three. Level one, as we know is 10. Then, to get level two's points, you would multiply 10 by 3, to get 30, & so on.

Level One:10

Level Two: 10x3=30

Level Three: 30x3=90

Level Four: 90x3=270

Level Five: 270x3=810

Level Six: 810x3=2430

Level Seven: 2430x3= 7290

*** If you are still confused, comment on this question, & I will be happy to walk you through the whole question. ***

Answer:

7290 :)

Step-by-step explanation:

Took the quiz.

Question 2
Find the volume.

Answers

Answer:

Volume of cone = 686π/3 or 718.67 in³

Step-by-step explanation:

Given the following data;

Radius, r = 7 in

Height, h = 14 inches

From the diagram, we can see that the object is a cone

To find the volume of a cone;

Mathematically, the volume of a cone is given by the formula;

[tex] V = \frac{1}{3} \pi r^{2}h[/tex]

Where;

V is the volume of the cone.

r is the radius of the base of the cone.

h is the height of the cone.

Substituting into the equation, we have;

[tex] Volume = \frac{1}{3} * \frac {22}{7} *7^{2}*14 [/tex]

[tex] Volume = \frac{1}{3} * 22 * 7 * 14 [/tex]

[tex] Volume = \frac{1}{3} * 2156 [/tex]

[tex] Volume = 718.67 [/tex]

Volume of cone = 718.67 in³ or 686π/3 in³

It costs Beverly $0.50 to produce each bracelet she makes. She sells each bracelet for $20, plus three times the production cost per bracelet. Which equation below shows the amount Beverly charges, C, per bracelet, b?

Answers

Answer:

(0.5b+20b)*3b=c

Step-by-step explanation:

The requried equation that shows the amount Beverly charges per bracelet is C = 21.5b

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

The amount Beverly charges, C, per bracelet, b, is given by:

C = 20 + 3(0.5)

C = 20 + 1.5

C = 21.5

So the equation that shows the amount Beverly charges per bracelet is:

C = 21.5b

Learn more about models here:
https://brainly.com/question/22591166
#SPJ3

HELP ME PLEASEEEEEEEEEEEE

Answers

Answer:

x=in5

Step-by-step explanation:

What is the probability that a randomly selected day in the summer will be rainy if it’s cloudy?

Answers

Answer:

0.872

Step-by-step explanation:

Given that :

P(cloudy) = P(C) = 0.94

P(cloudy and rainy) = P(C n R) = 0.82

Probability that a given day will be rainy if it is cloudy ; this is a conditional probability problem:

Recall ; P(A|B) = P(AnB) / P(B)

P(R|C) = P(C n R) / P(C) = 0.82 / 0.94 = 0.872

Michael and Sondra are mixing lemonade. In Michael’s lemonade, the ratio of lemons to water is 1:4. In Sondra’s lemonade, the ratio of lemons to water is 2:6. Several equivalent ratios for each mixture are shown in the ratio tables.

Michael
Lemons
Cups of Water
1 4
3 12
4 16
Sondra
Lemons
Cups of Water
2 6
4 12
6 18

Imagine that you want to compare Michael’s ratio to Sondra’s ratio. Which two ratios in the tables shown have a common denominator you could use to compare?

Answers

Answer:

1/4= 3/12 & 2/6 = 4/12

Step-by-step explanation:

Answer:

Its simply B

Step-by-step explanation:

If we are to express both ratios in their simplest form, we will have the ratio of Michael’s lemonade is 1:4 and that of Sondra is 1:3. The denominator that can be used in order to compare the ratios is that which can be divided by both ratios. For example, we have 12 as a denominator. The ratios can be expressed as 3/12 and 4/12. Also, the denominator can be 24 such that the ratios can be expressed as 6/24 and 8/24.

why is the growth factor 0.9?

Answers

Answer:

Actual growth of population - Birth - Death + In migration - Out Migration. ...

According to my calculation the answer is :I just need points to pass summer school please don’t report help me out and leave a like

Sand is being dumped from a conveyor belt and forms a conical pile. Assuming that the height of this cone is always exactly 3 times the size of the radius of its base, and that thesand is added at the rate of 10 m^3/min, how fast is the height increasing when the pile is15 m high?

