It looks like the given differential equation is
(3x² + y²) y + (y² - x²) x dy/dx = 0
Multiply both sides by 1/x³ to get
(3 + y²/x²) y/x + (y²/x² - 1) dy/dx = 0
(Note that in order to do this, we must have x ≠ 0, which means that if a solution exists, it would have to be on either (-∞, 0) or (0, ∞).)
Now substitute z = y/x, or y = xz, from which we get dy/dx = x dz/dx + z. Making this replacement and simplifying yields a separable equation:
(3 + z²) z + (z² - 1) (x dz/dx + z) = 0
(3 + z²) z + (z² - 1) x dz/dx + (z² - 1) z = 0
(z² - 1) x dz/dx = -(2z³ + 2z)
x dz/dx = (2z³ + 2z)/(1 - z²)
(1 - z²)/(2z (z² + 1)) dz = dx/x
Integrate both sides. On the left, split up the expression into partial fractions.
[tex]\dfrac{1-z^2}{z(z^2+1)} = \dfrac az + \dfrac{bz+c}{z^2+1}[/tex]
[tex]\dfrac{1-z^2}{z(z^2+1)} = \dfrac{a(z^2+1)+(bz+c)z}{z(z^2+1)}[/tex]
[tex]1-z^2 = (a+b)z^2 + cz + a[/tex]
for which we find a = 1, b = -2, and c = 0:
[tex]\dfrac{1-z^2}{2z(z^2+1)} = \dfrac12 \left( \dfrac1z - \dfrac{2z}{z^2+1} \right)[/tex]
Integrating and simplifying yields
1/2 ∫ (1/z - 2z/(z² + 1)) dz = ∫ dx/x
1/2 (ln|z| - ln(z² + 1)) = ln|x| + C
1/2 ln|z / (z² + 1)| = ln|x| + C
ln(√(z/(z² + 1))) = ln|x| + C
exp[ln(√(z/(z² + 1)))] = exp[ln|x| + C]
√(z/(z² + 1)) = exp[ln|x|] exp[C]
√(z/(z² + 1)) = Cx
z/(z² + 1) = Cx²
Replacing z = y/x then gives us an implicit solution of
(y/x) / (y²/x² + 1) = Cx²
xy / (y² + x²) = Cx²
y / (y² + x²) = Cx
y = Cx (y² + x²)
Cxy² - y + Cx³ = 0
though we can solve for y explicitly (assuming x > 0) using the quadratic formula to end up with
y = (1 + √(1 - Cx⁴))/(Cx)
(the other solution only differs by the sign on the square root)
A square is inscribed in a circle as shown below. The radius of the circle is
decreasing at a constant rate of ½ centimeter per second. When the
radius of the circle is 4√2 centimeters, what is the rate of change of the
area of the shaded region found outside the square but inside the circle.
Answer:
3
Step-by-step explanation:
What is the slope of the line?
Use set notation to write the members of the following set, or state that the set has no members. Odd numbers between 2 and 82 that are multiples of 9
Let the set of all Odd multiples of 9 between 2 and 82 be denoted by D, then, using set-builder notation,
[tex]D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}[/tex]
The odd multiples of 9, [tex]m[/tex], in the range [tex]2\le m \le 82[/tex] form the set
[tex]\{9,27,45,63,81\}[/tex]
Each member of the set is a term of the arithmetic progression
[tex]U_n=18n+9[/tex]
where the values of [tex]n[/tex] range from 0 to 4, or [tex]0\le n\le 4[/tex]
Putting these facts together, we get the result
[tex]D=\{ 18n+9 \mid n \in \mathbb{N}, 0\le n\le 4 \}[/tex]
Learn more about set-builder notation here: https://brainly.com/question/17238769
According to the central limit theorem, if a sample of size 100 is drawn from a population with a mean of 80, the mean of all sample means would equal _______. SHOW THE STEPS TO ARRIVE A T THE ANSWER (4 points)
Answer:
μX = the mean of X
σX = the standard deviation of X
If you draw random samples of size n, then as n increases, the random samples
¯¯¯¯¯
X
which consists of sample means, tend to be normally distributed.
¯¯¯¯¯
X
~ N (
μ
x
,
σ
x
√
n
)
The central limit theorem for sample means says that if you keep drawing larger and larger samples (such as rolling one, two, five, and finally, ten dice) and calculating their means, the sample means form their own normal distribution (the sampling distribution). The normal distribution has the same mean as the original distribution and a variance that equals the original variance divided by, the sample size. The variable n is the number of values that are averaged together, not the number of times the experiment is done.
