A particle is moving along the x-axis. The position of the particle at time t is given by x(t) = t³ - 6t + 9t - 2, 0 ≤ t ≤ 5. Find the total distance the particle travels in 5 units of time.

[tex]\bold{n + (n+1)^{2}}[/tex]

An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.

Well, in this case, I will use the variable n, to name the unknown number.

Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.

(grouping the data the following algebraic expression is obtained):

[tex]\bold{n + (n+1)^{2}}[/tex]

Answer:

(n + 1 )

Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.

..

The angle of your initial isosceles triangle was cut in half by drawing the vertical, therefore you multiply by two to determine theta top.

You may determine the base angles by using:

theta_base = arcos(m/2p)

The top angle can be calculated using:

theta_top = 2*arcsin(m/2p)

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Answer: there would be 8 men

Step-by-step explanation:

can you give me brainliest

Answer: I believe there would be 25 men

Step-by-step explanation: We can see there are 40 women and the ration is 5 (men) to 8 (women)

If we take 40 and divide it by 8 we get 5

so for every 8 women there are 5 men and we do that 5 times

we get: 40 women and 25 men.

Answer:

  332 cm²

Step-by-step explanation:

You want to know the surface area of a tin can that is 7 cm in diameter and 11.6 cm high.

The area of a cylinder is given by the formula ...

  SA = πd(d/2 +h) . . . . . where d is the diameter and h is the height

Using the given values, d=7 and h=11.6, we find the area to be ...

  SA = (3.14)(7 cm)(3.5 +11.6 cm) ≈ 332 cm²

About 332 square centimeters of tin are required to make the can.

We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.

First of all we put the vectors in terms of different variables, such as:

a1(1,-2,0)=(a,-2a,0);

a2(0,1,3)=(0,b,3b);

a3(6,-6,18)=(6c,-6c,18c);

To know that a vector is a linear combination we need to express it like a sum of other different vectors.

(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)

(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)

We express this sum like a system of equations.

a+6c=2

-2a+b-6c=-2

3b+18c=6

We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.

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There is 99% confidence that the population mean number of books read is between 1.51 and 26.69. This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69.

Confidence interval for the mean = (x - z(s/√n), x + z(s/√n))

Where x is the sample mean, s is the sample standard deviation, n is the sample size, and z is the critical value for the given confidence level (in this case, 99%).

Therefore, the confidence interval for the mean number of books read is:

(14.1 - 2.58(16.6/√1018), 14.1 + 2.58(16.6/√1018))

= (1.51, 26.69)

This confidence interval indicates that there is a 99% probability that the true mean number of books read by people in the past year falls between 1.51 and 26.69. In other words, it is likely that the average number of books read by people in the past year is between these values. This interval is an estimate of the population mean and the confidence level indicates how confident we can be that the true mean falls within this range.

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The expression are matched to the simplest form as shown below

simplest form   Equation

12 - 1/2r              (13 - 3/2 r) - (1 - r)

r - 13/6                (7r - 3/2) - (2/3 + 6r)

13r + 20              (6r + 7) + (13 + 7r)

-12 + r                 (-8 - r) + (2r - 4)

The simplest form is solved by evaluating each of the equation in the problem

Evaluating the expressions

(6r + 7) + (13 + 7r)

collecting like terms

6r + 7r + 13 + 7

13r + 20

(13 - 3/2 r) - (1 - r)

opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)

13 - 3/2 r - 1 + r

collecting like terms

13 - 1 - 3/2 r + r

12 - 1/2 r

(-8 - r) + (2r - 4)

collecting like terms

-8 - 4 - r + 2r

-12 + r

(7r - 3/2) - (2/3 + 6r)

opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)

7r - 3/2 - 2/3 - 6r

collecting like terms

7r - 6r - 3/2 - 2/3

r - 13/6

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An equation to represent this proportional relationship is y = 65x.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (3, 195) and (6, 390) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 195 = (390 - 195)/(6 - 3)(x - 3)

y - 195 = 195/3(x - 3)

y - 195 = 65(x - 3)

y = 65x - 195 + 195

y = 65x

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Answer:

x = 3000

Step-by-step explanation:

Answer:

x=3000

Step-by-step explanation:

Given that, 12% of x=360

 or, (x)× (12÷100)=360

 or, (12x ÷100)=360

 or, 12x=36000

 or, x=36000÷12

 or, x=3000

The product of the two polynomials is 16x^4 + 36x^3 - 4x^2 - 26x + 8. The solution is obtained by the method of polynomial multiplication.

