Let $f$ and $g$ be functions defined on a domain $A$. Prove that if $f$ is bounded, and $\displaystyle\lim_{x \rightarrow c} g(x)

A reference tool that is used to determine how the fiber is to be orientated for a particular ply of fabric is called a lay plan or lay direction.

A lay plan is a detailed diagram that shows the orientation of fibers in each layer of a fabric, and it is used as a guide for the manufacturing process. The lay plan indicates the direction in which the fibers should be oriented in each layer of the fabric, which is essential for achieving the desired strength, stretch, and durability of the final product.

The lay plan is also used to ensure that the fibers are aligned in the same direction in each layer, which helps to prevent warping or other issues that can occur during manufacturing.

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The above statement suggests that perhaps the curve's approximate length is 2.

Curve, An abstract phrase used only to describe the trajectory of a linearly stretching point in mathematics (see continuity). Usually, an equation will create such a route. The term may also be used to describe a linear model or a collection of connected line segments. The curve is referred to as a route, or a plot line (or just arc). If a curve is the continuous injective picture of either an interval or indeed a circle, it is considered simple.

Considering function is,

[tex]y=\sqrt{x-x^2}+\sin ^{-1} \sqrt{x}[/tex]

To determine the curve's actual length

First ,  Parametrise  the Curve  by x = sin²u

[tex]\begin{aligned}& y=\sqrt{\sin ^2 u-\sin ^4 u}+\sin ^{-1} \sqrt{\sin ^2 u} \\& y=\sin u \sqrt{1-\sin ^2 u}+\sin ^{-1} \sin u\end{aligned}[/tex]

y = sinucosu + u

[tex]\begin{aligned}& y=\frac{1}{2} \times 2 \sin u \cos u+u \\& y=\frac{\sin 2 u}{2}+u \\& \frac{\mathrm{d} y}{\mathrm{~d} u}=\frac{\mathrm{d}}{\mathrm{d} u}\left[\frac{\sin 2 u}{2}+u\right] \\& \frac{\mathrm{d} y}{\mathrm{~d} u}=\left[\frac{2 \cos 2 u}{2}+1\right]\end{aligned}[/tex]

[tex]\frac{\mathrm{d} y}{\mathrm{~d} u}=[\cos 2 u+1][/tex]

and, x = sin²u

[tex]\begin{aligned}& \frac{\mathrm{d} x}{\mathrm{~d} u}=\frac{\mathrm{d}}{\mathrm{d} u}\left[\sin ^2 u\right] \\& \frac{\mathrm{d} x}{\mathrm{~d} u}=[2 \sin u \cos u] \\& \frac{\mathrm{d} x}{\mathrm{~d} u}=[\sin 2 u] \\& \left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2=\left(\frac{\mathrm{d} x}{\mathrm{~d} u}\right)^2+\left(\frac{\mathrm{d} y}{\mathrm{~d} u}\right)^2 \\& \left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2=(\sin 2 u)^2+(1+\cos 2 u)^2\end{aligned}[/tex]

[tex]\begin{aligned}\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =\left[\sin ^2 2 u+1+\cos ^2 2 u+2 \cos 2 u\right] \\\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =[1+1+2 \cos 2 u] \\\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =[2+2 \cos 2 u] \\\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =4 \cos ^2 u \\\left(\frac{\mathrm{d} s}{\mathrm{~d} u}\right)^2 & =2 \cos u\end{aligned}[/tex]

Currently, the curve's exact length is,

[tex]\begin{aligned}& =\int_0^{\Pi / 2} 2 \cos u d u \\& =2 \int_0^{\Pi / 2} \cos u d u \\& =2[\sin u]_0^{\Pi / 2} \\& =2\left[\sin \frac{\Pi}{2}-\sin 0\right]\end{aligned}[/tex]

= 2

As a result, the curve's exact length is 2

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To find the domain and range of a system of inequalities, you need to solve the system of inequalities, plot the solution, determine inequality sign for solution, shade area of solution, then the x-values of the area represent domain and y values represent range.

Solve the system of inequalities for x and y in terms of each other.

Plot the solutions on a coordinate plane. Each solution will be a boundary line for the solution set.

Determine the inequality signs for each solution. Solutions with < or > signs will be represented as a dashed line, while solutions with ≤ or ≥ signs will be represented as a solid line.

Shade the portion of the coordinate plane that satisfies all of the inequalities.

The shaded area represents the solution set for the system of inequalities.

The domain is the set of all x-values that are included in the solution set and the range is the set of all y-values that are included in the solution set.

