I am not understanding

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

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The solution for the system of equations 3x + 6y = 6 and 2x + 2y = 6 is

B) There is one unique solution, (4, -1).

The solutions for a system of equation is the intersecting points between them

We know that system of equations has an infinite number of solutions when they coincide with each other as every point of a line falls into another line.

Systems of equations have a unique solution when they intersect each other and that intersecting point is the solution.

The system of equations has no solution when they are parallel to each other.

So, now we'll graph this system of equations and observe where they lie in XY coordinate.

Observing the graphs of both of these equations we can conclude that they have a unique solution (4,-1).

We can also solve these equations by multiplying equation(ii) by 3 and subtracting it from equation(i) and obtaining the values of (x,y).

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Answer:

168

Step-by-step explanation:

4x6=24

24x7=168

Answer:

36 cm

Step-by-step explanation:

Blank bank as well as Thank bank earn equal interest.

In this question, Blank Bank offers an annual rate of r% for y years.

and Thank Bank offers a rate of ry% for 1 year.

Assuming $x is deposited into a savings account, we need to determine which bank earn more interest.

We know that, Interest = principal × rate × time

Now we convert the rates to decimals and to do that we divide by 100.

So, the annual rate of the Blank bank = 0.0r

And the annual rate of the Thank Bank = 0.0ry

Using above formula of interest,

For Blank bank, the interest would be,

I_B = x × 0.0r × y

I_B = xy(0.0r)

I_B = 0.0rxy                         ....................(1)

here, we find the interest for 'y' years

And for the Thank Bank, the interest would be,

I_T = x × 0.0ry × 1

I_T = I_B = 0.0rxy              ....................(2)

From (1) and (2),

I_B = I_T

Both the banks earn equal interest.

Therefore, Blank bank as well as Thank bank earn equal interest.

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Answer:

Animal bread

food dog

animal— dog

food — bread

slope = Y2 - Y1

————

X2 - X1

Answer:

see explanation

Step-by-step explanation:

calculate the slope m using the slope formula and equate to the given slope

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

(a)

(x₁, y₁ ) = (- 3, - 4 ) and (x₂, y₂ ) = (0, y )

[tex]\frac{y-(-4)}{0-(-3)}[/tex] = [tex]\frac{y+4}{0+3}[/tex] = [tex]\frac{y+4}{3}[/tex] , then

[tex]\frac{y+4}{3}[/tex] = 2 ( multiply both sides by 3 )

y + 4 = 6 ( subtract 4 from both sides )

y = 2

ordered pair is (0, 2 )

(b)

(x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (x, 5 )

[tex]\frac{5-2}{x-(-2)}[/tex] = [tex]\frac{3}{x+2}[/tex] , then

[tex]\frac{3}{x+2}[/tex] = [tex]\frac{3}{7}[/tex] ( cross- multiply )

3(x + 2) = 21 ( divide both sides by 3 )

x + 2 = 7 ( subtract 2 from both sides )

x = 5

ordered pair is (5, 5 )

(c)

(x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (1, - 5 )

[tex]\frac{-5-5}{1-x}[/tex] = [tex]\frac{-10}{1-x}[/tex] , then

[tex]\frac{-10}{1-x}[/tex] = [tex]\frac{-5}{2}[/tex] ( cross- multiply )

- 5(1 - x) = - 20 ( divide both sides by - 5 )

1 - x = 4 ( subtract 1 from both sides )

- x = 3 ( multiply both sides by - 1 )

x = - 3

ordered pair is (- 3, 5 )

(e)

(x₁, y₁ ) = (- 6, y ) and (x₂, y₂ ) = (8, 2 )

[tex]\frac{2-y}{8-(-6)}[/tex] = [tex]\frac{2-y}{8+6}[/tex] = [tex]\frac{2-y}{14}[/tex] , then

[tex]\frac{2-y}{14}[/tex] = - [tex]\frac{1}{7}[/tex] ( cross- multiply )

- 7(2 - y) = 14 ( divide both sides by - 7 )

2 - y = - 2 ( subtract 2 from both sides )

- y = - 4 ( multiply both sides by - 1 )

y = 4

ordered pair is (- 6, 4 )

Answer:

24 25 26

Step-by-step explanation:

guess and check..................