What is polynomial multiplication?

The process of multiplying two or more polynomials together is known as polynomial multiplication. To obtain the final polynomial, the terms of the first and second polynomials are multiplied. We can multiply polynomials in a variety of ways depending on the kinds we are using. Each form of polynomial has a different set of guidelines for multiplication. Polynomials are multiplied by multiplying the coefficient by another coefficient and the variable by another variable.

We are given two polynomials

Polynomial 1: 4x^2 + 5x − 4

Polynomial 2: 4x^2 + 4x − 2

Multiplying both, we get

⇒(4x^2 + 5x − 4)*(4x^2 + 4x − 2)

⇒16x^4 + 16x^3 - 8x^2 + 20x^3 + 20x^2 - 10x - 16x^2 - 16x + 8

⇒16x^4 + 36x^3 - 4x^2 - 26x + 8

Hence, the product of the two polynomials is

16x^4 + 36x^3 - 4x^2 - 26x + 8.

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The length of the remaining candle is equal to the total length of the candle minus the length of the candle that has been burned, or (total length - b).

The length of the remaining candle can be calculated by subtracting the length of the candle that has been burned (b) from the total length of the candle. This is because when a candle is burned, the length of the candle decreases. To calculate the remaining length of the candle, start by determining the total length of the candle. Then, subtract the length of the candle that has been burned (b). The result is the length of the remaining candle. The formula for this calculation is (total length - b).  The length of the candle remaining is (b - 2). For example, if the total length of the candle is 6 inches and 2 inches of the candle have been burned, the remaining length of the candle would be 4 inches (6 - 2 = 4).

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A complete question: Based on your answer(s) to part (a), complete the following statement to represent the length of candle remaining in terms of the burned length bb.

It would take 12 minute for them to mow their lawn if they work together

An equation is an expression showing the relationship between numbers and variables.

John can mow his lawn in 3 hours and his sister, Julie, can mow it in 2 hours.

Let t represent the time it would take them to mow their lawn if they work together, hence:

(1/3hours) * t + (1/2hours) * 2 = 1

t(1/3 + 1/2) = 1

(5/6)t = 1

t = 6/5 hours = 1 hour 12 minutes

It would take 12 minutes

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x is an int variable and y is a double variable and the input is: 10 20.7.The output will be x = 10, y = 20.7

given that

x is an int variable

y is a double variable

The C++ double should have a floating-point precision of up to 15 digits as it contains a precision that is twice the precision of the float data type.

When you declare a variable as double, you should initialize it with a decimal value. For example, 3.0 is a decimal number. However, if you initialize it with 3, it will also work fine because although 3 and 3.0 seem to be identical i.e., an integer, there is a big difference in their internal representation.

the input is: 10, 20.7

after execution of the statement

cin >> x >> y

The output will be x = 10, y = 20.7

because x is declared as integer variable so it will print the same

y is declared as double integer variable so it will print same as given input , if it is declared as integer variable then it will be printed as 20

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1/6

The probability of an event is the number of ways the event can happen divided by the number of possible outcomes. In this case, the possible outcomes are the numbers on the die, which are 1, 2, 3, 4, 5, and 6.

The event of rolling a number greater than 5 or less than 3 can happen in two ways: rolling a 6 or rolling a 1 or 2. So the probability of this event is:

P(greater than 5 or less than 3) = (number of ways the event can happen) / (number of possible outcomes) = 2/6 = 1/3

So the answer is option D. 1/6

The output is determined by the pattern of the input.

Pattern is a repeated design or motif used to create a visually pleasing effect. Patterns are often seen in nature, architecture, clothing, and artwork. Patterns can be used to create shapes, textures, and decorations. They can add interest and depth to a design. Patterns can be made up of geometric shapes, lines, curves, and combinations of those elements. They can be created with a variety of materials and techniques, including weaving, printing, embroidery, and painting. Patterns can be used to create continuity, emphasize a focal point, or provide a sense of balance. Patterns can be used to draw the eye to a particular area, or to create a sense of order and organization.