To put it more formally, if you draw random samples of size n, the distribution of the random variable
¯¯¯¯¯
X
, which consists of sample means, is called the sampling distribution of the mean. The sampling distribution of the mean approaches a normal distribution as the sample size n increases.
The random variable
¯¯¯¯¯
X
has a different z-score associated with it from that of the random variable X. The mean
¯¯¯
x
is the value of
¯¯¯¯¯
X
in one sample.
z =
¯¯¯
x
−
μ
x
σ
x
√
n
μ
x
=
μ
¯¯¯
x
(mean of X = mean of
¯¯¯¯¯
X
. )
σ
¯¯¯
x
=
σ
x
√
n
= standard deviation of
¯¯¯¯¯
X
and is called the standard error of the mean.
Step-by-step explanation:
sorry if its hard/ confusing
ILL GIVE BRAINLIEST!!! Maya has $15 to spend. She spent $5.50, including tax, to buy a notebook. She needs to save $7.75, but she wants to buy a snack. If cookies cost $0.25 per package including tax, what inequality would show the maximum number of packages that Maya can buy?
Answer:
The answer is 7 she Can Buy 7 packages of cookies.
Step-by-step explanation:
1. 15-5.50=9.50
2.9.50-7.75=1.75
3. 1.75-0.25*7=0
She wouldn't have any money left over to buy it
please help with this math
A colony of bees doubles in size every month. If there are initially 5000 bee, create a model for the bee population
we know that the colony is doubling, namely the rate of growth is 100% of whatever is existent, thus
[tex]\textit{Amount of Population Growth} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=\textit{elapsed time}\dotfill &t\\ \end{cases} \\\\\\ A = 5000e^{1\cdot t}\implies \boxed{A = 5000e^t}[/tex]
Jen has 93 beads ana has 46 red beads and 29 blue beads.How many more beads does Ana need to have 93 beads Also?
Answer: 18
Step-by-step explanation: 93 - (46 + 29) = 18
Evan and Brayden want to know if they have more X Box games than Reid and Bryce do
combined. Evan has 43 and Brayden has 42. Reid has 76 and Bryce has 23. Which pair of
boys has more? How much more do they have?
Answer:
Step-by-step explanation:
Evan has 43 and Brayden has 42. Reid has 76 and Bryce has 23. Which pair of boys has more? How much more do they have?
Reid and Rryce have more. If you add 43 and 42 you get 85 and when you add 76 and 23 you get 99. So now subtract 99 and 23 which is 76.
ill mark brainliest thanks
Answer:
x=10
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
6x-7 = 26+2x+7
Combine like terms
6x-7 = 2x+33
Subtract 2x
6x-7-2x =2x+33-2x
4x-7 = 33
Add 7 to each isde
4x-7 +7 = 33+7
4x=40
Divide by 4
4x/4 = 40/4
x=10
if 5c-2=3c, then 24c=
Answer:
24
Step-by-step explanation:
Step-by-step explanation:
24 is 3×8
so, when
3c = 5c-2
then
8×3c = 24c = 8×(5c-2) = 40c - 16
what 5 + 5- just asnwer pls
Answer:
5+5=10
but if you mean
5+-5 then that = 0
Step-by-step explanation:
The initial population of a town is 3800, and it grows with a doubling time of 10 years. What will the population be in 8 years?
Please show step by step!
Answer:
The population was 3040 people in 8 years.
Step-by-step explanation:
find unit rate;
3800/10 = 380
380 x 8 = 3040
A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are in the table below.
Completed Homework Did not Complete Homework Total
Passed the Course 25 7 32
Did not Pass the Course 5 18 23
Total 30 25 55
A student from the class is randomly selected. Determine the following probabilites. Enter your results as percents rounded to two decimal places.
What is the probability a student passed the course given that they completed their homework?
%
What is the probability a student passed the course given that they didn't complete their homework?
28
Correct%
What is the probability a student completed their homework given that they passed the course?
%
What is the probability a student didn't complete their homework given that they didn't pass the course?
%
Probabilities are used to determine the chances of an event.
Let P represents the event that a student passes the course, and C represents the event that a student completes the assignment
(a) The probability a student passed the course given that they completed their homework?