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0.5x + 6 = 4x - 1

3.5x = 7

x = 2

Only one solution exists for the given equation.

Answer:

one

Step-by-step explanation

For a polynomial function, the number of solutions, or zeros, is generally equivalent to the highest degree. For example, a cubic function (e.g. [tex]x^3+2x^2[/tex]) has 3 real zeros (x=-2, x=0, and x=0) and a quadratic (e.g. [tex]x^2-1[/tex]) has 2 real zeros (x=-1 and x=1).

For your problem, [tex]\frac{1}{2} (x+12)=4x-1[/tex], the highest degree is 1 since this is a linear function. To prove there is only one solution, let's bring all the terms to one side, simplify, and solve for x.

There only one solution to the equation as shown above and as can be seen in step 4, the x is only to the first degree ([tex]x=x^1[/tex]) which indicates that there is only one solution, 2.

A single song may be downloaded for $0.35. Adjusting the solution c = 0.35s yields the answer because c/s = 0.35.

An equation is an mathematical statement that uses an equal sign to express the relationship across two or more objects, such as variables or integers. Equations can be used to represent relationships between physical, chemical, and other sorts of events as well as to solve mathematical problems. An equation in mathematics is a claim made regarding the equivalence of two expressions. A assertion claiming two expressions equal equal is what an equation is, in other words.

This indicates that each music download costs $0.35. Consequently, it costs $0.35 to buy a single song.

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6 points were scored in the 11th game.

Mean is the arithmetic average of a set of given numbers. Therefore the mean in math is often referred to as simply the average.

The mean is the total number of points scored divided by the number of games.

So if the mean is 17 points per game for the first 10 games, the total number of points scored in the first 10 games is 17 * 10 = 170.

Similarly,

if the mean is 16 points per game after the 11th game, the total number of points scored in the first 11 games is 16 * 11 = 176.

To find the number of points scored in the 11th game

we can subtract the total number of points scored in the first 10 games from the total number of points scored in the first 11 games:

176 - 170 = 6

Therefore, 6 points were scored in the 11th game.

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First of all, we need to know what the units are in this problem.

We can see that there is yards, inches, and feet.

(Keep in mind that yd = yard, ft = feet, and in = inches)

1yd = 3ft

1ft = 12in

Let's figure out how many inches are in a yard.

If we know that 3 feet are in every yard, and 12 inches are in every foot, we can make an equation that looks like this:

(1yd × 3ft) × 12 = 36

This means that there are 36 inches in every foot.

Now that we know how many inches are in a yard, lets figure out how many inches are in 10 yards.

36 × 10 = 360

There are 360 inches in 10 yards.

Now, let's figure out how much 360 inches exceeds 192 inches.

360 - 192 = 168

To convert this to feet, we need to use an equation that looks like this:

168 ÷ 12 = 14

Therefore, the amount of feet that the length of the room exceeds the width is 14 feet.

The polyhedron with 10 vertices and 7 faces has 15 edges.

What is polyhedron?

A polyhedron is a three-dimensional object or solid that has flat faces, straight edges, and sharp corners or vertices. It is a geometric shape that is bounded by a finite number of polygons, which are shapes with straight sides.

Based on the Euler's formula for polyhedra, which states that the number of vertices plus the number of faces minus the number of edges is always equal to 2, we can solve for the number of edges:

10 (vertices) + 7 (faces) - E (edges) = 2

Simplifying the equation:

10 + 7 - E = 2

17 - E = 2

E = 17 - 2

E = 15

Therefore, the polyhedron with 10 vertices and 7 faces has 13 edges.

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As per the ratio proportion, the length of 600 miles freeway is 6 inches on the map.

What is ratio proportion?

Ratio proportion is an equation where two sides of it are equal. A ratio or proportion maintains the equality between two fractions.

Given, 0.5 inches represent 50 miles.

Let, x inches represent 600 miles.

Therefore, as per the ratio proportion, we can write:

0.5 : 50 = x : 600

⇒ 0.5/50 = x/600

⇒ x = (600 × 0.5)/50 = 6.

Therefore, the length of 600 miles freeway is 6 inches on the map.

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The word "correlation" is made by join forces the words "co" and "relation". The word "co" means jointly, thus, correlation means the relationship between any set of data when examine together.

In Statistics, the correlation coefficient is a compute defined between the numbers -1 and +1 and act for the linear interdependence of the set of data.

This data is then divided by the product of standard deviations for these variables.

The equation given below recap the above concept:

ρxy=Cov(x, y)/σxσy

Cov(x,y)=covariance of variables x and y

σx=standard deviation of x.

σy=standard deviation of y.

