Yes, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2
Here,
The differential equation (1-xy)y' = y^2
And, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2.
What is Differential equation?
A differential equation is a mathematical equation that relates some function with its derivatives.
Now,
To show y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2, we have to find the solution of differential equation.
The differential equation is;
[tex](1-xy)y'=y^2\\\\\\\\[/tex]
[tex](1-xy) \frac{dy}{dx} = y^2[/tex]
[tex]\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }[/tex]
It is form of [tex]\frac{dx}{dy} + Px = Qy[/tex],
Where, P is the function of y and Q is the function of x.
Hence, Integrating factor = [tex]e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y[/tex]
The solution is;
[tex]x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c[/tex]
[tex]xy = lny + c[/tex]
Take c = 0, we get;
[tex]xy = lny\\\\y = e^{xy}[/tex]
Hence, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2
Learn more about the differential equation visit:
https://brainly.com/question/1164377
#SPJ4
11) Mike is thinking of two numbers. Their difference is 12. If one of the numbers is 19, what is the other
number? Is there only one answer? If not, what is the other possibility for the second numbe? Explain
your reasoning.
Answer: 7, and 31
Step-by-step explanation:
7 + 12 = 19 or 19 - 12 = 7
19 + 12 = 31
The other number will be - 7.
Yes, There is only one answer.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The difference of two numbers is 12.
And, one of the numbers is 19.
Now,
Let two numbers are x and y.
So, We get;
x + y = 12
Here, one of the numbers is 19.
So, x = 19
We get;
x + y = 12
19 + y = 12
y = 12 - 19
y = - 7
Thus, The other number will be - 7.
Yes, There is only one answer.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
Raíz cuadrada de 864
Raíz cuadrada de 864
Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:
The general equation of ellipse is given as, x2a2+y2b2=1 x 2 a 2 + y 2 b 2 = 1 , where, a is length of semi-major axis and b is length of semi-minor axis.
centro: (0,0)
focus : (0, -√28) , (0, √28)
eje conjugado = 2√3
por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:
de los focos podemos obtener que: √28
y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:
b = √3
podemos utilizar la siguiente fórmula para obtener a:
si despejamos a en la ecuación obtenemos lo siguiente:
ahora podemos sustituir los valores:
a=5
así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:
si graficamos la hipérbola, queda como en el documento adjunto.
To learn more hipérbola
Visit : https://brainly.com/question/24223341
#SPJ9
which value of x is a solution...
Answer:
(4), -5/6
Step-by-step explanation:
[tex]13-36x^2-13=-12-13\\-36x^2=-25\\\frac{-36x^2}{-36}=\frac{-25}{-36}\\x^2=\frac{25}{36}\\x=\sqrt{\frac{25}{36}},\:x=-\sqrt{\frac{25}{36}}[/tex]For x^2 = f(a), x = f(a), -f(a)
[tex]x=\sqrt{\frac{25}{36}},\:x=-\sqrt{\frac{25}{36}}\\\sqrt{\frac{25}{36}}\\\sqrt{25}\\\sqrt{5^2}=5\\=\frac{5}{\sqrt{36}}\\\sqrt{36}\\=\sqrt{6^2}=6\\=\frac{5}{6}[/tex]
Reverse the same equation from the negative side
[tex]=-\frac{\sqrt{25}}{\sqrt{36}}\\\sqrt{25}\\=\sqrt{5^2}\\=5\\=-\frac{5}{\sqrt{36}}\\\sqrt{36}\\=\sqrt{6^2}\\=6\\=-\frac{5}{6}[/tex]
Therefore,
[tex]x=\pm\frac{5}{6}[/tex]
Jasmin babysits for the Smith family with 2 children. They pay her $10 an hour. She babysat 12 hours for the Smiths this week. Jasmin babysits for the Johnson family with 5 kids. They pay her $15 an hour. She babysat 6 hours for the Johnson's this weekend.
How much was she paid altogether?