From the table, we have:
[tex]\mathbf{n(P\ n\ C) = 25}[/tex]
[tex]\mathbf{n(C) = 30}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(C)}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{25}{30}}[/tex]
[tex]\mathbf{Pr = 0.8333}[/tex]
Express as percentage
[tex]\mathbf{Pr = 83.33\%}[/tex]
Hence, the probability a student passed the course given that they completed their homework is 83.33%
(b) The probability a student passed the course given that they didn't complete their homework
From the table, we have:
[tex]\mathbf{n(P\ n\ C'= 7}[/tex]
[tex]\mathbf{n(C') = 25}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C')}{n(C')}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{7}{25}}[/tex]
[tex]\mathbf{Pr = 0.28}[/tex]
Express as percentage
[tex]\mathbf{Pr = 28\%}[/tex]
Hence, the probability a student passed the course given that they didn't complete their homework is 28%
(c) The probability a student completed their homework given that passed the course?
From the table, we have:
[tex]\mathbf{n(P\ n\ C) = 25}[/tex]
[tex]\mathbf{n(P) = 32}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(P)}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{25}{32}}[/tex]
[tex]\mathbf{Pr = 0.78125}[/tex]
Express as percentage
[tex]\mathbf{Pr = 78.125\%}[/tex]
Approximate
[tex]\mathbf{Pr = 78.13\%}[/tex]
Hence, the probability a student completed their homework given that they passed the course is 78.13%
(d) The probability a student didn't complete their homework given that they didn't pass the course
From the table, we have:
[tex]\mathbf{n(P'\ n\ C'= 18}[/tex]
[tex]\mathbf{n(P) = 23}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P'\ n\ C')}{n(P')}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{18}{23}}[/tex]
[tex]\mathbf{Pr = 0.7826}[/tex]
Express as percentage
[tex]\mathbf{Pr = 78.26\%}[/tex]
Hence, the probability a student didn't complete their homework given that they didn't pass the course is 78.26%
Read more about probabilities at:
https://brainly.com/question/11234923
Ninety (90) milliliters is equal to how many tablespoons?
Answer: 6.087 tablespoons. or rounded to nearest whole, 6
Step-by-step explanation:
I just know
Help help help help help help help help help help help
Answer:
Step-by-step explanation:
A' = (2 + 3, 1 + 2) = (5, 3)
B' = (-1 + 3, -3 + 2) = (2, -1)
C' = (3 + 3, -3 + 2) = (6, -1)
HELPPP LAST ATTEMPT!!
Hello, Sorry To bother you nice ppl but more questions awaits u :)
Answer:
B. -2x + 10 is the correct answer
Answer:
(C) -2x + 10
Step-by-step explanation:
This is going to be multiplication from the first number outside the "Bubble"
-2 multiplied by x = -2x ,
why ? because a negative times a positive makes a negative
Next is -2 multiplied by -5 = 10
why ? because a negative times a negative = equals a positive !
now .. you add up all of the sums together to make an equation ..
Answer would be -2x+10
y=7x+7 standard form
Answer:
7x - y = -7
Step-by-step explanation:
Hope this helps!
Veronica has two offers for a $65,000 student loan. The first loan has a 6.3% interest rate for 15 years, and the second loan has a 4.8% interest rate for 20 years. Both loans have interest compounded every month. Veronica is interested in finding the loan that minimizes the amount of interest that she will pay over the life of the loan. Which loan has a lower amount of interest paid?
The second option has a lower amount of interest paid.
In order to determine the loan option that minimizes loan payment, the future value of both loan options has to be determined.
FV = P (1 + r)^nm
FV = Future value
P = Present value
R = interest rate
m = number of compounding
N = number of years
First loan option
65000( 1 + 0.063/12)^300 = 312,707.21
Second loan option
65000( 1 + 0.048/12)^240 = 169,435.51
A similar question was answered here: https://brainly.com/question/23082103
(PHOTO) please help need this done by tomorrow thank you.
Answer: 125
Step-by-step explanation: ∠4 and 55 are supplementary angles. This means that ∠4 and 55 add up to 180. We can use this to solve for ∠4.
180 - 55 = ∠4
125 = ∠4
So, ∠4 is equal to 125 degrees.
Would appreciate brainly <3
Selina has a balance of $1,200 in his First State Bank checking account. He deposits a $387.89 paycheck, a $437.12 dividend check, and a personal check for $250 into his account. He wants to receive $400 in cash. How much will he have in his account after the transaction?
