What is the solution of second order differential equation?

The amount of time it would take for both Keith and Donna to complete each lap based on the question is given below:

Factor two numbers 12 and 8:

12= 2. 2. 3

8= 2. 2. 2

Find the LCM,

The LCM of (12,8)=  2. 2. 3. 2 = 24

Hence,

1. It will take 24 minutes for Keith and Donna to meet again at the starting line.

2. Keith will complete 2 laps

3. Donna will complete 3 laps.

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Trapezoid JKLM is shown on the coordinate plane, the coordinates of L should be (8,-6) if the rule is (x + 5, y - 4), because the coordinates are (3, -2), and you have to add 5 to x, and -4 to y.

The origin of the coordinate system is the intersection of the axes, and the first and second coordinates are known as the abscissa and the ordinate of P, respectively. The coordinates are often represented as two integers enclosed in parenthesis and placed in that particular order, all separated by commas. Coordinates are two integers (Cartesian coordinates) or, in certain cases, a letter and a number that point to a specific place on a grid known as a coordinate plane. The x axis (horizontal) and y axis are the two axes of a coordinate plane, which contains four quadrants (vertical).

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The complete question is as follows:

By algebra properties, the radical equation [tex]3 \cdot \sqrt[4]{(x - 2)^{3}} - 4 = 20[/tex] has the following extraneous solution: x = - 14.

A solution for a radical equation is extraneous when result leads to an absurdity (i.e. 3 = 4). In this problem, we proceed to show how to solve a radical equation by means of algebra properties. First, write the entire radical equation:

[tex]3 \cdot \sqrt[4]{(x - 2)^{3}} - 4 = 20[/tex]

Second, use compatibility with addition:

[tex]3\cdot \sqrt [4]{(x-2)^{3}} = 24[/tex]

Third, use compatibility with multiplication:

[tex]\sqrt [4] {(x - 2)^{3}} = 8[/tex]

Fourth, use a relationship between powers and roots:

[tex](x - 2)^{\frac {3}{4}} = 8[/tex]

Fifth, elevate both sides to 4 / 3 to cancel exponent on left side:

[tex]x - 2 = 8^{\frac {4}{3}}[/tex]

Sixth, solve the power constant:

x - 2 ≈ ± 16

Seventh, apply absolute value properties:

x - 2 = 16 or x - 2 = - 16

Eighth, use compatibility with addition once again:

x = 18 or x = - 14

Ninth, check for extraneous solutions:

x = 18

[tex]3\cdot \sqrt [4]{(18-2)^{3}} = 24[/tex]

24 = 24

x = - 14

[tex]3\cdot \sqrt [4]{(- 14-2)^{3}} = 24[/tex]

NaN

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Answer:

IF you do A + B you will get P, p is = to enis which is AB.

Step-by-step explanation:

In linear equation, The resultant speed is 48.27m/s and the bearing is 235.65 degrees. The vertical component is given by vsinθ = 32sin34° = 17.89 miles per hour.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                                 Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

OP = 59m/s represents the plane that has a bearing of 214 degrees.

PW = 21m/s represents the wind that is blowing at an angle of N14W.

OW =  represents the resultant vector.

The angle that OP makes with west direction = 270-214=56 degrees. Therefore the angle that OP makes with the vertical is 90-56=44 degrees

In the ΔOPW,  ∠WPO = 14+44=58 degrees.

Using law of cosines, we can find the magnitude of OW

      Using law of sines we can calculate ∠WOP

  21/Sin∠WOP = 48.27/sin58

Therefore sin∠WOP = 21.SIN58/48.27  = = 0.368895

Therefore ∠WOP = sin-1 (0.368895) = 21.65 degrees

Therefore the bearing of OW is 214 + 21.65 = 235.65 degrees.

The resultant speed is 48.27m/s and the bearing is 235.65 degrees.

The horizontal component is given by vcosθ = 32cos34° = 26.53 miles per hour

The vertical component is given by vsinθ = 32sin34° = 17.89 miles per hour.

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Answer:

C

Step-by-step explanation:

15 (-42 x + 40) = 15 (- 8 x + 244)

15 cancelled on each side

-42x+40= -8x+244

move all the x to one side & numbers to the other,

-34x =204

x=6

A histogram is a graph used to represent the frequency distribution of a few data points of one variable.

