A square rug has an inner square in the center. The side length of inner square is x inches and the width of the outer region is 11 inches. What is the area of the outer part of the rug?

After answering the presented question, we can conclude that equation Therefore, the answer is: 8 adults and 12 children went to the movies.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

system of equations -

[tex]x + y = 20 \\9x + 6y = 144 \\x = 20 - y\\9(20 - y) + 6y = 144\\180 - 3y = 144\\-3y = -36\\y = 12\\x + 12 = 20\\x = 8\\[/tex]

So there were 8 adults who went to the movies.

Therefore, the answer is: 8 adults and 12 children went to the movies.

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A = | 1  1  2 |
| 3  4 -1 |
| -1  1  1 |

B = | 1  1  2 | 6 |
| 3  4 -1 | 5 |
| -1  1  1 | 2 |

The coefficient matrix A for the given system is the matrix that contains the coefficients of the variables in the system of equations. The augmented matrix B is the matrix that contains both the coefficients of the variables and the constants on the right-hand side of the equations.

For the given system:

X1 + x2 + 2x3 = 6
3x1 + 4x2 - x3 = 5
-x1 + x2 + x3 = 2

The coefficient matrix A is:

| 1  1  2 |
| 3  4 -1 |
| -1  1  1 |
And the augmented matrix B is:

| 1  1  2 | 6 |
| 3  4 -1 | 5 |
| -1  1  1 | 2 |

So, the coefficient matrix A and the augmented matrix B for the given system are:

A = | 1  1  2 |
| 3  4 -1 |
| -1  1  1 |
B = | 1  1  2 | 6 |
| 3  4 -1 | 5 |
| -1  1  1 | 2 |

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The correct expression is option 1: 0-100(1.05+5)' + 50.

Expression in math is a combination of numbers, symbols and operations used to represent a value or a mathematical relationship. Examples of expressions include algebraic expressions, polynomials, matrices, and trigonometric functions. They are often used to solve equations or solve for a certain value. Expressions are used to express relationships between variables, and can be used to describe real-world problems or situations.

This expression translates to the following: take the result of -100 multiplied by 1.05, then add 5 to it, then take the result and multiply it again by -100. Finally, add 50 to the result.

This expression is used to describe the graph of -100(1.05) shifted to the right 5, and up 50 units. This is because when the graph is shifted to the right 5, it is essentially adding 5 to the result of -100 multiplied by 1.05. When the graph is shifted up 50 units, it is adding 50 to the result. Therefore, the expression 0-100(1.05+5)' + 50 accurately expresses the function g(t) whose graph is the graph of -100(1.05) shifted to the right 5, and up 50 units.

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To find the expression that represents the length of the wallpaper, we need to use the given equation for the area of the rectangular piece of wallpaper, which is y = 5x² + 20x + 20.

We know that the area of a rectangle can be found by multiplying its length by its width. In this case, the width of the wallpaper is given by the expression (x + 2), so we can write:

length * width = y

Substituting the expression for the area of the wallpaper given by y = 5x² + 20x + 20 and the expression for the width of the wallpaper given by (x + 2), we get:

length * (x + 2) = 5x² + 20x + 20

To solve for the length, we can divide both sides of the equation by (x + 2):

length = (5x² + 20x + 20) / (x + 2)

Now we have an expression for the length of the wallpaper in terms of x. We can simplify this expression by using polynomial long division or factoring, but it is already in its simplest form.

Therefore, the expression that represents the length of the wallpaper is:

length = (5x² + 20x + 20) / (x + 2)

To summarize, we used the formula for the area of a rectangle and the expression for the width of the wallpaper to derive an expression that represents the length of the wallpaper. The resulting expression is (5x² + 20x + 20) / (x + 2). This expression can be used to calculate the length of the wallpaper for different values of x.

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Answer:

204

Step-by-step explanation:

let the number of people who viewed wetland exhibit be x

so 3x -10 =602

we add 10 on both sides

3x-10+10=602+10

3x=612

divide both sides by 3

3x/3= 612/3

x=204

The number of people who viewed the wetland exhibit are 204

Is the cost of a small art paintbrush $0.095 or $0.95?