Answer:
$1,875.01
Step-by-step explanation:
Cash in Bank :
DEBIT(+) :
+ $1,200.00
+ $387.89
+ $250.00
+ $437.12
CREDIT (-) :
- $400.00
Capital:
DEBIT (-) :
- $400.00
CREDIT (+) :
+ $1,200.00
+ $387.89
+ $250
Accounts Payable :
DEBIT (-):
0
CREDIT (+):
+ $437.12
Find the inequality represented by the graph in the picture
(Khan academy)
Answer:
[tex]y < 3x - 4[/tex]
Step-by-step explanation:
We can tell right away, that the line has a positive slope, since it goes upwards and to the right. To find the slope exactly, we will use rise/run. We will count the units from the first given point until we reach the next point.
So we can tell that the slope is 3/1 or just 3.
Also, since the line crosses the y-axis at -4, this will be the y-intercept.
Next, since the line is dotted, we know that the inequality sign will either be the "greater than" sign, or the "lesser than" sign. In this case, since the shaded area is below the line, we will use the "lesser than" sign.
So all together, we have y < 3x - 4.
Hope this helps you :)
The force in Newtons acting on a particle located x meters from the origin is given by the function F(x)=12x2+7. What is the work done in Joules when moving the particle from x=2 to x=5?
[tex]W = \displaystyle \int^{5}_{2} F(x) ~ dx\\\\\\= \displaystyle \int^{5}_{2} \left(12x^2 +7\right) ~dx\\\\\\= 12\displaystyle \int^{5}_{2} x^2 ~dx + \displaystyle \int^{5}_{2} 7~ dx\\\\\\=12 \left[\dfrac{x^3}3 \right]^{5}_{2} + 7\left[x\right]^{5}_{2}\\\\\\=4(5^3-2^3) + 7(5-2) = 468 + 21 = 489~ J[/tex]
PLEASE HELP ME!
Find the x- and y-intercepts of the graph of -x+2y=6. State each answer as an integer or an improper fraction in simplest form.
Select all the statements that are true for △ABC.A. AH is an altitude.
B. IH is a median.
C. JC is a median.
D. The medians and altitudes intersect at the same point.
E. The altitudes intersect outside of the triangle.
The relationships between the two medians and an altitude marked on
ΔABC can be used to determine the true statements.
The true statements are;
A. AH is an altitudeC. JC is a medianReasons:
A median line is a line that extends from the vertex to the midpoint of the
opposite side, bisecting the opposite side.
In the figure, we have;
The median of ΔABC are; JC, and BI
The point of intersection is the point K
The altitude is a perpendicular line from a vertex to the opposite side
known as the base of the triangle.
The given altitude of ΔABC is; AH
Therefore, the statements that are true are;
A. AH is an altitude
C. JC is a median
Learn more about the median line and altitude of a triangle here:
https://brainly.com/question/2141396
https://brainly.com/question/4420798
what is the first three elements of an arithmetic sequence are -13 , -8 and -3, which elements is 182?
If you own a car with an assessed value of 23,300 in the state of West Virginia, which has a 1.66% tax rate, what would your property taxes be for your vehicle
Answer:
Average County Tax Rate
0.520%
(Mercer County)
Property Taxes
$121
(Annual)
Step-by-step explanation: I'm assuming this is the answer, if you can please can you mark me Brainliest.
Help please i need to know this answer
Answer:
976
SA=2(S1)+2(S2)+S3
S1=14*24/2
S1=168
S2=25*10
S2=250
S3=14*10
S3=140
SA=2(168)+2(250)+140
SA=976 cm
A class of 22 students has taken an exam, and the mean of their scores is 76.5. One student takes the
exam late, and scores 92. After including the new score, what is the mean score for all 23 exams? Round
to the nearest hundredth.
The mean score for all 23 students is 77.17.
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number.
The first step is to determine the total scores of the 22 students.
Total scores = mean score x number of students
22 x 76.5 = 1683
The second step is to add the score of the student that took the exam late tot he total scores.
New total score = 1683 + 92 = 1775
The third step is to determine the new mean score.
new mean score = new total score / total number of students
1775 / 23 = 77.17
To learn more about the mean of a set of numbers, please check: https://brainly.com/question/15420908?referrer=searchResults