1. For a positive correlation: the values increase together.

2. For a negative correlation: one value decreases as the other increases.

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The experiment's predicted outcome is that the markers will either be farther apart or closer together, proving that the tectonic plates are in fact moving and not static.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability.

A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

Hence, The experiment's predicted outcome is that the markers will either be farther apart or closer together, proving that the tectonic plates are in fact moving and not static.

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Answer:

-4

Step-by-step explanation-

y2-y1

-------- = m = slope

x2-x1

8-12        -4

--------- =  ---- = -4

-2-(-3)      1

12 13 14 15 16 17 18 19 20 at the fisher farm, the weights of zucchini squash are normally distributed,  then Weight represents the top 10% of the zucchinis is 5.9

The formula for calculating a z-score is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

We're looking for:

Weight is 10% of zucchinis at the top.

Top 10% = 90% of the population

90th percentile Z score is 1.282.

Hence

1.282 = x - 5 / 0.7

1.282 × 0.7 = x - 5

0.8974 = x - 5

x = 5 + 0.8974

x = 5.8974

5.9 ounces, roughly.

The top 10% of the zucchinis have a weight of 5.9 ounces.

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Answer:

57 grey plates

Step-by-step explanation:

304 = 3 : 8 : 5

304 = 16x

[tex] \frac{ \\ 304}{16} = \frac{16x}{16} [/tex]

x = 19

by solving systematically for the grey plate

3 × 19 = 57 grey plates.

Additional solvings.

by solving systematically for the white plates

8 × 19 = 152 white plates

by solving systematically for the black plates

5 × 19 = 95 black plates

Total plates

57 + 152 + 95 = 304

I hope this helped

Answer: -1 2/5 i think im not sure (check explaination)

Step-by-step explanation:

slope formula= y2-y1/x2-x1
-3-4/8-3=-7/5,-1 2/5

Answer:

A.  293 dolls each

B.  710 beads

C.  (n+n)/3 >2xy

Step-by-step explanation:

1.  Let A be the number of dolls collected by Gelyn and B the number collected by Geraldine.  

At the start:

 A = 1,178, and

 B = 588

Girlie gets the same number of dolls from both, which we'll say is x.  The situation is then:

Gelyn:  A - x

Geraldine = B - x

Girlie = 2x

After the transfer, we find that A-x = 3(B-x)  [Gelyn had 3 times as many dolls left as Geraldine]

Lets rearrange this last expression:

A-x = 3(B-x)

A-x = 3B-3x

2x=3B-A

Use the values of A and B to find x:

2x=3(588)-(1,178)

2x = 586

x =  293

Gelyn  and Geraldine each gave Girlie 293 dolls.

========

2.  Let A, B, and C stand for the number of beads in Boxes A, B, and C, respectively.  We are told that:

 A + B + C = 4342 [Box A, Box B, and Box C contain 4,342 beads altogether]

and learn that:  

A+18 = B, and  [There are 18 more beads in Box B than Box A]

C = 3B              [There are 3 times as many beads in Box C as in Box B]

How many beads in Box A?

We have three equations.  Lets find a way to substitute so that we can eliminate the unknowns B and C.

Look at:   A + B + C = 4342

If we can rearrange the other equations to express the variables B and C in terms of A, we could solve the problem.

A+18 = B becomes B=A+18  [We can now calculate B from A]

The second, C = 3B, does not have A, but we can use the above expression for B, which will allow C to be expressed as a function of A:

C = 3B

C = 3(A+18)

C = 3A + 64   [We can now calculate C from A]

Use these definitions of B and C in the first equation (substitution):

A + B + C = 4342

A + (A+18) + (3A + 64) = 4342

6A + 82 = 4342

6A = 4260

A = 710   Box A has 710 beads

3.  The sum of x and n divided by 3 more than twice the product of x times y

          (n+n)/3        [The sum of x and n divided by 3]

         >2xy            [more than twice the product of x times y]

Put these together:

    (n+n)/3 >2xy

The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The dramatization club is offering passes to their play to fund-raise for the show's costs. Every understudy ticket sells for $6.50 and every grown-up ticket sells for $11.50. The dramatization club should make at least $1300 from ticket deals to take care of the show's expenses.

Let 's' and 'a' be the number of tickets sold to students and adults, respectively. Then the inequality is given as,

6.5s + 11.5a ≥ 1300

The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.