The amount Jasmin was paid altogether was $210
From the question, we are to determine how much Jasmin was paid altogether
From the given information,
The Smith family pay her $10 an hour.
and
She babysat for the Smith family for 12 hours
Thus,
The amount she was paid by the Smith family is 12 × $10 = $120
Also,
The Johnson family pay her $15 an hour
and
She babysat for the Johnson family for 6 hours
Thus,
The amount she was paid by the Johnson family is 6 × $15 = $90
Therefore,
The amount she was paid altogether = $120 + $90
The amount she was paid altogether = $210
Hence, the amount Jasmin was paid altogether was $210
Learn more on Calculating amount here: https://brainly.com/question/19338501
#SPJ1
Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary
The surface area and the volume of the triangular prism are 26.88 square cm and 7.68 cubic cm.
What is a triangular prism?When a triangle is, stretch it out to produce a stack of triangles, one on top of the other. A triangular prism is a name given to this novel 3D object.
It is given that:
The triangular prism is given in the picture:
The surface area = 4x2 + 2x2.4 + 3.2x2 + 2(1/2)3.2x2.4
The surface area = 8 + 4.8 + 6.4 + 7.68
The surface area = 26.88 square cm
The volume = (1/2)x3.2x2x2.4
The volume 7.68 cubic cm
Thus, the surface area and the volume of the triangular prism are 26.88 square cm and 7.68 cubic cm.
Learn more about triangular prisms here:
brainly.com/question/16909441
#SPJ1
Use the Angle Addition Postulate to find the measure of the unknown angle
Answer:
Hey there!
Step-by-step explanation:
This is ur answer....
61 + 42 = 103ABC = 103Hope it helps!
Brainliest pls!
Follow me!
hat is the domain of the given function? {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)} {x | x = –4, –1, 3, 5, 6} {y | y = –2, 0, 1, 4, 9} {x | x = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9} {y | y = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9}
Option 1, {x | x = –4, –1, 3, 5, 6} is the domain of the given function.
For any function, domain is the set of all input values that are accepted by the given function. For example, if there is a function, say f(x) = x + 2, then all the values of x will make up the domain of f(x).
Here, we are given a function {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
In this case, all the input values = all the x values
and all the output values = all the y values
Thus, the domain of the given function will be a set containing the following x values-
3, 6, -1, 5, -4
Arranging these values in the ascending order we get,
-4, -1, 3, 5, 6
Therefore, the domain of the function can be represented as {x | x = –4, –1, 3, 5, 6}.
Learn more about domain here-
https://brainly.in/question/3358149
#SPJ9
Solve the simultaneous equation
-4x+3y=1
6x-y=2
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
Halla tres enteros pares consecutivos tales que 6 veces el primer entero sea 26 más que la suma del segundo y tercer enteros.
The consecutive even integers are 8, 10 and 12.
How to calculate the value?Let the integers be x, x + 2, and x + 4.
Therefore, the equation will be:
6(x) = x + 2 + x + 4 + 26
6x = 2x + 32
Collect like term
6x - 2x = 32
4x = 32
Divide
x = 32/4.
x = 8
The numbers are 8, 10 and 12.
Learn more about integers on:
brainly.com/question/17695139
#SPJ1
order these following rational numbers from least to greatest:
3.4 -0.01 1/4 12% -26.1
Answer:
3.4, 1/4, 12%, -0.01, -26.1
Step-by-step explanation:
The simplest way to do these type of problems is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.
12% is already a percentage
-0.01 = -1%
1/4 = 25%
3.4 = 340%
-26.1 = -2610%
Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):
3.4, 1/4, 12%, -0.01, -26.1
FINAL ANSWER: 3.4, 1/4, 12%, -0.01, -26.1
What is (1 2/3) divided by (1/8)?
Answer:
13 1/3
____
Work[tex]1\:2/3 = 5/3\\1/8 = 1/8\\\\5/3 \div 1/8\\=\frac{5\cdot8}{3\cdot1}\\= \frac{40}{3}\\= 13\:1/3[/tex]
When working with mixed numbers that are being divided, you know where to start. Start by converting mixed numbers to fractions, then multiply the fractions together to divide them. Simplify your improper fraction by counting how many times it surpasses the denominator.
In an apartment building block there are apartments with 2 rooms and with 3 rooms. in the building there are 20 apartments and 45 rooms in total. how many appartments with 3 rooms are in the building?
