Q.1 Determine whether y = (c - e ^ x)/(2x); y^ prime =- 2y+e^ x 2x is a solution for the differential equation Q.2 Solve the Initial value problem ln(y ^ x) * (dy)/(dx) = 3x ^ 2 * y given y(2) = e ^ 3 . Q.3 Find the general solution for the given differential equation. (dy)/(dx) = (2x - y)/(x - 2y)

Q.1 Determine Whether Y = (c - E ^ X)/(2x); Y^ Prime =- 2y+e^ X 2x Is A Solution For The Differential

Answers

Answer 1

(Q.1)

[tex]y = \dfrac{C - e^x}{2x} \implies y' = \dfrac{-2xe^x-2C+2e^x}{4x^2} = \dfrac{-xe^x-C+e^x}{2x^2}[/tex]

Then substituting into the DE gives

[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{2\left(\dfrac{C-e^x}{2x}\right) + e^x}{2x}[/tex]

[tex]\dfrac{-xe^x-C+e^x}{2x^2} = -\dfrac{C-e^x + xe^x}{2x^2}[/tex]

[tex]\dfrac{-xe^x-C+e^x}{2x^2} = \dfrac{-C+e^x - xe^x}{2x^2}[/tex]

and both sides match, so y is indeed a valid solution.

(Q.2)

[tex]\ln\left(y^x\right)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]

This DE is separable, since you can write [tex]\ln\left(y^x\right)=x\ln(y)[/tex]. So you have

[tex]x\ln(y)\dfrac{\mathrm dy}{\mathrm dx} = 3x^2y[/tex]

[tex]\dfrac{\ln(y)}y\,\mathrm dy = 3x\,\mathrm dx[/tex]

Integrate both sides (on the left, the numerator suggests a substitution):

[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 + C[/tex]

Given y (2) = e ³, we find

[tex]\dfrac12 \ln^2(e^3) = 6 + C[/tex]

[tex]C = \dfrac12 \times3^2 - 6 = -\dfrac32[/tex]

so that the particular solution is

[tex]\dfrac12 \ln^2(y) = \dfrac32 x^2 - \dfrac32[/tex]

[tex]\ln(y) = \pm\sqrt{3x^2 - 3}[/tex]

[tex]\boxed{y = e^{\pm\sqrt{3x^2-3}}}[/tex]

(Q.3) I believe I've already covered in another question you posted.


Related Questions

A Line passes through the .4 -6 and has a slope of -3 and four which is the equation of the line

Answers

Answer:

(in the image)

Step-by-step explanation:

I'm not sure I understood your question completely but I hope this helps.

FREE
Circle O has a circumference of approximately 250 ft.
What is the approximate length of the diameter, d?
O 40 ft
O 80 ft
O 125 ft
O 250 ft
Save and Exit
Next
Submit
Mark this and return

Answers

Answer:

Step-by-step explanation:

circumference = πd ≅ 250 ft

d ≅ 250/π ≅80 ft

By converting to an exponential expression, solve log2 (x + 5) = 4

Answers

Step-by-step explanation:

just insert a base of two at on both sides and solve.

The solution of the logarithmic equation ㏒ (x + 5) / ㏒ 2 = 4 will be 11.

What is the solution to the equation?

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The logarithmic equation is given below.

㏒₂(x + 5) = 4

Simplify the equation, then we have

㏒ (x + 5) / ㏒ 2 = 4

㏒ (x + 5) = 4 × ㏒ 2

㏒ (x + 5) = ㏒ 2⁴

Take antilog on both sides, then we have

(x + 5) = 2⁴

(x + 5) = 16

x = 11

The solution of the logarithmic equation ㏒ (x + 5) / ㏒ 2 = 4 will be 11.

More about the solution of the equation link is given below.

https://brainly.com/question/545403

#SPJ2

if cosA=3√2/5,then show that cos2A=11/25

Answers

Answer:

Step-by-step explanation:

Cos 2A = 2Cos² A - 1

             [tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]

HELP HELP HELP MATH⚠️⚠️⚠️⚠️⚠️

Find four consecutive integers with the sum of 2021

Answers

Answer:

This problem has not solution

Step-by-step explanation:

lets the  integers be:

x

x+1

x+2

x+3

so:

x+(x+1)+(x+2)+(x+3)=2021

x+x+x+x+1+2+3=2021

4x+6=2021

4x=2021-6=2015

x=2015/4=503.75

x is not a integer

Probabilityyyyyyyyyyyyyyy

Answers

Answer:

Reduce if needed, asked or necessary

Step-by-step explanation:

1. 4/10

2. 2/6

3. 4/10

4. more likely

Answer:

Since Probability Is Usually Written In Fraction Form OR Ratios

(Although It Really Doesn't Matter):

1.  4/10 (2/5)

2.  2/6  (1/3)

3.  6/10 (3/5)

(All Fraction Form)

Last Question:

I can't really see the bottom but probably its 'More likely' since you can already see a bunch of red marbles.

