CAN SOMEONE HELP WITH THIS QUESTION?✨

the answer for this question is  i don't know

So , bye

(a) This differential equation can be written in the form (*) with P(x) = 1, Q(x) = 2x, and n = 2.

(b) The substitution u = 1/y will transform it into the linear equation Du/dx +  0u = -2x

(c)Using the substitution in part (b), we rewrite the initial condition in part  u(1) = 1/y(1) = 1/4.

(d) the linear equation in part (b) is y = 1/(C - x) and  the solution that satisfies the initial condition in part (c) U(x) = -y⁻¹ = -x + C,

(e) Finally, solve for y(x) = 1/(1/4 + 1 - x) = 4/(5 - x).

What is  Bernoulli differential equation?

A Bernoulli differential equation is a type of non-linear ordinary differential equation of the form:

dy/dx + P(x)y = Q(x)yⁿ

where P(x) and Q(x) are functions of x and n is a constant. The equation is named after the Swiss mathematician Jakob Bernoulli.

These types of differential equations are important in various fields of science, such as physics, engineering, and economics. They are non-linear, meaning that the dependent variable y appears in both linear and non-linear terms, making them difficult to solve in general.

a) This differential equation can be written in the form (*) with P(x) = x, Q(x) = 2x, and n = 2.

b) The substitution u = y⁻¹ will transform it into the linear equation du/dx - xu = -2x.

c) Using the substitution in part (b), we rewrite the initial condition as u(1) = 1/4.

d) Now we solve the linear equation in part (b). The characteristic equation is given by d/dx(e[tex]\mathrm{(\int -xdx))}[/tex] = -xe[tex]\mathrm{(\int -xdx))}[/tex] which has the general solution u(x) = Ce[tex](-x^2/2)[/tex].

Using the initial condition, we find C = 1/4, so u(x) = 1/4e[tex](-x^2/2)[/tex].

e) Finally, we solve for y. From u = y⁻¹, we have y = 1/u = 4e[tex](-x^2/2)[/tex].

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The expression that represents the sum of a number, half the number and 5 times the number is given as follows:

6.5x.

In which x is the number.

The number in this problem is unknown, hence the variable that represents the number is given as follows:

x.

Half the number is given as follows:

x/2 = 0.5x.

Five times the number is given as follows:

5x.

Then the sum of all these amounts is given as follows:

x + 0.5x + 5x = 6.5x.

We just combine the like terms, as they all have the same letter and exponent, hence we just add the coefficients.

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Answer:

A

Step-by-step explanation:

Because (--3) is equal to 3 becuas ethe negative is not oustide the value and -(-4) is euqal to =4

So therefore, A is correct.

The correct graph for the supplements is attached below.

A bar chart is a graph that uses bars to represent and compare data. The length of the bar represents the magnitude of the data being displayed, with longer bars indicating larger values.

Bar charts can be used to display data for one or more categories, and can be either vertical or horizontal. They are commonly used to compare and visualize the distribution of categorical data.

The correct bar graph that shows the distribution of the supplements have been shown in the image that is attached to the answer that we have here.

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The domain of [tex]f^{-1}[/tex] is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.

A domain is an area of administrative autonomy, authority, or control within the Internet. Domains are defined by the organization or entity that owns them, and are made up of a series of letters and/or numbers that follow the “dot” or period. For example, a domain name may be “example.com” or “example.org”. Domain names are used to identify and locate computers on the Internet and to route email.

The domain of f is the set of all the x-values of the ordered pairs, which are {-6, -13, -2, 11, 8}.

The range of f is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.

The domain of f-1 is the set of all the y-values of the ordered pairs, which are {11, -2, -12, -9, 1}.

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Answer: $8000 is invested for 6 years

Step-by-step explanation:P=$3,000 r= 7%= 0.07 t= 4 n= 2

The cumulative frequency distribution table is present below. Cumulative frequency for speed less than 30 is 4 , less than 60 is 20 , less than 90 is 80 less than 120 is 100. So, correct answer is option (b).

The cumulative frequency of a variable's value is the number of values in the collection of data that are less than or equal to the variable's value. Example: Let the raw data be 2, 2, 1, 5, 5, 6, 5, 3, 7, 7, 5, 6. Cumulative frequency of 3 = 4. Cumulative frequency is a frequency distribution table for the predecessor total. The final value is always equal to the sum of all observations, since all frequencies have already been added to the previous sum. We have a data corresponds to the frequencydistribution.

Speed Number of cars

0-29 4

30-59 16

60-89 60

90-119 20

We have to construct the cumulative frequency distribution for the above frequency distribution.Using the above rules we can construct distribution as,

Speed Number of cars Cumulative Freq

0-29 4 4

30-59 16 16 + 4 = 20

60-89 60 60 + 20= 80

90-119 20 20 + 80 = 100

-----------

Total 100

Thus , cumulative frequency for speed less than 30 is 4 , less than 60 is 20 , less than 90 is 80

less than 120 is 100.

Hence, we got the required cumulative frequencies for frequency distribution.