Histograms often classify data into various “bins” or “range groups” and count how many data points belong to each of those bins.

Option (b)  is correct.

Because, virtually all the common causes variations with time

Option (c) special and command variation

Which are two important variation

Option (a) location is the correct option here as histogram can not show the location.

Because, histogram shows shape and spread of data, also it shows variation over time. hence the correct option is a according to histogram data.

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The equation used is 3 (x - 5) = 60, the cost of each rashguard at full price is $25

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Price of rash guard on sale =$5

Number of rashguard miguel purchased= 3

Now, Let the full price of each rashguard be x,

Rashguards sell for $5 less than full price;

x - 5

Miguel purchases 3 rashguards and pays a total of $60;

3 (x - 5) = 60

x - 5 = 60 / 3

x - 5 = 20

x = 20 + 5

x = 25

Therefore, the algebraic solution for x will be 25;

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The matrix's entry of 1.00 on the diagonal denotes that it is an identity matrix, which means that all values besides 1 along the diagonal are 0.

The matrix is an identity matrix, as evidenced by the entry of 1.00 on its diagonal. A square matrix called an identity matrix is one in which the primary diagonal's elements are all ones and the other components are all zeros. The letter "I" stands for this particular sort of matrix. In several branches of mathematics, such as matrix theory and linear algebra, identity matrices are employed. Calculations and equations can also be made simpler by using identity matrices. An identity matrix, for instance, is created by multiplying it by any other matrix. This characteristic can be used for matrix inversion or to solve a set of linear equations. In group theory and abstract algebra, the identity element is also represented by identity matrices.

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Answer:

The value of ? is 1004.

Step-by-step explanation:

I'll use x instead of ?:

[tex]9^x+9^x+9^x=3^{2009}\\3\cdot9^x=3^{2009}\\3\cdot(3^2)^x=3^{2009}\\3\cdot3^{2x}=3^{2009}\\3^{2x+1}=3^{2009}\\2x+1=2009\\2x=2008\\x=1004[/tex]

The solution of the differential equation with the given initial condition is[tex]()=⟨7⋅e^2x, 5⋅e^2x, 3⋅e^2x⟩.[/tex]

Let () be a vector-valued function in three-space. Then the solution of the differential equation ′()=2() with the initial condition [tex](0)=⟨7,5,3⟩[/tex] can be found by solving the system of differential equations:

[tex]′1()=2⋅1()\\′2()=2⋅2()\\′3()=2⋅3()[/tex]

where 1(), 2(), and 3() denote the components of ().

Solving for the general solution of each equation yields:

[tex]1()=7⋅e^2x\\2()=5⋅e^2x\\3()=3⋅e^2x[/tex]

Therefore, the solution of the differential equation with the given initial condition is:

[tex]()=⟨7⋅e^2x, 5⋅e^2x, 3⋅e^2x⟩.[/tex]

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Answer:

Let's call the radius of the cylinder and cone "r".

The surface area of the cylinder is: 2πr(r + h) = 2πr^2 + 2πrh

The surface area of the cone is: πr(l + r) = πrl + πr^2

The total surface area of the solid object is the sum of the surface area of the cylinder and the cone: 2πr^2 + 2πrh + πrl + πr^2 = (2π + π)r^2 + 2πrh + πrl

We are given that the total cost of painting the solid object is Rs. 2851.20 and the rate of painting is Rs. 140 per 100 sq cm.

So the total surface area of the solid object is: 2851200/140 = 20580 sq cm

Now we can substitute the values we know into the equation for the total surface area: 20580 = (2π + π)r^2 + 2πrh + πrl

We also know that the height of the cylinder is 28 cm and the slant height of the cone is 17 cm.

We can use the Pythagorean theorem to find the height of the cone: h^2 + r^2 = (l/2)^2

Solving this equation for h, we get: h = √(l^2/4 - r^2)

Now we can substitute the given values and solve for the height of the cone:

h = √(17^2/4 - r^2) = √(289/4 - r^2)

We don't have any information about the radius of the cylinder and cone, so we cannot solve for h in terms of r, but we can find the height of the cone by assuming the value of radius.

Let's assume the radius of the cylinder and cone is 5cm.

h = √(289/4 - 5^2) = √(289/4 - 25) = √(289/4 - 25) = √(64) = 8cm

So, the height of the cone is 8cm.