Step-by-step explanation:

This is the basic fraction form :  ____ / ____

Based on what they ask, like the probability of picking out a black marble, count the number of black marbles in the particular bag and put that number as the numerator. The denominator is the total amount of marbles in that particular bag. Hope this helps!

Please answer & number. Thank you! <33

Answers

Answer:

2)=2

4)=3

5)=5

8)=-1

Step-by-step explanation:

just divide the number by the number with variable

if side of square is 4.05 find its area ​

Answers

Answer:

A

16.4

please give brain list

is there a formula for this?
help asap!!

Answers

Answer:

yes

Step-by-step explanation:

the answer is c well thats what my teacher said

Answer:

B

Step-by-step explanation:

using sine rule

[tex] \frac{y}{sin \: 45} = \frac{5}{sin \: 45} \\ y = 5[/tex]

using sin rule

[tex] \frac{x}{sin \: 90} = \frac{5}{sin \: 45} \\ \\ 5sin90 = xsin45 \\ \\ x = \frac{5 \: sin \: 90}{sin \: 45} \\ x = \frac{5}{0.7071} \\ x = 7.071[/tex]

x=5√2

Simplify. v80

A. 16v5
B. 5v4
C. 4v5
D. 20v4

Answers

Hi!

√80 = √(16 • 5) = √(4² • 5) = 45

For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. What is the percent of wolves that are female but do not hunt in medium-sized packs?

Answers

20% is the answer
55%-20%-15%=20%

i need help solving this .

Answers

Answer:b

Step-by-step explanation:

Answer:

just be smart trust me u dont need us to give u the answer ur super smart

Step-by-step explanation:

make me brainliest to help people be encourage

sets A and B have 3 and 6 elements respectively. what can be the minimum number of elements in AUB

Answers

Answer:

6

Step-by-step explanation:

n(AUB) = n(A) + n(B) - n(AnB)

n(AUB) can have the minimum number of elements if n(AnB) has the maximum number of elements.

n(AnB) maximum = 3

so n(AUB) = 3+6-3 = 6

The original price of a set lunch was 30 dollars. It is now sold at a 20%
discount. There is an extra discount of 10% for students. How much
should a student pay to order a set lunch?

Answers

Find out the total discount percentage that students receive.

20% + 10% = 30%

30/100 x 30 = 9 dollars

30 - 9 = 21 dollars (Final answer)
20% of $30 = $6
30 - 6 = $24
10% of $24 = $2.40
24 - 2.40 = $21.60 cost of student lunch

You have to do each percent separate to get the cost.
If you just take 30% off from the original cost of $30 it will be the wrong answer.

HELP ASAP! I don’t know how to solve this problem nor where to start. Can someone please help me out here?

Answers

Answer:   344

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

Explanation:

It might help to draw out the picture as shown below. The pool itself (just the water only) is the inner rectangle. The outer rectangle is the pool plus the border of those 1 by 1 tiles.

The pool is a rectangle 90 feet by 80 feet. If we add on the tiles, then we get a larger rectangle that is 90+2 = 92 feet by 80+2 = 82 feet.

We add on 2 since we're adding two copies of "1" on either side of each dimension.

The larger rectangle's area is 92*82 = 7544 square feet

The smaller rectangle's area is 90*80 = 7200 square feet

The difference in areas is 7544-7200 = 344 square feet.

Each 1 by 1 tile is of area 1*1 = 1 sq foot, meaning that 344 tiles will get us the 344 square foot border around the pool.

A farmer picks pumpkins from a large field. The farmer makes samples of 260 pumpkins and inspects them. If one in fifty pumpkins are not fit to market and will be saved for seeds, what is the standard deviation of the mean of the sampling distribution of sample proportions?

Answers

Answer:

[tex]\mu = 5.2[/tex]

[tex]\sigma = 2.257[/tex]

Step-by-step explanation:

Given

[tex]n = 260[/tex] -- samples

[tex]p = \frac{1}{50}[/tex] --- one in 50

Solving (a): The mean

This is calculated as:

[tex]\mu = np[/tex]

[tex]\mu = 260 * \frac{1}{50}[/tex]

[tex]\mu = 5.2[/tex]

Solving (b): The standard deviation

This is calculated as:

[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]

[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]

[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]

[tex]\sigma = \sqrt{5.096}[/tex]

[tex]\sigma = 2.257[/tex]

ab=6cm ac=12 calculate the length of cd

Answers

Answer:

is that the full question?

Answer:

Solution:-

Given,

ab =perpendicular (p)= 6cm

ac =hypotenuse (h)= 12cm

cd =base (b)= ?

using , Pythagoras theorem we have ,

b²=√h²-p²

or,cd²=√ac²-ab²

= √12²-6²

= √144-36

=√108

=√10.8²

=10.8cm

the length of cd is 10.8 cm

hope it is helpful to you

F(x) =-2x-4 find x if f(x)=14

Answers

Answer:

14=-2x-4

18=-2x

x=-9

Hope This Helps!!!

Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 196 people from the city. The average height of your sample is 68 inches, while the standard deviation of the heights in your sample is 7 inches. The standard error of your estimate of the average height in the city is

Answers

Answer:

The standard error of your estimate of the average height in the city is 0.5 inches.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

You begin by collecting the heights of a random sample of 196 people from the city.

This means that [tex]n = 196[/tex]

The standard deviation of the heights in your sample is 7 inches.

This means that [tex]\sigma = 7[/tex]

The standard error of your estimate of the average height in the city is

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{7}{\sqrt{196}} = 0.5[/tex]

The standard error of your estimate of the average height in the city is 0.5 inches.

Which of the following consists of discrete​ data?
A. Number of suitcases on a plane.
B. Amount of rainfall.
C. Hair color.
D. Tree height.

Answers

Answer:

A

Step-by-step explanation:

Number of suitcases on a plane is discrete because you can only have an integer amount. You can't have a fraction of a suitcase on a plane.

What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
Use the button on your calculator to complete this
problem.
V=
cm3

Answers

Answer:4778.3 cm^3

Step-by-step explanation: The formula for volume of a cone is V=1/3h pi r^2. By plugging in the height and the radius we get our answer.

Answer:

4778.4 :)

Step-by-step explanation:

Create a circle such that its center is point A and B is a point on the circle.

Answers

Answer:

The center of a circle is the point in the circle which is equidistant to all the edges of thr circle. The point a is the center, while point b is an arbitrary point in the circle. Find attachment for the diagram.

A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 volt, and the manufacturer wishes to test volts against volts, using units. In your intermediate calculations, use z-scores rounded to two decimal places (e.g. 98.76).
(a) The acceptance region is_____. Find the value of a.
(b) Find the power of the test for detecting a true mean output voltage of 5.1 volts.

Answers

Answer: hello your question was poorly written but i was able to the get missing parts online which enabled me resolve your question

answer:

a) a = 0.1096

b) 1.89 watts

Step-by-step explanation:

Std of output voltage = 0.25 volt

H0 : μ = 5 volts

Ha : μ ≠ 5 volts

n = 16

a) Acceptance region = 4.9 ≤ X ≤ 5.1  

Determine the value of a

value of a = 0.0548 + 0.0548

                 = 0.1096

attached below is the reaming solution

note : a is a type 1 error

b) power of test

True mean output voltage = 5.1 volts

P = - 1.89 watts

power cant be negative hence the power of the test  = 1.89 watts

Follow the process of completing the square
to solve 2x2 + 8x - 12 = 0.
After adding B2 to both sides of the equation in step 4, what is the constant on the right side of the equation?

Answers

2x^2 + 8x - 12 = 0..divide by 2

x^2 + 4x - 6 = 0

x^2 + 4x = 6...add 4 to both sides of the equation

x^2 + 4x + 4 = 6 + 4

(x + 2)^2 = 10....<== ur constant is 10

x + 2 = (+-)sqrt 10

x = -2 (+ - ) sqrt 10

x = -2 + sqrt 10

x = -2 - sqrt 10

Solve the system of equations using the elimination method 5x+10y = 3
10x + 20y = 8

Answers

Answer:

No solution

Step-by-step explanation:

5x+10y=3 equation 1

10x+20y=8 equation 2

-2(5x+10y)=-2(3) multiply equation 1 by -2 to eliminate x

-10x-20y=-6 equation 1 multiplied by -2

10x+20y=8 equation 2

0  +  0  =2. Add above equations

    0      =2  

no solution

Which of the following is a like radical to cube rt of 7x

Answers

Answer:

[tex]\sqrt[3]{7x}[/tex]

Step-by-step explanation:

Given

[tex]7x[/tex]

Required

The radical statement

Cube root is represented as:

[tex]\sqrt[3]{}[/tex]

Considering [tex]7x[/tex], the expression is:

[tex]\sqrt[3]{7x}[/tex]

i need helpp pleaseee

Answers

To plot the point (3,-7) start at the origin (0,0) and move right three (3) units and then down seven (7) units.

In a family of 3 children, what is the probability that there will be exactly 2 boys assuming that the sexes are equally likely to occur in each birth​

Answers

Answer:

There is a 60.00 percent probability of a particular outcome and 40.00 percent probability of another outcome.

Need help with this really fast

Answers

Answer:

6

Step-by-step explanation:

You can apply the proportion of 9/6 to 4 to get 6:

6*(9/6)= 9

So

4*(9/6) = Length LA

6= Length LA

Answer:

Option C, or [tex]2\frac{2}{3}[/tex]

Explanation:

We can see that the Line FM in the smaller triangle dialates to Line LK in the bigger triangle by the scale factor of:

FM/LK

6/9 or 2/3

So we would know that to find out the value of LA in the bigger triangle we would have to dialate it’s corresponding side FI in the smaller triangle by the same scale factor:

4 * 2/3

=> [tex]2\frac{2}{3}[/tex] = LA

Hope this helps!

Identify the transformation that occurs to create the graph of h(x).
H(x)=f(x+3)

Answers

Answer: The graph moved left 3 units.

(x, y) = (x - 3, y)

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