In this example, each output number is the sum of the two numbers before it. Therefore, the output is 6 (1 + 2), 12 (2 + 4), 18 (4 + 5), 24 (5 + 6), and 30 (6 + 8).

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The equation represents this relationship between the variables 'x' and 'y' will be y = -2x.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

If y varies directly from x. Then the proportionality is given as,

y ∝ x

If the proportionality signature is removed then a constant is introduced. Then the equation is given as,

y ∝ x

y = kx

The constant of variation is -2. Then the equation is given as,

y = - 2x

The equation represents this relationship between the variables 'x' and 'y' will be y = -2x.

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Yes, this is reasonable. The circumcenter of a triangle is found by taking the average of the x-coordinates of the three points and the average of the y-coordinates of the three points, so for this triangle, the circumcenter would be at (5.67, 2.67).

The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.

1. Calculate the average of the x-coordinates of the three vertices: (1 + 7 + 8) / 3 = 16 / 3 = 5.67

2. Calculate the average of the y-coordinates of the three vertices: (5 + 5 + 0) / 3 = 10 / 3 = 2.67

3. Therefore, the circumcenter of the triangle is (5.67, 2.67).

The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.

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The domain of a function is the set of possible values that can be plugged into it.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The collection of all possible inputs and outputs constitutes a function's domain and range, respectively. Important features of a function are the domain and range. The domain accepts all potential input values from the set of real numbers, and the range accepts all function output values.

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The general solution of the first-order linear differential equation y' - (ln x)y = [tex]3 x^x[/tex] is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]

As per the give,n data the given differential equation is:

y' - (ln x) y = 3 [tex]x^x[/tex]

Here have to determine the general solution of the first-order linear differential equation.

The differential equation is linear if the dependent variable y and its derivative only occur in the first degree.

Then, [tex]$\frac{d y}{d x}-(\ln x) y=3 x^x$[/tex]

This is of the form [tex]$\frac{d y}{d x}[/tex] + P(x)y = Q(x) which is the linear equation.

In order to solve this kind of differential equation, we have to multiply it by an integrating factor.

Here, P = - ln (x), Q(x) = 3 [tex]x^x[/tex]

I F = [tex]e^{\int P d x}[/tex]

I F = [tex]e^{-\int \ln (x)}[/tex]

I F = [tex]e^{-(x \ln x-x)}[/tex]

I F = [tex]e^{x-x \ln x}[/tex]

I F = [tex]\frac{e^x}{e^{x \ln x}}[/tex]

I F = [tex]\frac{e^x}{x^x}[/tex]

Hence, the general solution is

[tex]& y(I F)=\int Q(x)(I F) d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 x^x\left(\frac{e^x}{x^x}\right) d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 e^x d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=3 e^x+c \\[/tex]

[tex]& \Rightarrow y=3 x^x+c x^x e^{-x}[/tex]

Hence, the general solution is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]

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The sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.

What is the eigenvalue?

Eigenvalues are the special set of scalar values that are associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed characteristic roots.

To find the eigenvalues of matrix A, we can solve the characteristic equation |A - λI| = 0, where λ is a scalar and I is the identity matrix.

|A - λI| = 3- λ 1 4 0 2- λ 6 0 0 5- λ

= (3-λ)(5-λ) - 24 = λ^2 - 8λ - 15

Setting λ^2 - 8λ - 15 = 0, we can find the eigenvalues of the matrix by solving the quadratic equation.

λ^2 - 8λ - 15 = 0

λ = (8 ± √(8^2 + 4*15))/2

λ = (8 ± √(64 + 60))/2

λ = (8 ± √124)/2

So the eigenvalues of matrix A are λ_1 = (8 + √124)/2 and λ_2 = (8 - √124)/2

The sum of eigenvalues is λ_1 + λ_2 = (8 + √124)/2 + (8 - √124)/2 = 8

The product of eigenvalues is λ_1 * λ_2 = (8 + √124)/2 * (8 - √124)/2 = -15

Hence, the sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.