Using algebraic expressions and equations to solve this problem, there are 15 apartments with 2 rooms and 5 apartments with 3 rooms.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
If there are 20 apartments, we can write the equation for the sum of two different kind of apartments.
let x = number of apartments with 2 rooms
y = number of apartments with 3 rooms
x + y = 20 (equation 1)
If there are x apartments with 2 rooms and y apartment with 3 rooms and there are 45 rooms in total, we can express this as the equation:
2x + 3y = 45 (equation 2)
Rewriting equation 1 as an equation of y in terms of x,
x + y = 20 (equation 1)
y = 20 - x
Substitute this expression of y to equation 2, and solve for x.
2x + 3y = 45 (equation 2)
2x + 3(20 - x) = 45
2x + 60 - 3x = 45
-x = 45 - 60
-x = -15
x = 15
Substitute the value of x in either equation 1 or 2 and solve for y.
x + y = 20 (equation 1)
15 + y = 20
y = 20 - 15
y = 5
If x is the number of apartments with 2 rooms and y is the number of apartments with 3 rooms, then there are 15 apartments with 2 rooms and 5 apartments with 3 rooms.
Learn more about algebraic expressions and equations here: brainly.com/question/13818690
#SPJ4
Which of the following options are examples of how you can name the angle?
Answer:
<STP
Step-by-step explanation:
Some Math i can’t helppp
Annually The amount after 10 years = $ 7247.295
quarterly compound after 10 years = $7393.5
Continuously interest =$7,419
Given:
P = the principal amount
r = rate of interest
t = time in years
n = number of times the amount is compounding.
Principal = $4500
time= 10 year
Rate = 5%
To find: The amount after 10 years.
The principal amount is, P = $4500
The rate of interest is, r = 5% =5/100 = 0.05.
The time in years is, t = 10.
Using the quarterly compound interest formula:
A = P (1 + r / 4)4 t
A= 4500(1+.05/4)40
A= 4500(4.05/4)40
A= 4500(1.643)
Answer: The amount after 10 years = $7393.5
Using the Annually compound interest formula:
A = P (1 + r / 100) t
A= 4500(1+5/100)10
A= 4500(105/100)10
Answer: The amount after 10 years = $ 7247.295
Using the Continuously compound interest formula:
e stands for Napier’s number, which is approximately 2.7183
[tex]A=Pex^{rt} \\A=4500(e)^{.5} \\A= 4500(2.71)^{.5}[/tex]
A= $2,919
Answer: The amount after 10 years = $4500+$2,919=$7,419
More details :brainly.com/question/13307568
#SPJ9
-2(7-x) + 4= -4
what’s “x” equal
Answer: x=3
Step-by-step explanation:
-2(7-x) + 4= -4
-14 + 2x + 4= -4
2x - 10= -4
2x = 6
x=3
one advantage of the experimental method over the correlational method is that the experiment , but the correlational study does not.
The experimental method has one advantage over the correlational method in that it "determines cause and effect," whereas the correlational study does not.
What is defined as correlational method?Quantitative methods are used in both experimental and correlational research to investigate interactions between variables. However, there are significant differences with how data is gathered as well as the conclusions that can be drawn.
A correlational research design looks into interactions between variables without allowing the researcher to control or manipulate any of them.A correlation is a measurement of the strength and/or direction of a relation between two (or more) variables. A correlation's direction may be positive or negative.What is defined as experimental method?Experimental research is scientific research that employs two sets of variables. The first set serves as a constant against which the differences in the second set are measured. Experimentation is used in quantitative research, for example.
If you lack sufficient information to back up your decisions, you should first establish the facts. Experimental research collects the information needed to make better decisions.Experimentation is used in any research done under scientifically acceptable conditions.To know more about the correlational method, here
https://brainly.com/question/4272060
#SPJ4
..........................................................................................................................................................................
Answer:
0.012÷2=12 thousandths ÷ 2
Find the perimeter of a rectangle with a length of 9 yards and a width of 6 yards.
Answer:
30 yards
Step-by-step explanation:
9+9+6+6=30yards
B
Set-up an equation and solve for x.
2x-12
H
C
x+9
12
D
+
|| || ||
0000
Answer:
2x – 12 + 12 = x + 9
2x = x + 9
x = 9
Jorge Rodriguez earns an annual salary of $48,000. What are his weekly wages?
Answer:
923.08
Step-by-step explanation:
48000/52 weeks
Answer:
923.08
Step-by-step explanation:
There are 52.1429 weeks in a year, so divide.
Kenzie runs at an average speed of 6.25mi/h. The length of her typical run is within one mile of 6 miles long.