She invested $5,000 at 7% and $4,000 at 9%

How much is invested at each rate of return?

The amount invested at 7% can be assumed to be x, such that the amount invested at 9% would be total investment of $9000 minus x, which has been invested at the initial rate of 7%

total interest at 7%=interest rate*amount invested

interest rate=7%

amount invested=x

total interest at 7%=7%*x=0.07x

total interest at 9%=9%*(9000-x)

total interest at 9%=810-0.09x

total interest on both accounts=0.07x+810-0.09x

total interest on both accounts=810-0.02x

total interest earned=$710

710=810-0.02x

0.02x=810-710

0.02x=100

x=100/0.02

x=amount invested in the account which earns 7%=$5,000

amount invested at 9%=$9000-$5000

amount invested at 9%=$4,000

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The area of one wall of the room is 72 square feet.

The area of a square is given by -

A{S} = a²

where -

{a} is side of square.

Given is a square room has a floor area of 144 square feet. The height of the room is 6 feet.

It is given that -

floor area = 144

a² = 144

a = √(144)

a = √(12 x 12)

a = 12

The area of the wall will be equivalent to -

A{W} = h x a

A{W} = 6 x 12

A{W} = 72 square feet.

Therefore, the area of one wall of the room is 72 square feet.

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In order for Abraham to receive an A, he will need to earn a total of 1.5 points, which is the rational number that may be used to represent that amount.

It is important to keep in mind that a number is considered rational if it can be expressed in the form of a fraction.

It is possible when decimals and numbers have worked effectively.

In light of the fact that Abraham must get a grade of A– in mathematics in order to achieve an A, the rational number that can be used to symbolize the number of points that Abraham must earn in order to get an A will be the number 1.5.

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Percent of residents have at least one traffic violation with 80% held a valid driver’s license,10% has at least one traffic violation and 30% does not have valid license is 14%.

As given,

A=Person has a driver license

A'=Person does not have a driver license

P(A)=0.80

P(A')=0.20

For A, 10% has at least one traffic violation

For A', 30% had at least one traffic violation.

Probability with at least one traffic violation

=Probability of( A and one traffic violation +A' and one traffic violation)

=0.80(0.10)+0.20(0.30)

=0.08+0.06

=0.14

=14%

Therefore, percent of the residents with at least one traffic violation is 14%.

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The value of both the interior angles of the triangle is calculated as 70° and 35°.

If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.

Now, as per the given question;

The exterior angle of a triangle is 105°.

Let one of the interior angle is 'x'.

Then, the other interior angle is 35 degree less; x - 35°.

By the exterior angle property.

Sum of interior angles = exterior angle

x + x - 35° = 105°

2x = 105° + 35°

2x = 140°

x = 70°

The other interior angle is; x - 35°

= 70° - 35°

= 35°

Therefore, the two interior angles of the triangles are estimated as 70° and 35°.

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Answer:

Leon has $15 and Laci has $61

Step-by-step explanation:

Let x = the amount Leon has.  So 4 times that plus $1 would be 4x+1.  Our equation is:

x + (4x+1) = 76

Combine like terms

5x + 1 = 76

Subtract 1 from both sides

5x = 75

Divide both sides by 5

x = 15.  This is Leon.  Laci is 4(15) +1, or 61.

The specified value of n for trapezoidal rule, the midpoint rule, and simpson's rule is 10.36 , 10.72 and 10.52.

Trapezoidal Rule: In Calculus, “Trapezoidal Rule” is one of the important integration rules. The name trapezoidal is because when the area under the curve is evaluated, then the total area is divided into small trapezoids instead of rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions.

The trapezoidal rule is mostly used in the numerical analysis process. To evaluate the definite integrals, we can also use Riemann Sums, where we use small rectangles to evaluate the area under the curve.

Midpoint rule : In mathematics, the midpoint rule, also known as the midpoint Riemann sum or midpoint method, is a method of estimating the integral of a function or the area under a curve by dividing the area into rectangles of equal width. The midpoint rule formula is. The midpoint method formula works by summing the areas of each of the rectangles to produce an estimate for the area under a curve.