Answer: 5

Step-by-step explanation: The answer is 5 because if you do 4.75 divided by 0.95 you will get 5.

Answer:

o prove that f(x) is continuous at every point except x = 0, we need to show that:

f(x) is defined at every point except x = 0

lim(x→a) f(x) exists for every a ≠ 0

lim(x→0) f(x) exists

First, we note that f(x) is defined for all values of x except x = 0 because we have defined it as such.

Next, we consider the limit as x approaches a for a ≠ 0:

lim(x→a) f(x) = lim(x→a) 1/x = 1/a

Since the limit exists and is finite for all values of a ≠ 0, we conclude that f(x) is continuous at every point except x = 0.

Finally, we consider the limit as x approaches 0:

lim(x→0) f(x) = lim(x→0) 1/x

This limit does not exist because the function approaches positive infinity as x approaches 0 from the right, and negative infinity as x approaches 0 from the left. Therefore, we conclude that f(x) is not continuous at x = 0.

Hence, we have shown that f(x) is continuous at every point except x = 0

Step-by-step explanation:

The greatest profit that can be earned is given by profit(c) = 2P - kQ(c).

To get the greatest profit that can be earned from a commuter railway with a certain number of passengers per day and a fare of two dollars per day, follow these steps:

Step 1: Let the number of passengers per day be denoted by P.

Step 2: The amount earned from the fare each day is calculated as 2P dollars.

This is the revenue earned by the commuter railway.

Step 3: Let the fare be increased by x cents.

Therefore, the new fare per day is (200 + x) cents, or (2 + x/100) dollars.

Note that the original fare is 200 cents, or 2 dollars.

Step 4: Let the number of passengers who travel by the train after the fare is increased by x cents be denoted by Q(x).

Step 5: It is assumed that the fewer people travel by train as the fare increases.

Therefore, Q(x) is a decreasing function of x, i.e. as x increases, Q(x) decreases.

Additionally, Q(0) = P, since the number of passengers traveling when the fare is unchanged is P.

Step 6: Let C(x) denote the cost of running the commuter railway after the fare is increased by x cents.

This cost is assumed to be proportional to the number of passengers traveling by the train, since a higher number of passengers would require more trains and staff to run them.

Therefore, C(x) = kQ(x),

where k is a constant of proportionality.

Step 7: The profit earned by the commuter railway after the fare is increased by x cents is calculated as the difference between the revenue earned and the cost of running the train.

Therefore, profit(x) = 2P - kQ(x).

Step 8: The greatest profit that can be earned is obtained by finding the value of x that maximizes the profit.

This is equivalent to finding the value of x that minimizes the cost, since the revenue is fixed.

Therefore, we need to find the value of x that minimizes C(x). This is achieved by minimizing Q(x), since C(x) is proportional to Q(x).Step 9: To minimize Q(x), we can use the mean value theorem.

This theorem states that for any decreasing function f(x) and any value of a, there exists a unique value of x between 0 and a such that f(x) = f(a)/a * x.

This value of x is denoted by m(a) and is called the mean value of f(x) on [0, a].

Step 10: Applying this theorem to Q(x), we get Q(x) = Q(0) * (200 + x)/200 * m(x/200).

Therefore, to minimize Q(x), we need to find the value of x that maximizes m(x/200).

This value is denoted by c and is called the critical value of x. It satisfies the equation Q(c) = Q(0)/2.

Step 11: To find c, we need to solve the equation Q(c) = Q(0)/2 for c.

This is equivalent to solving the equation kQ(c) = kQ(0)/2 for c,

since C(x) = kQ(x).

Therefore, we need to find the value of c that satisfies the equation 2P - kQ(c) = P.

This is equivalent to solving the equation Q(c) = P/k.

Therefore, we need to find the value of c that satisfies the equation Q(c) = P/k/2.

Step 12: To find the greatest profit that can be earned, we need to substitute c into the expression for profit(x).

This gives the value of the profit that can be earned when the fare is increased by the critical value c.