Write an absolute value equation to represent the situation. Find the shortest or longest amount of time for Kenzie’s run. Round to the nearest minute.
Answer: 13512
100332
Step-by-step explanation:
The shortest time for her run is approximately 36 minutes and the longest time is approximately 67 minutes.
To represent Kenzie's situation, we can use an absolute value equation. Let x represent the length of her run in miles.
The equation would then be |x - 6| ≤ 1, which means the distance between x and 6 is less than or equal to 1.
To find the shortest or longest amount of time for Kenzie's run, we need to consider the speed.
The time can be found by dividing the distance by the speed, so the minimum time would be (6 - 1)/6.25 hours,
which is approximately 0.6 hours or 36 minutes.
The maximum time would be (6 + 1)/6.25 hours,
which is approximately 1.12 hours or 67 minutes.
Learn more about Absolute value equation here:
https://brainly.com/question/32899684
#SPJ3
In exercises 21 and 22, find the indicated angle measure. (See photo)
Answer:
42°, 101°
Step-by-step explanation:
These answers come from the angle subtraction postulate.
Round 9.7 to the nearest whole number.
Answer:
10
Step-by-step explanation:
If the decimal is .5 or above, round up to the next whole number. If the decimal is below .5, round down to the last whole number. Because .7 is greater than .5, we round up to 10.
Answer:
10
Step-by-step explanation:
In rounding, we look at the digit one place to the right of what we are rounding to. If that digit that is one place to the right is 5 or greater, we increase our digit by one. If that digit that is one place to the right is 4 or less, we leave our digit as it is.
Point D is 1n of the way from C(−2.5, 1.25) to E(5, 15). What are the coordinates of D if n = 5?
Answer:
Coordinates of D are (-1, 4)
Step-by-step explanation:
I have assumed that what you wrote as 1n is actually 1/n otherwise the question does not make sense
1/n with n = 5 ==> that D is 1/5th of the distance from C on the CD line segment
Point D is 1/5th of the way from C to D
I will represent the (x, y) coordinates of points C, D and E as
[tex](x_C, y_C), (x_D, y_D) , (x_E, y_E)[/tex] respectively
Then the x-distance from C to E = [tex]x_E - x_C[/tex] and the y-distance from C to E will be [tex]y_E - y_C[/tex]
[tex]\text{1/5th of }[/tex] [tex]x_E - x_C = \dfrac{x_E - x_C}{5}[/tex] but this is relative to the location of [tex]x_C[/tex].
So we have to add this to [tex]x_C[/tex] to get the absolute x-coordinate of D
So
[tex]\displaystyle \large x_{D}=x_{C}+\dfrac{x_{E}-x_{C}}{5}[/tex]
and similarly
[tex]{\displaystyle y_{D}=y_{C}+\dfrac{y_{E}-y_{C}}{5}}[/tex]
Putting in the values for these coordinates we get
[tex]x_{D}=-2.5+\dfrac{5-(-2.5)}{5} \\\\= -2.5 + \dfrac{5 + 2.5}{5}\\\\\= -2.5 + \dfrac{7.5}{5}\\\\= - 2.5 + 1.5\\\\= -1.0[/tex]
[tex]y_{D}=1.25+\dfrac{15-1.25)}{5} \\\\= 1.25+ \dfrac{15 - 1.25}{5}\\\\\ = 1.25+ \dfrac{13.75}{5}\\\\= 1.25+ 2.75\\\\= 4.0[/tex]
So the coordinates of D are:
[tex]\boxed{D(-1, 4)}[/tex]
The graph shows the point D is indeed 1/5th of the distance from C to D
Last year, Chau invested his money in two purchases. He purchased a certificate of deposit for 1000 that paid 2% interest per year and purchased 3000 in corporate bonds paying 7% interest per year.
The total interest earned at the end of first year is $250 and the percentage of interest for his total investment is 6.25%.