Simpson's Rule: Simpson's rule is used to find the value of a definite integral (that is of the form b∫ₐ f(x) dx) by approximating the area under the graph of the function f(x). While using the Riemann sum, we calculate the area under a curve (a definite integral) by dividing the area under the curve into rectangles whereas while using Simpson's rule, we evaluate the area under a curve is by dividing the total area into parabolas. Simpson's rule is also known as Simpson's 1/3 rule (which is pronounced as Simpson's one-third rule).

Now,

a=1,b=4,Δx =(b-a)/n =3/6 =1/2

f(x)=4√(ln(x))

trapezoidal rule:

∫4√(ln(x)) dx =(Δx /2)[f(1)+2*[f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)]+f(4)]

∫4√(ln(x)) dx =((1/2) /2)[4√(ln(1))  +2*[4√(ln(1.5)) +4√(ln(2)) +4√(ln(2.5)) +4√(ln(3)) +4√(ln(3.5))] +4√(ln(4))]

∫4√(ln(x)) dx =10.365336

midpoint rule :

∫4√(ln(x)) dx =(Δx)[f(1.25)+f(1.75)+f(2.25)+f(2.75)+f(3.25)+f(3.75)]]

∫4√(ln(x)) dx =(1/2)[4√(ln(1.25))  +4√(ln(1.75)) +4√(ln(2.25)) +4√(ln(2.75)) +4√(ln(3.25)) +4√(ln(3.75)) ]

∫4√(ln(x)) dx =10.724182

simpsons rule:

∫4√(ln(x)) dx =(Δx /3)[f(1)+4*f(1.5)+ 2*f(2)+ 4*f(2.5)+  2*f(3)+  4*f(3.5)]+f(4)]

∫4√(ln(x)) dx =((1/2) /3)[4√(ln(1))  +4*4√(ln(1.5)) +  2*4√(ln(2))  +4*4√(ln(2.5))  +2*4√(ln(3)) + 4*4√(ln(3.5)) +4√(ln(4))]

∫4√(ln(x)) dx =10.527905

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Answer:

1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

y = -2x - 3

Step-by-step explanation:

The slopes of two perpendicular lines are negative reciprocals of each other. So slope of s is -2

using m = -2, x = 2, y = -7

y = mx + b

-7 = (-2)(2) + b

-7 = -4 + b

b = -3

y = -2x - 3

Answer:

Pretty sure it’s x>12

Step-by-step explanation:

Answer x > 12

thats the whole thing

[tex]-7,5 + 4,2 = -3.3[/tex]

[tex]-0,9 \cdot 2,7 = -2.43[/tex]

Answer:

15 units

Step-by-step explanation:

By using the Pythagoras Theorem,

C^2 = A^2 + B^2

Substitute in the given values,

25^2 = a^2 + 20^2

625 = a^2 + 400

625 - 400 = a^2 + 400 - 400

a^2 = 225

[tex]a = \sqrt{225} [/tex]

= 15

Hope this too helped! ^^

I'd recommend watching a video or two on the topic of Pythagoras Theorem, if this explanation isn't clear enough.

Answer:

2+0.12x=time on scooter bill

x is minutes and x is 157 minutes on the scooter

Step-by-step explanation:

Answer:

A person will pay $5.37

Step-by-step explanation:

6.8 pounds of bananas x $0.79 per pound = $5.37.

I hope this helps and have a blessed day! :)

Mansi can cover 1 mile of the distance in just 12 minutes.

The unit rate can be expressed in any unit for instance minute per mile, miles/hour, etc

There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.

Lets consider Mansi covers 3 miles in 36 minutes, her unit rate in minutes per mile is expressed as:

Unit rate = 36min/3miles

Unit rate = 12 minutes/mile

Here,

This shows that Mansi can cover 1 mile of the distance in just 12 minutes.

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Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.

Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.

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Answer:  Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm. You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm². Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm.

Step-by-step explanation:

Answer:

82,337

Step-by-step explanation:

   76,749

      5565

+         23
   82,337

Hope it helps!!!

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Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by Continuous random variables.

What is Continuous Random Variable ?

A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.

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Answer:

16 1/4

Step-by-step explanation:

4*10=40, add one more 1/4 and you get 41. So simplified, 41/4 = 10 1/4

Add the 6 and you get 16 1/4