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The question involves solving initial value problems (IVPs) using explicit solutions wherever possible. We're given five different IVPs, which are as follows:

(a) dy/dx = xy, y(1) = 1

(b) dy/dt = y^2 + 1/t^2 + 1, y(0) = 1

(c) dy/dx = 3t^2/x, y(0) = e

(d) du/dt = (u^2 - 1)t, u(0) = 0

(e) dy/dt = (cos^2y)(cos^2t), y(0) = π/4

Below are the solutions to each of these IVPs. We'll begin by discussing the meaning of an initial value problem.

What is the definition of an initial value problem (IVP)?

An initial value problem (IVP) is a differential equation that also includes an initial value or condition that specifies the value of the function at a particular point.

In other words, an IVP specifies the value of a function and its derivative at a particular point. As a result, the solution to an IVP is a specific function that satisfies the differential equation as well as the initial condition. We'll move on to solving the IVPs in question.

(a) Solution to the initial value problem dy/dx = xy, y(1) = 1

First, let's write this as a separable differential equation.

(dy/dx) = xy

(dy/y) = xdx

Integrate both sides to get the following:

ln|y| = 1/2(x^2) + C

Expanding e to the power of each side gives the following:

y = Ce^(x^2/2)

Plug in y(1) = 1 to obtain:

C = e^(-1/2)

The explicit solution for this initial value problem is y = e^(x^2/2 - 1/2).

(b) Solution to the initial value problem dy/dt = y^2 + 1/t^2 + 1, y(0) = 1

First, let's write this as a separable differential equation.

dy/(y^2 + 1/t^2 + 1) = dt

Integrate both sides to get the following:

arctan(y) + arctan(t) = t + C

Plug in y(0) = 1 and t = 0 to obtain:

C = π/4

The explicit solution to this IVP is arctan(y) + arctan(t) = t + π/4.

(c) Solution to the initial value problem dy/dx = 3t^2/x in x x(0) = e

First, let's write this as a separable differential equation.

(dy/dx) = (3t^2/x)

dy = 3t^2(x)dx

Integrate both sides to get the following:

y = (3/2)x^2 + Cln|x|

C = ln(e^(-3/2)) = -3/2

The explicit solution to this IVP is y = (3/2)x^2 - (3/2).

(d) Solution to the initial value problem du/dt = (u^2 - 1)t, u(0) = 0

First, let's write this as a separable differential equation.

du/(u^2 - 1) = tdt

Integrate both sides to get the following:

0.5 ln|u -

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The number of degrees of freedom is 14. The t-statistic is 3.50. The probability of finding 15 households with a sample mean of 3.26 children or less is 0.998. The t-statistic for the second poll is 2.14. The probability of finding 15 households with a sample mean between 2.72 and 3.26 children and a standard deviation of 2.12 is 0.050.

1) The number of degrees of freedom is calculated by subtracting 1 from the sample size. In this case, the sample size is 15, so the degrees of freedom would be 15-1=14. Therefore, the number of degrees of freedom is 14.

2) The t-statistic is calculated by subtracting the population mean from the sample mean and then dividing by the sample standard deviation divided by the square root of the sample size. In this case, the t-statistic would be (3.26-1.86)/(2.12/sqrt(15))=3.50. Therefore, the t-statistic is 3.50.

3) The probability of finding 15 households with a sample mean of 3.26 children or less can be found by using the t-distribution table with 14 degrees of freedom and a t-value of 3.50. The probability is 0.998. Therefore, the probability of finding 15 households with a sample mean of 3.26 children or less is 0.998.

4) The t-statistic for the second poll is calculated in the same way as the first. The t-statistic would be (2.72-1.86)/(2.12/sqrt(15))=2.14. Therefore, the t-statistic for the second poll is 2.14.

5) The probability of finding 15 households with a sample mean between 2.72 and 3.26 children and a standard deviation of 2.12 can be found by using the t-distribution table with 14 degrees of freedom and t-values of 2.14 and 3.50. The probability is 0.976-0.926=0.050. Therefore, the probability of finding 15 households with a sample mean between 2.72 and 3.26 children and a standard deviation of 2.12 is 0.050.