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Complete question:

Construct the cumulative frequency distribution that corresponds to the given frequency distribution. Number Speed of cars 0-29 4 30-59 16 60-89 60 90-119 20 a)Speed Cumulative Frequensy

Less than 30 100

Less than 60 80

Less than 90 82

Less than 120 1

b)Speed Cumulative Frequency

Less than 30 4

Less than 60 20

Less than 90 80

Less than1 20 100

c) speed Cumulative Frequency

Less than 30 0.04

Less than 60 0.20

Less than 90 0.80

Less than120 1.00

Answer: Its perimeter is 45 cm.

Step by step explanation:

Data :

We have a triangle with a measure of 15 cm

We must simplify taking into account that it is an equilateral triangle, all its sides are equal, therefore the perimeter is the sum of its sides:

[tex]\bf P= 15 + 15 + 15[/tex]

[tex]\boxed{\bf \: P = 45 \: cm}[/tex]

Rpt: Its perimeter is 45 cm.

A library manager is interested in the number of people using the library. She decides to perform a count every 28th day for one year, starting next Monday. The systematic sampling method is this.

Hence, option (a) is the correct choice.

The library manager employs systematic sampling as a sample approach.

Systematic sampling is a form of probability sampling approach in which sample members are drawn from a larger population at random but with a set, periodic interval.

The sampling interval is determined by dividing the population size by the desired sample size.

Systematic sampling is a technique for picking a sample from a larger population at regular intervals. In this scenario, the library manager selects a sample of library users by tallying the number of persons every 28th day.

It is a systematic sampling approach since the intervals (28th day) are fixed and systematic.

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Answer:

aₙ = aₙ₋₁ - 3, a₀ = 8

Step-by-step explanation:

Minus three every time thus the recursive equation would be aₙ = aₙ₋₁ - 3, a₀ = 8

Let x be the cost of the small bag.

The large bag costs x + 30 more than the small bag.

So the cost of the large bag is x + (x + 30) = 2x + 30

The two-piece set of luggage cost is the sum of the cost of the small and large bag, so

122 = x + (2x + 30)

Solving this equation for x, we get:

x = 42

Therefore, the small bag costs 42 dollars and the large bag costs 2*42 +30 = 114 dollars.

The function for distance jogged is d(t) = 3.3t and the inverse of the function is d(t)⁻¹ = 3.3/t.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Let, 'd' be the distance covered in miles, and 't' is the time in hours.

Therefore, From the given information d(t) = 3.3t.

Let, d(t) = y.

So, y = 3.3t.

t = 3.3/y.

d(t)⁻¹ = 3.3/t.

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The perimeter of the polygon is 169 inches.

The perimeter of a polygon is the total length of its sides. The tangents from a given circle are used to create the polygon in this problem.

We will apply the idea that if two tangents are drawn from the same point outside of a given circle, their lengths will always be identical.

This polygon has eight sides, which indicates that there are four pairs because their lengths are equal.

Therefore, the perimeter is equal to double the total of the four sides that were supplied to us.

Radius = 2(22+27+22+98)

perimeter is two (169)

Diameter: 338 inches

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Complete question -

PROBABLITY

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Answer:

Where is the equation?

Step-by-step explanation:

I need it to solve this problem

Therefore , the solution of the given problem of coordinate plane comes out to be Y coordinates comes out to be -3 , -2, -1 , 0, 1,2,3

By portraying the inputs and outputs as a horizontal number line (the x axis) and a vertical number line (the y axis), respectively, the Cartesian coordinate plane enables us to perceive ordered pairs. The quantity in the x component is moved horizontally. Move to the right if x is positive. Move to the left if x is negative.

Here,

Given :

=> -30 , -20 ,-10 ,0 ,10, 20 , 30

=> So ,

Y coordinates comes out to be :

=> -3 , -2, -1 , 0, 1,2,3

An ordered pair of numbers, or x-coordinate and y-coordinate on the x-axis respectively, can be used to represent each point.

Written in parenthesis are ordered pairings (x-coordinate, y-coordinate). The source is situated at (0,0).

Check your coordinates, which are two numbers enclosed in parenthesis and separated by a comma, to see how to graph a point on the coordinate plane.

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The number of cigarettes smoked in 1925 was approximately 1.3 billion.

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The required incorrect step is step 1, circle B should have been translated 7 units right and 9 units up. Option A is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

Here,
Circle A with a center at (3, 4) and a radius of 2 is similar to circle B with a center at (−4, −5) and a radius of 3.
To translate the circle B over circle A is given as 7 units right and 9 units up.

Thus, the required incorrect step is step 1, circle B should have been translated 7 units right and 9 units up. Option A is correct.

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The false statement regarding Legendre polynomials is given as follows:

E) [tex]P_{2k}(0) = (-1)^k\frac{(2k)!}{2^{2k}k!}, k \in N[/tex]

The Legendre function of order v is the function that is a solution to the differential equation presented as follows:

(1 - x²)y'' - 2xy' + v(v + 1)y = 0.