Given, Chau invested his money by purchasing the following:
a certificate of deposit for $1000 at the rate of 2% per year, and
corporate bonds for $3000 at the rate of 7% per year.
we know that simple interest is calculated by multiplying the amount invested P by the interest rate r times the number of years invested t.
therefore, I = P × r × t
a. The first investment has a principal of P = $1,000, r = 2% = 0.02, t = 1 yr
I₁ = 2000 × 0.04 × 1
I₁ = 40
The second investment has a principal P = $3,000, interest rate r = 7% = 0.07 and time t = 1yr
I₂ = 3000 × 0.07 × 1
I₂ = 210
Therefore, total interest = I₁ ₊ I₂
= 40 ₊ 210
= $250
b. The overall rate of interest can be found by dividing:
Total interest/Total amount invested × 100
= 250/(1000 ₊ 3000) × 100
= 250/4000 × 100
= 25/4
= 6.25%
Hence we get the total interest earned at the end of first year as $250 and its overall rate of interest as 6.25%
Learn more about Simple interest here:
brainly.com/question/20690803
#SPJ9
Your question was incomplete. Please find the missing content here.
Last year, Chau invested his money in two purchases. He purchased a certificate of deposit for $1000 that paid 2% interest per year and purchased $3000 in corporate bonds paying 7% interest per year.
(a) What was the total investment earned at the end of 1 year?
(b) What was the percentage interest for her total investment?
Line l passes through point (6,0) and line p is the graph of 2x-3y=4. If l is perpendicular to line p, what is the equation of l.
Equation of line p:
[tex]{\sf{2x - 3y = 4}}[/tex]
[tex]{\sf{y = \frac{2x}{3} - \frac{4}{3}}}[/tex]
Slope of line p (m):
[tex]{\sf{\frac{2}{3}}} [/tex]
Since, l is perpendicular to line p, the product of slopes of line l & p should be -1. We assume slope of line l be m2
Hence,
[tex]{\sf{m \times m2 = - 1}}[/tex]
[tex]{\sf{ \frac{2}{3} \times m2 = - 1}}[/tex]
[tex]{\sf{m2 = \frac{ - 3}{2}}}[/tex]
Since, line l passes through points (6, 0).
We apply,
[tex]{\sf{(y - y1) = m2(x - x1)}}[/tex]
[tex]{\sf{y - 0 = \frac{ - 3}{2}(x - 6)}} [/tex]
[tex]{\sf{2y - 0 = - 3x + 18}}[/tex]
[tex]{\sf{3x + 2y - 18 = 0}}[/tex]
The equation of line l:
[tex]{\sf{\red{\boxed{\sf{3x+2y-18=0}}}}}[/tex]
Caleb's vegetable garden yielded 48 pounds of bell
peppers. He gave of the yield to his neighbor, Jacob.
Caleb Sold to a local restaurant He saved the rest of
the bell peppers. How many pounds of bell peppers did
he give Jacob? How many pounds did he sell? How
many pounds did he save for himself?
Answer:
16 each
Step-by-step explanation:
Since you didn't say how much of the yield Jacob gave to the restaurant or the neighbor, I'm going to assume he kept an even share and gave them each the same share.
Assuming that, we would have to divide his harvest by 3
48/3 = 16
this means that 16 went to his neighbor, 16 to the restaurant and 16 were saved for himself.
Hope this helps! ^^
PLEASE HELP ME!!!
WILL GIVE YOU A FOLLOW
what is the Inverse of
Y=2x-1?
Answer:
y = [tex]\frac{x+1}{2}[/tex]
Step-by-step explanation:
y = 2x - 1
switch the x and y variables
x = 2y - 1
solve for y
x + 1 = 2y
[tex]\frac{x+1}{2}[/tex] = y
The expression
³√x²y³ = x²y³
where x and y are non-negative real numbers.
r, the exponent of X, is:
s, the exponent of y, is:
Using exponent power property, ³√x²y³ = x^r y^s, where x and y are non-negative real numbers.
r, the exponent of x, is: 2/3
s, the exponent of y, is: 1
What is Exponent power property?According to the Power of a Power Property, you can multiply the exponents if one exponent is increased to a higher exponent. This characteristic may be used to resolve the equation (3 x 2) 3.
³√x²y³ = x^r y^s
Cubing on both sides,
x²y³ = x^3r y^3s
As base is same, equating the powers
⇒ 2 = 3r; r = 2/3
⇒ 3 = 3s; s = 1
The correct question is -The expression
³√x²y³ = x^ry^s
where x and y are non-negative real numbers.
r, the exponent of X, is:
s, the exponent of y, is:
To learn more about exponent power property from given link
https://brainly.com/question/3187898
#SPJ9