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Answer:

[tex]y=-\frac{2}{3}x+4[/tex]

Step-by-step explanation:

[tex]y=\frac{4-0}{0-6}=-\frac{2}{3} \\ \\ b=4 \implies y=-\frac{2}{3}x+4[/tex]

a) Yes, overdetermined systems can be consistent. For example, the system of equations below is consistent because it has the solution (2,4)

x1=2, x2=4, x1+x2=6

An overdetermined system of linear equations can have infinitely many solutions if the equations are dependent, meaning they are linearly dependent and can be derived from one another by a linear combination. If a system of equations is dependent, it means that the equations are not providing new information.

b) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.

x1=2, x2=4, x1+x2=8

An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.

d) No, overdetermined systems cannot be consistent because there are no free variables. For example, the system of equations below has no solution.

x1=2, x2=4, x1+x2=24

An overdetermined system of linear equations that is not dependent means that the equations are providing new information, but the system has no solutions because there are no free variables, which means there is no way to satisfy all the equations.

c) is not a valid option as it contains a mix of concepts of dependent and independent systems and also the system of equations is inconsistent.

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El número A = 52 es una solución del sistema de ecuaciones lineales.

En esta pregunta tenemos un sistema de dos ecuaciones lineales con dos incógnitas, de modo que existe la posibilidad de una solución única. Primero, escriba el sistema de ecuaciones descrito en el enunciado de la pregunta:

A / 4 = B / 9

A + B = 169

Segundo, despeje la variable A de la segunda ecuación del sistema de ecuaciones:

B = 169 - A

Tercero, elimine la variable B en la primera ecuación del sistema de ecuaciones y despeje la variable A:

A / 4 = (169 - A) / 9

9 · A = 4 · (169 - A)

9 · A = 676 - 4 · A

13 · A = 676

A = 52

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Answer:

2.00 m in front of the concave mirror with a focal length of 30.0 m

Step-by-step explanation:

To find the distance from a concave mirror with a focal length of 30.0 m at which a 7.00-m-long baby blue whale must be placed to get a real image the size of a mature blue whale, we can use the mirror equation:

1/u + 1/v = 1/f

Where u is the distance between the object and the mirror, v is the distance between the image and the mirror, and f is the focal length of the mirror.

We know that v is negative because the image is real, and the same size of the mature blue whale that is 28m.

So, we can substitute the values we know into the equation:

1/u - 1/28 = 1/30

We can solve for u by multiplying both sides by 30u and getting:

30 - 28u = u

So u = 2m

Therefore, the 7.00-m-long baby blue whale must be placed 2.00 m in front of the concave mirror with a focal length of 30.0 m to get a real image the size of a mature blue whale.

Using the table your total monthly fixed expenses is 977.43.

Rent payment $953. 20/month

Auto payment $165. 87/month

Telephone $56. 98/month

Auto insurance $714. 36/six months

Once-a-week outing $35. 00/week

= 953.20 + 165.87 + 56.98 + 714.36/6 + (35*4)

= 1435.11

= 2412.54 - 1435.11

=977.43.

An expense is something that calls for the transfer of funds, or fortune in general, from one person or organization to another as payment for a good, service, or other type of cost. Rent is a cost to a tenant. Tuition is a cost to parents or students. Purchasing anything like food, clothing, furniture, or a car is frequently referred to as a cost.

A cost that is "paid" or "remitted" usually in exchange for anything of value is referred to as an expense. "Expensive" refers to something that appears to be very expensive. "Inexpensive" refers to something that appears to be inexpensive. "Expenses of the table" include costs associated with eating, drinking, a feast, etc.

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Check the picture below.

Answer:

[tex]\boxed{\displaystyle f^{-1}(x) =\left(\dfrac{x-2}{4}\right)^5 + 1\\}[/tex]

This is the last choice on the screenshot you provided

Step-by-step explanation:

Use y to represent f(x)

[tex]y=4\sqrt[5]{x-1}+2[/tex]

Replace x with y and y with x:

[tex]x=4\sqrt[5]{y-1}+2[/tex]

Solve for y in terms of x and that will be the inverse of f(x)

Answer: Last choice on the screen, namely

[tex]\boxed{\displaystyle f^{-1}(x) =\left(\dfrac{x-2}{4}\right)^5 + 1\\}[/tex]

The probability of rolling doubles with three rolls of two fair six-sided dice is 0.512.

How do you calculate probability?

Probability is the likelihood that something will happen. Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes.

The probability of rolling doubles with one roll of two fair six-sided dice is 16/36, or 1/6. This means that the probability of not rolling doubles with a single roll is 5/6.

The probability of not rolling doubles with two rolls is (5/6)^2, or 25/36.

The probability of not rolling doubles with three rolls is (5/6)^3, or 125/216.