Please note that this is a theoretical height as it is based on the assumption of radius being 5cm, the actual height of the cone may be different if the radius is different.

There is a ''negative correlation'' in the data set.

Hence, Option B is correct.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, By the graph;

The graph shows points that are grouped together and are decreasing.

And, The gathered data shows that there is a possibility to get correlation between them.

Thus, The group of data is decreasing.

So, the correlation of the data will be negative in nature.

Therefore, It can be said that the "There is a negative correlation in the data set".

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Answer:

Your answer is B

Both a and b are knights. This is the only possible answer because, according to the native's statements, a said they were both knights, and b said a was a knave. However, this contradicts what a said, so they must both be knights.

Knights are members of the nobility or military class in medieval Europe, typically depicted as armored warriors on horseback. They were typically sworn to serve their lord and protect his lands and people. Knights were expected to uphold a code of honor and show courage and loyalty in battle.

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This does not make sense as x is a discrete variable, so it cannot take on a value of 3.5.

A binomial variable is a discrete variable, meaning it can only take on certain values. In this case, x can take on values from 0 to 10 (inclusive). Since 3.5 is not one of these values, it does not make sense to calculate the probability that x equals 3.5.

This does not make sense as x is a discrete variable, so it cannot take on a value of 3.5.

A binomial variable is a discrete variable, meaning it can only take on certain values that are determined by the given parameters. For example, if the binomial variable x is defined as the number of heads in 10 flips of a coin, then x can only take on values from 0 to 10 (inclusive). Since 3.5 is not one of these values, it does not make sense to calculate the probability that x equals 3.5.

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In order for a function to be continuous at a point, then,

The limit of f(x) as x approaches the x coordinate of the point from the left and the right equals the value of the function at that point.

What does the term "continuous function" mean?

A continuous function in mathematics is a function that causes the value of the function to continuously vary as a result of a continuous variation of the argument, or a change without a leap.

                            This indicates that there aren't any discontinuities, or sharp shifts in value.

What does it mean when a function is continuous or discontinuous?

If one can sketch a function without picking up a pencil, one can say that it is continuous. A function is considered discontinuous if it is not.

                          If there is no break in the graph of the given function at the point, then a function f(x) in calculus is continuous at x = c.

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If a calculator displays an angle measure in radians instead of degrees, it would make you question whether the calculator is in the right mode. Radians and degrees are two different units of measuring angles, with radians being the standard unit in mathematics and degrees being more commonly used in everyday life and geography.

Because the range of values for angles in radians is between 0 and 2π, while the range for angles in degrees is between 0 and 360. So, if a calculator gives an angle measure in radians that is outside the range of 0 to 2π or gives an angle measure in degrees that is outside the range of 0 to 360, it would indicate that the calculator is not in the correct mode for the desired unit of measurement.

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this is the answer

(x+x+10)*2=4x+20

In (a) and (d), the -1 is a reciprocal, as -1 is being multiplied by f(p) or f(p⁻¹) respectively, and the solutions for p are p = 2 and p = -7/3 respectively. In (b) and (c), the -1 is an inverse, as it is part of the inverse of f(p), and the solutions for p are p = 7 and p = 5/3 respectively.

(a) f(p) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f(p) = 5 and solve for p. We do this by subtracting 2 from both sides of the equation to get 3p = 3, and then dividing both sides by 3 to get p = 1.

(b) f⁻¹(p) = 5 is an inverse and we can solve for p using the equation f⁻¹(p) = 5. To do this, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.

(c) (f(p))⁻¹ = 5 is a reciprocal and we can solve for p using the equation (f(p))⁻¹ = 5. To do this, we first divide both sides of the equation by 5 to get 1/f(p) = 1. Then, we multiply both sides by f(p) to get f(p) = 5. Finally, we subtract 2 from both sides to get 3p = 3, and then divide both sides by 3 to get p = 1.

(d) f (p⁻¹) = 5 is not an inverse or a reciprocal. To solve for p, we can use the equation f (p⁻¹) = 5 and solve for p. We do this by multiplying both sides of the equation by p⁻¹ to get f(p) = 5p⁻¹. Then, we subtract 2 from both sides to get 3p = 5p⁻¹ - 2, and then multiply both sides by 3 to get 9p = 5p⁻¹ - 6. Finally, we add 6 to both sides to get 9p + 6 = 5p⁻¹, and then divide both sides by 4 to get p = 1.