Answers

Answer:

dh/dt =  0.4 m/min

Step-by-step explanation:

The volume of the cone is:

V(c) = (1/3)*r² *h              if always  h = 3r    then    r = h/3

The volume of the cone as a function of h will be:

V(h)  =  (1/3)* (h/3)²*h

V(h) =  (1/27)*h³

The increasing rate of the volume is equal to the rate of sand added the:

D(V)/dt   = (1/27)*3*h²*dh/dt

D(v) / dt  =  10 m³/min

h =  15 m      and   dh/dt is the rate of increasing of the height

By substitution

10 m³/min  = ( 1/9)* 225 * dh/dt  (m²)

dh/dt =  90 / 225   m/min

dh/dt =  0.4 m/min

Anya contributed $1,200 toward the purchase
of a $2,000 computer. Her brother contributed
$240 toward the same computer. Her parents
provided the rest of the money for the computer. What percentage of the total cost of the computer did Anya's parents pay?

Answers

Answer:

Parent's share would be : 28%

Step-by-step explanation:

Cost of the computer = $2000

Anya's share = $1200

Brother's share = $240

Parents paid rest. That will be : 2000 - 1200 - 240 = $560

Percentage of parents share :

                                             [tex]\frac{560}{2000} \times 100 = 28 \%[/tex]

Evaluate the following expression. "12 more than 5"

Answers

Answer:

17

Step-by-step explanation:

12+5

gold that is 24 karat is 100% pure gold. gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper,zinc,silver, or nickel. What percent of 14 karat gold if pure gold.

help im confused

Answers

It would be 58.3%

100% is 14+10=24

14 divided by 24 = 0.583
Move decimal over to the right twice is 58.3%

find the area of the following figure.

Answers

39 square meters
Explanation:
Divide figure into two triangles:

Area of triangle to the left (1/2•base•height):
1/2 • 6 • 4 = 12 square meters

Area of triangle to the right:
1/2 • 6 • 9 = 27 square meters

Add the area of both triangles:
27 + 12 = 39
FINAL ANSWER: 39 square meters
Hope this helps!

a cylinder water tank carries a volume of 150L when it is full. The water tank has a base surface with a diameter of 140 cm. what is the height of the water tank?​

Answers

Answer:

9.74418019cm=h

~ 9.7442

Step-by-step explanation:

volume of a cylinder=πr²h

radius=½of diameter

=½×140cm

=70cm

1l=1000cm³

150l=150l/1l×1000cm³

=150000cm³

150000cm³=π(70cm)²×h

150000cm³=15393.8040cm²h

150000cm³/15393.8040cm²=15393.8040cm²h/15393.8040cm²

150000cm³/15393.8040cm²=h

9.74418019cm=h

Use the method of least squares to solve the following problem.
Given the data set below, find the line of best fit? Then find the y-value for when x=7. Yes, there are supposed to be
two 6's.
Х
1
2
4
5
6
6
8
9
Y
14
10
12
8
9
6
3
4

Answers

purr fbfbfbffjhfbfbfbfbfbfbf

Can someone please answer and explain this.

Answers

Answer:

x =74

Step-by-step explanation:

540 degrees is the sum of all the angles

90 +90 + 2x+10 + x + 2x-20 = 540

Combine like terms

5x+170=540

Subtract 170 from each side

5x = 370

Divide by 5

5x/5 = 370/5

x =74

Please help me!!! WILL MARK BRAINLIEST AND THANK

Answers

Answer:

2 is the same as 4

Step-by-step explanation:

A card is drawn randomly from a standard 52 card deck. Find the probability of drawing the given card. NO LINKS!!!!

Answers

Answers:

Problem 7)  1/26Problem 8)  1/13Problem 9)  10/13Problem 10)  1/2Problem 11)  11/13Problem 12)  3/13

===================================================

Explanations:

Problem 7)

There are 2 red aces (hearts, diamonds) out of 52 cards total, so 2/52 = 1/26 is the probability of picking a red ace.

---------------------------

Problem 8)

There are 4 kings out of 52 cards total, so 4/52 = 1/13 are the odds of picking a king.

This is the same as say focusing on one suit (eg: clubs) and finding the probability of pulling out a king.

---------------------------

Problem 9)

There are 3 face cards per suit (Jack, Queen, King) so 3*4 = 12 face cards in all. The odds of picking a face card are 12/52 = 3/13. That makes 10/13 the odds of not picking a face card, since 3/13+10/13 = 1.

---------------------------

Problem 10)

The answer is 1/2 because half of the cards are red.

You could say 26/52 = 1/2 since there are 26 red cards out of 52 cards total.

---------------------------

Problem 11)

There are 4 copies of '2' and 4 copies of '3', so there are 4+4 = 8 cards we want to avoid. The probability of picking either of them is 8/52 = 2/13. The odds of not picking any of these cards is 11/13  (refer to problem 9).

---------------------------

Problem 12)

We have 4 copies each of '7', '8' and '9'

That gives 4*3 = 12 cards total we want to pick.

So 12/52 = 3/13 is the answer.

Other Questions
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