Examples of Legendre polynomials are given as follows:

From the polynomial of order 2, with k = 2, we have that:

[tex]P_4(0) = 0.375[/tex]

While:

[tex](-1)^2 \times \frac{4!}{16 \times 2!} = \frac{24}{32} = 0.75[/tex]

Different result, hence statement D is false.

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Answer:

-3y

Step-by-step explanation:

-√(9y²) = -√((3y)²)

= -3y

The LCM of 1-x^2 and (x-1)^3 is (x-1)^3.

To find the LCM, we take the polynomial with the highest degree (which determines the degree of the LCM) and then make sure that it contains all the terms from the other polynomials.

The degree of (x-1)^3 is 3 and the degree of 1-x^2 is 2.

So, we take (x-1)^3 as the starting point for the LCM and then add any missing terms from 1-x^2.

In this case, (x-1)^3 already contains all the terms from 1-x^2, so the LCM is (x-1)^3.

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The simplified form of the expression (2x+8)^6 is[tex]64x^6 + 1536x^5 + 15360x^4 + 819204x^3 + 245760x^2 + 393216x + 262144.[/tex]

To simplify the expression (2x + 8)^6, we need to raise the binomial (2x + 8) to the power of 6. This can be done using the binomial theorem.

The Binomial Theorem states that for any positive integer n and real numbers a and b, the expansion of the expression (a + b)^n is a sum of terms of the form (a^(n-k) * b^k * C(n,k)), where C(n,k) represents the binomial coefficient, which is equal to n!/(k!(n-k)!).

[tex](a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1) b^1 + ... + C(n, n-1)a^1 b^(n-1) + C(n, n)a^0 b^n[/tex]

Where C(n, k) is the binomial coefficient, given by C(n, k) = n! / (k! (n - k)!).

In this case, a = 2x and b = 8. So, substituting these values into the binomial theorem:

[tex](2x + 8)^6 = C(6, 0)(2x)^6 8^0 + C(6, 1)(2x)^5 8^1 + ... + C(6, 5)(2x)^1 8^5 + C(6, 6)(2x)^0 8^6[/tex]

Expanding each term, and combining like terms, we get:

[tex](2x + 8)^6 = 64x^6 + 1536x^5 + 15360x^4 + 819204x^3 + 245760x^2 + 393216x + 262144[/tex]

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The stability limit depends on the specific form of the equation, so you may need to adjust this value based on the specific equation you are working with.

The stability condition for the Euler's method applied to the equation

y' = f(x,y) is given by the following inequality:

|hf(x,y)| <= 1,

where h is the step size. To determine the largest step size for which Euler's method is stable, we need to find the maximum value of |hf(x,y)|. This maximum value is often referred to as the stability limit.

In your case, the equation is close to the simpler equation y' = a, which has the solution y = a*x + b. The stability limit for the Euler's method applied to this equation is 1, so we can take h <= 1 as the largest step size for which the method is stable. However, the stability limit depends on the specific form of the equation, so you may need to adjust this value based on the specific equation you are working with.

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The estimated mean of the distribution for the given question will be 10.

Mean = 13 + 52 + 48 + 28 + 28 + 23 + 14 + 13 + 10 + 4 + 2 + 4 + 2 + 1 + 1 + 0 + 2 + 0 + 0 + 0 + 1 + 1 + 1 + 1 + 1

Total number =25

Now, divided the sum by 25

We get, the mean is equal to 10.

In mathematics, particularly in statistics, there are various types of means. Every mean serves to condense a specific set of data, frequently to help understand the overall significance of a particular data set. Only numerical variables, whether continuous or discrete, can be used to calculate the mean. Simply dividing the total number of values in a data set by the sum of all of the values yields it. The calculation can be performed on unprocessed data or data that has been combined into a frequency table.

Note that the illustration for graph is: (check the attached image)

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The area of a sector of a circle is equal to the central angle multiplied by the radius squared, divided by 2. In this case, the sector of the circle has an area of 20 square feet, the radius is 5 feet, and we need to find the central angle.

The central angle will be 6.28 radians.

To find the central angle, we can rearrange the equation to solve for the angle:

Central Angle = (2 * Area) / (Radius^2)

Substituting the given values, we get:

Central Angle = (2 * 20) / (5^2)

Simplifying, we find that the Central Angle equals 6.28 radians.

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Answer:

Vertical Line Test

Step-by-step explanation:

If a vertical line is drawn on a graph of a relation and only intersects the graph at one point, then that graph represents a function. If there is no vertical line intersecting the graph at two or more points, then the graph does not represent a function.

Answer:

14 is a polynomial.

x+1 is a polynomial.

14vx is not a polynomial.

x-2 -2x+4 is a polynomial.

14 is a polynomial, x+1 is a polynomial, 14vx is not a polynomial, x-2 -2x+4 is a polynomial.

A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.

Polynomials are algebraic expressions with indeterminates and constants in them. Polynomials can be thought of as a mathematical dialect. They are used to express numbers in practically every subject of mathematics and are quite significant in others, such as calculus.

Polynomials cannot include the following:

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The value of r is equal to the cube root of (V * (3π/4)).

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Put n = 10

t(10) = 3(10) - 5 = 30 - 5 = 25