Therefore, the probability of rolling doubles with three rolls of two fair six-sided dice is (216-125)/216, or 91/216, or 0.512.

P(doubles on 1 roll) = 1/6

P(not doubles on 2 rolls) = (5/6)^2 = 25/36

P(not doubles on 3 rolls) = (5/6)^3 = 125/216

P(doubles on 3 rolls) = 1 - (125/216) = 91/216 = 0.512

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The value of the equation is y = 0.75x , where y is the total cost of the ticket and x is the original cost of the ticket

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the original cost of the ticket be represented as x

Let the discounted price of the ticket be y

Now , the percentage of discount = 35 %

So , the discounted price of the ticket y = original cost of the ticket - ( 35/100 ) x original cost of the ticket

Substituting the values in the equation , we get

The discounted price of the ticket y = x - 0.35x

On simplifying the equation , we get

The discounted price of the ticket y = 0.75x

y = 0.75x   be equation (1)

Now , the cost of the ticket cannot be a negative value so it should lie in the first quadrant

Hence , the equation is y = 0.75x

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The largest possible quotient of a positive 3-digit number divided by the sum of its digits if the 3 digits must be different is 41

The largest possible quotient of a positive 3-digit number divided by the sum of its digits is obtained when the 3 digits are as large as possible, subject to the constraint that they must be different.

The largest possible 3-digit number is 987, which has digits 9, 8, and 7.

The sum of its digits is 9 + 8 + 7 = 24.

The quotient of 987 divided by 24 is:

987/24 = 41.125

otherwise when expressed as a mixed number is read as 41 whole number 3/24

In conclusion, the largest possible quotient of a positive 3-digit number divided by the sum of its digits, when the 3 digits must be different, is 41.

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The supplied statement states that the function f(maverage )'s rate of change is 0.78 cm, representing the fish's original length.

A function in mathematics is an expression, rule, or law that determines the link between two variables, one of which is an independent variable (the dependent variable). Functions may be present everywhere in mathematics, and they are essential for building physical connections in the sciences.

The fish's original length, which is represented by the graph's y-intercept, is 5 cm.

The function f(maverage )'s rate of change at m = 3 to m = 7

m = 3 => f(3) = 5(1.08) = 5.4 cm

m = 7 => f(7) = 5(1.08)⁷ = 8.55 cm

Change in 9 - 1 = 8 months = 8.55 - 5.4 = 3.15 cm

The function's average variation at m = 3 through m = 7 is given.

= (3.15/4)

= 0.78 cm per month

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The general solution of the given higher-order differential equation is y(x) = e2x + x2 + c4e3x + c5e-3x.

A general solution is an answer that can be applied to a wide range of problems. It is a broad-based approach that can be used to solve any problem, regardless of its complexity or specific details. General solutions take into account the overall goal of a problem, rather than its individual elements, and look for a way to achieve the desired result. Additionally, they are often easy to implement and can be applied to a variety of scenarios.

The general solution of the given higher-order differential equation, y(4) + y''' + y'' = 0, is given by

y(x) = c1e2x + c2e-2x + c3x2 + c4e3x + c5e-3x + c6x3.

Here, c1, c2, c3, c4, c5 and c6 are constants of integration.

To determine the values of these constants, we must use initial conditions. Suppose we are given y(0)=1 and y'(0)=2, then we can solve for the constants using this information.

Substituting y(0)=1 and y'(0)=2 into the equation, we get

1 = c1 + c2 + c3(0)2 + c4 + c5 + c6(0)3
2 = 2c3 + 3c6(0)2

Solving these equations, we get c1 = 1, c2 = 0, c3 = 1 and c6 = 0.

Therefore, the general solution of the given higher-order differential equation is

y(x) = e2x + x2 + c4e3x + c5e-3x.

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Voting rights for various segments in the United States was extended in stages from the time the United States gained independence, to the late 1900s.

In the late 1700s and early 1800s, voting rights were expanded to include more people, such as white men who owned property. The 15th Amendment was ratified in 1870, and prohibits the federal and state governments from denying a citizen the right to vote based on that citizen's "race, color, or previous condition of servitude."

The 19th Amendment was then ratified in 1920, and prohibits the federal and state governments from denying the right to vote to citizens of the United States on the basis of sex. Then the Voting Rights Act of 1965 was passed to overcome legal barriers at the state and local levels that denied African Americans the right to vote under the 15th Amendment. It was one of the most effective pieces of legislation passed during the Civil Rights Movement.

The 26th Amendment lowered the national voting age from 21 to 18 for all federal, state, and local elections.

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Full question is:

Extending Voting Rights; how have voting rights been extended in the United States since independence ?