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(aA+bB)t = aAt + bBt for any A,B\epsilonMmxn(F) and any a,b\epsilonF. is

for any A,B∈Mmxn(F) and any a,b∈F, (aA+bB)t = aAt + bBt.  

Proving that (aA+bB)t = aAt + bBt for any A,B∈Mmxn(F) and any a,b∈F is fairly straightforward. First, let's take a look at the definition of matrix transpose: the transpose of a matrix A is the matrix At obtained by interchanging its rows and columns.

From this definition, it can be seen that At can be obtained by multiplying each element of A by its corresponding scalar in the set {a, b}. Thus, for any given A,B∈Mmxn(F) and any a,b∈F, (aA+bB)t = aAt + bBt.

Furthermore, multiplying each element of A by its corresponding scalar can be generalized to any number of matrices. That is, given any n matrices A1, A2, A3, ..., An and scalars a1, a2, a3, ..., an (all ∈F), (a1A1+a2A2+a3A3+...+anAn)t = a1A1t + a2A2t + a3A3t +...+anAnt.

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If probability of winning a teddy bear at a carnival is 0.89 and 40 turns are taken, then he should have won about 35 teddy bears.

The probability of winning a teddy bear at a carnival is = 0.89, then

The probability of not winning a teddy bear is = 1 - 0.89 = 0.11,

We use binomial-distribution to calculate the probability of winning "k" teddy bears in "n" turns,

Where probability of winning (p) = 0.89,

The formula for the binomial distribution is,

⇒ P(k) = C(n,k) × p^k × (1-p)^(n-k),

The probability of winning "k" teddy bears in 40 turns is :

⇒ P(k) = C(40,k) × 0.89^k × 0.11^(40-k),

To find "expected-number" of teddy bears won, we multiply the probability of winning k teddy bears by k, and sum over all possible values of k,

⇒ E(number of teddy bears won) = [tex]\[ \sum_{k=0}^{40} \][/tex] k × P(k),

⇒ [tex]\[ \sum_{k=1}^{40} \][/tex] k × C(40,k) × 0.89^k × 0.11^(40-k),

On further solving ,

We get,

⇒ E(number of teddy bears won) ≈ 35.6,

Therefore, we expect to win about 35 teddy bears if we take 40 turns .

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(i) The probability can select the team of 7 members with exactly three girls in[tex]${7\choose3}$[/tex] ways.(ii) The teacher can select the team of 7 members with no girl in [tex]${9\choose7}$[/tex] ways.(iii) The teacher can select the team of 7 members with at least three girls in[tex]${7\choose3}+{7\choose4}+{7\choose5}+{7\choose6}+{7\choose7}$[/tex]ways.

Excursions are an important part of education as they help students learn more than what is taught in the classroom. When a class of XI was planning an excursion to Ajanta and Ellora caves, 9 boys and 4 girls were willing to go. In order to select the team of 7 students, the class teacher had three choices. The first choice was to select the team of 7 members with exactly three girls. The teacher had[tex]${7\choose3}$[/tex]ways to do this. The second choice was to select the team of 7 members with no girls. The teacher had [tex]${9\choose7}$[/tex] ways to do this. The third choice was to select the team of 7 members with at least three girls. The teacher had[tex]${7\choose3}+{7\choose4}+{7\choose5}+{7\choose6}+{7\choose7}$[/tex]ways to do this. The teacher had to select the team carefully in order to ensure that the excursion was both educational and enjoyable for the students. The teacher also had to consider the safety of the students while selecting the team. The excursion was a great success and the students learnt a lot from the experience.

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If ker(A)=im(B), the product of the two matrices AB will be the zero matrix.

A linear transformation is a function that can be represented as a matrix transformation, and the kernel is the set of all inputs which produce an output of 0. In this example, the kernel of the linear transformation is the line spanned by A = 1 in R3.

If we consider an n x p matrix A and a p x m matrix B, and if the kernel of matrix A (ker(A)) is equal to the image of matrix B (im(B)), then the product of the two matrices AB will be the zero matrix. This is because all elements in the product matrix will be the result of multiplying a row vector of A by a column vector of B. But, since the kernel of A is equal to the image of B, this means that all of the row vectors of A and all of the column vectors of B are equal, so the result of multiplying any of them together will be the zero vector.