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Answer: 4.761 (Not Rounded)

Step-by-step explanation: Divide 25/5.25 and that will give you each card price.

Answer:

1 card = $0.21
25 cards = $5.25

Answer: [tex]x=3.5, y=4.25[/tex]

Step-by-step explanation:

[tex]3x+2y=19 \implies 6x+4y=38\\\\(6x+4y)-(2x+4y)=38-24 \implies 4x=14 \implies x=3.5\\\\\therefore 3(3.5)+2y=19 \implies 2y=8.5 \implies y=4.25[/tex]

6x² - 31 x + 40, after factorization we get: (2x - 5) (3x - 8).

correct option: a

Expanding brackets is done in reverse when factorising. By eliminating the most common factors, an expression is fully factored when it is enclosed in brackets. The simplest method of factorization is to identify the term in the equation with the largest common factor. The Grouping technique, the Difference in Two Squares, the Sum or Difference in Cubes, and the Greatest Common Factors (GCF) are the four primary methods of factoring.

Similar to this, factoring is a very useful technique in algebra that is utilised at all levels. Additionally to, of course, simplifying complex expressions, it offers a standard way for solving quadratic equations. Graphing functions also makes advantage of it.

= 6x² - 31 x+40

= 6x² - 15 x - 16 x +40

= 3x (2x - 5) - 8 (2x - 5)

= (2x - 5) (3x - 8)

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The average Honda beat the Dodge but couldn't pass the Smart Car, and the Mini couldn't pass the Audi, so the Audi won the race.

The Honda was able to defeat the Dodge but was unable to pass the Smart Car, so it was the Audi that arrived first in the race.

The Mini was then forced to settle for defeating the Smart Car after failing to pass the Audi. The Audi was the only vehicle that was able to stave off the competition and maintain its lead all the way to the finish line, making it the eventual race winner. Following the Audi in that order, the Honda, Dodge, Smart Car, and Mini were all overrun by the vehicle in front of them before the Mini was able to surpass the Smart Car and finish in fourth place.

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A direction field for this system of linear differential equations can be drawn by plotting the values of x' for various values of x.  As t → ∞, the solutions approach either the equilibrium point (1,0) or (3,0).

a) A direction field for this system of linear differential equations can be drawn by plotting the values of x' for various values of x, and then using arrows to indicate the direction of the solution curves at each point.

In general, the solution curves will approach the equilibrium points, which are points where x' = 0. In this case, there are two equilibrium points: (1,0) and (3,0). The solutions that start near the equilibrium point (1,0) will approach it as t → ∞, and the solutions that start near the equilibrium point (3,0) will approach it as t → ∞.

b) As t → ∞, the solutions approach either the equilibrium point (1,0) or (3,0), and thus they settle down to a constant value.

c) The general solution of the system of equations can be found using the matrix exponential:

x(t) = e^(At)x₀

where x₀ is the initial condition and A is the matrix:

A = (3 -4| 1 -1)

The matrix exponential can be found using a variety of methods, including diagonalization and Jordan form. Once the matrix exponential is found, the general solution can be written in terms of x₀, which represents the initial condition.

--The question is incomplete, answering to the question below--

"x' = [tex]\left[\begin{array}{cc}3&-4\\1&-1\end{array}\right] x[/tex]

(a) draw a direction field and sketch a few trajectories.

(b) describe how the solutions behave as t → [infinity].

(c) find the general solution of the system of equations."

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Answer: 60% boys and 40% girls

Step-by-step explanation:

The total amount of kids in the class would be 13 + 9 = 22 kids.

Boys would make up 13 / 22 = 60% of the class,

Girls would make up 9 / 22 = 40% of the class

Answer:

56

The range is calculated by subtracting the lowest value from the highest value.

The highest value of the set is 78.

The lowest value of the set is 22.

78 - 22 = 56

Step-by-step explanation:

Hope it helps! =D

Answer:

56

Step-by-step explanation:

The positive value of the parameter t corresponding to a point on the parametric curve x = t^2 + 7, y = t^2 + t for which the tangent line passes through the origin is t = 7 + √56.