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Answer:

see below

Step-by-step explanation:

there are 3 points given

diff in y / diff in x = slope

so plug in any 2 points' Y and x and get the slope

because it's downward shaped, you  know the slope MUST be negative.

so diff in Y = 23-29 = -6

diff in X = 3-7 =2

so slope is +3

intercept is given, when x=0 y = 32

it represents what F is when it's 0C°

The measure of angle 1 is 92 and the measure of angle 2 is 83.

Lines are straight with little depth or width. Perpendicular lines, intersecting lines, transversal lines, and other types of lines will be covered. An angle is a shape formed by two rays emerging from a common point. In this field, you may also come across alternate and corresponding angles.

Given that ABCD is given, the interior angle at vertex B is 97 degrees and the exterior angle at vertex A is 88 degrees. Lines AB and CD are parallel.

The measure of angle 1 is,

∠1 = 180 - 92 = 88

The measure of angle 2 is,

∠2 = 180 - 97 = 83

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Considering the definition of probability, the probability that the selected student is in none of the clubs listed is 0.375 or 37.5%.

Probability is the greater or lesser chance that a given event will occur.

In other words, the probability establishes a relationship between the number of favorable events (number of cases in which event A may or may not occur)  and the total number of possible events through the Laplace's Law as follow:

P(A)= number of favorable cases÷number of total cases

In this case, you know:

Replacing in the definition of probability:

P(A)= 15÷40

Solving:

P(A)= 0.375

Expressed as a percentage:

P(A)= 37.5%

Finally, the probability is 0.375 or 37.5%.

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(s+12)^3

I am wasting space here as you can tell but no fr the answer is (s+12)^3

The table indicates that purchase price is a function of demand, as each demand is mapped to a single purchase price.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The input and output variables for this problem are given as follows:

In the table, there are no repeated demand values, meaning that the purchase price is a function of the demand, as there are no inputs mapped to multiple outputs.

The table is given by the image presented at the end of the answer.

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Step-by-step explanation:

g(f(x)) means that we first take x and calculate f(x).

then we take that result and use as input value for g(x).

x = -5

f(-5) = (-5)² + -5 - 12 = 25 - 5 - 12 = 8

and now

g(8) = -2×8 - 15 = -16 - 15 = -31

g(f(-5)) = -31

Li earns more than 78percentage of recent college graduates, and is in the 78th percentile of salaries earned.

1. Calculate the total number of recent college graduates surveyed: Multiply the total number of responses to the survey by 100 to get the total number of graduates surveyed.

2. Calculate the number of recent college graduates who earn less than or equal to Li's salary: Multiply the percentile (78%) by the total number of graduates surveyed to get the number of graduates who earn less than or equal to Li's salary.

3. Calculate the percentage of recent college graduates who earn less than or equal to Li's salary: Divide the number of graduates who earn less than or equal to Li's salary by the total number of graduates surveyed to get the percentage of graduates who earn less than or equal to Li's salary. The result will be 78%.

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The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.

1. Start by subtracting the largest coin value from the total amount.

2. If the difference is greater than 0, add the coin to the total and repeat the process.

3. If the difference is 0, move onto the next smallest coin value.

4. Repeat the process until the total amount is reached.

5. Once the total amount is reached, the minimum amount of coins needed to arrive at the total will be displayed.

The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.

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The angular momentum of the flywheel is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s.

1. Determine the angular momentum of the flywheel:

Angular momentum = Torque × Time × Moment of Inertia

= 2.5 Nm × 10.0 s × 2.0 kg m2

= 50 kg m2/s

The angular momentum of an object can be determined from the product of the applied torque, the time interval, and the moment of inertia. The moment of inertia is the rotational inertia of an object, which is the resistance to changes in its angular velocity. The angular momentum of the flywheel in this question is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s. This means that the flywheel will have an angular momentum of 50 kg m2/s after the 10-second interval when the torque is applied. The angular momentum of the flywheel will remain constant until another torque is applied to change it.

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The set X can therefore be written as follows: The expression "A is the set of elements x such that x is a natural number less than 7" can be translated as "A is the set of elements x such that x is a natural number less than 7." A = x: x N, x 7 is another way to express the above set.

The Complete Question is  Set Builder .

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