Given the parametric curve {x = t^2 + 7, y = t^2 + t}, we want to find the positive value of t corresponding to a point on the curve for which the tangent line passes through the origin (0, 0).

First, we find the derivative of the x and y equations to obtain the slope of the tangent line at the point (t^2 + 7, t^2 + t). The derivative of x = t^2 + 7 is

dx/ dt = 2t

and the derivative of y = t^2 + t is

dy/dt = 2t + 1

So, the slope of the tangent line at the point (t^2 + 7, t^2 + t) is

dy/dx = (dy/dt) / (dx/dt)

dy/dx = (2t + 1)/ 2t

dy/dx = 1 + 1/(2t)

Next, we use the fact that the slope of the tangent line is equal to the ratio of the change in y to the change in x between the point and the origin (0, 0). Since the origin is located at x = 0 and y = 0, we have:

(t^2 + t - 0) / (t^2 + 7 - 0) = 2t + 1)/ (2t)

2t(t^2 + t) = (2t + 1) (t^2 + 7)

2t^3 + 2t^2 = 2t^3 + t^2 + 14t + 7

t^2 - 14t = 7

t^2 - 14t + 49 = 7 + 49

(t - 7)^2 = 56

t - 7 = ±√56

t = 7 ± √56

As we require only positive value t = 7 + √56

--The question is incomplete, answering to the question below--

"find the positive value of the parameter t corresponding to a point on the parametric curve { x = t^2 + 7, y = t^2 + t for which the tangent line passes through the origin. answer exactly."

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In most cases, the area of the shaded zone is obtained by deducting the area of a smaller inner form from the area of a larger outer shape.The expression for the area of the shaded region is x² - 23x - 49.

In most cases, the area of the shaded zone is obtained by deducting the area of a smaller inner form from the area of a larger outer shape.The area of the shaded region is the difference between the total area of the polygon and the area of its unobscured interior.

There are two ways for polygons to have the area of the shaded region.

Depending on the shape of the polygon, the shaded area may be on one or both of its sides.

Area of a rectangle

area = lw

where

l = length

w = width

Therefore,

The area of the shaded region  = area of the big rectangle - area of the small rectangle

Therefore,

area of the big rectangle = (x+10)(2x+5) = 2x² + 5x + 20x + 50 = 2x² + 25x + 50

area of the small rectangle = (x+1)(x+1) = x² + x + x + 1 = x² + 2x + 1

area of the shaded region = 2x² + 25x + 50 - ( x² + 2x + 1)

area of the shaded region =  2x² + 25x + 50 - x² - 2x - 1

area of the shaded region = x² - 23x - 49

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(a) The probability that there are less than 2 accidents occur between 3-7pm is 0.2465.

(b) The probability that the next accident occurred within 30 minutes on both days is 0.1358.

Suppose that accidents occur at a rate of 1 per hour from 3-5pm and 6-7pm, and 4 per hour from 5-6pm as Poisson process.

(a) We have to determine the probability that there are less than 2 accidents occur between 3-7pm.

We may use the Poisson distribution to determine the likelihood that there would be less than two accidents between 3 and 7 pm.

The total of the rates for each individual hour represents the rate of accidents during this time period, which is

= 1 + 1 + 4 + 1

= 7 accidents per hours

So the Poisson variable λ = 7

So the probability that there are less than 2 accidents occur between 3-7pm is:

P(X < 2) = P(X = 0) + P(X = 1)

P(X < 2) = [tex]e^{-7}[/tex] × (7^0/0!) + [tex]e^{-7}[/tex] × (7^1/1!)

After simplifying

P(X < 2) = 0.2465

(b) Suppose that on day 1, there was an accident at 3pm and on day 2, at 5pm, then we have to determine the probability that the next accident occurred within 30 minutes on both days.

Since accidents occur in a Poisson process, we may use the Poisson distribution to determine the likelihood that an accident will occur within the next 30 minutes.

Since there are 4 accidents every hour between 5 and 6 o'clock, the likelihood that one will happen in the next 30 minutes is:

P(X = 1) = [tex]e^{-1}[/tex] × (1^1 / 1!)

P(X = 1) = 0.3679

The likelihood that the following event will occur within 30 minutes on both days would thus be

= 0.3679 × 0.3679

= 0.1358

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