To summarize, if the kernel of A is equal to the image of B, the product of the two matrices AB will be the zero matrix.

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Number of bunches of flowers that can the florist make is 23 flowers

If 60% of the flowers in a bunch are lilies, then there are 40 x 0.6 = 24 lilies in each bunch.

That means there are 40 - 24 = 16 roses and carnations in each bunch.

The ratio of carnations to roses = 3 : 5

Let's call the number of carnations in each bunch "3x" and the number of roses in each bunch "5x". That means

3x + 5x = 16 (the total number of carnations and roses)

8x = 16

x = 2

So there are 3 x 2 = 6 carnations in each bunch.

If the florist has only 140 carnations, they can make 140 / 6 = 23.333... bunches of flowers. However, since they can't make a fraction of a bunch, the florist can only make 23 bunches of flowers.

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Step-by-step explanation:

Given Equation:
-2 (-3x^2 - 2 + 5y^3)

Rearrange terms:
-2 (5y^3 - 3x^2 - 2)

Distribute:
-2 (5y^3 - 3x^2 - 2)

-2 (5y^3) = -10y^3
-2 (-3x^2) = 6x^2 (POSITIVE not NEGATIVE (neg times a neg = pos) )
-2 (-2) = 4  (POSITIVE not NEGATIVE (neg times a neg = pos) )

Therefore your answer of -10y^3 + 6x^2 + 4!

Triangles can be formed when three angles add up to 180 degrees. Therefore, three angles with values of 25 degrees, 35 degrees, and 120 degrees cannot form a triangle as the sum of the angles is only 180 degrees.

However, if the angles are assumed to be part of a larger triangle, then it is possible to calculate the number of triangles that can be made.To begin, we need to find the total area of the triangle. The area of a triangle is equal to the base times the height divided by two. To find the base and height, we need to use trigonometry. The base of the triangle is equal to the sine of the angle of 25 degrees multiplied by the length of the side opposite to it. The height is equal to the sine of the angle of 120 degrees multiplied by the length of the side opposite to it.Once the base and height have been calculated, the area of the triangle can be found. In this case, the area of the triangle is equal to 8.6 square units.Now that the area of the triangle is known, we can calculate the number of triangles that can be made. The total area of the triangle is equal to the sum of the areas of the individual triangles. Therefore, the number of triangles that can be made is equal to the total area of the triangle divided by the area of each individual triangle. In this case, the number of triangles that can be made is equal to 8.6 divided by the area of each individual triangle. This result is equal to 2.15, which means that two and a quarter triangles can be made with the angles of 25, 35, and 120 degrees.

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so let's check how much is each interior angle in the pentagon first.

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=5 \end{cases}\implies 5\theta =180(5-2) \\\\\\ 5\theta =180(3)\implies 5\theta =540\implies \theta =\cfrac{540}{5}\implies \theta =108[/tex]

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The minimum value of 8x³ + 54x + 27³x + 36x  is  81√6/7.

The minimum value of 8x³ + 36x + 54x + 27³x  for positive real numbers x is 81√6.

We have the expression: 8x³ + 36x + 54x + 27³x

Let's factorize it in the following way : 8x³ + 54x + 27³x + 36x = 8x³ + 3³x(3²x + 2) + 3²(3x²) = 8x³ + 3³x(3²x + 2) + 9(3x²)

Let's consider the AM-GM inequality : a + b ≥ 2√ab, for any real positive numbers a and b.

So, we have :

8x³ + 3³x(3²x + 2) + 9(3x²) = 8x³ + 9(3x²) + 3³x(3²x + 2)≥ 3√[8x³ × 9(3x²) × 3³x(3²x + 2)]

This implies : 8x³ + 9(3x²) + 3³x(3²x + 2) ≥ 18x√[2x]

This is because 8x³ × 9(3x²) × 3³x(3²x + 2)

= 81(2x)³x²(3²x + 2)

= 1458(2x)³x³(3²x + 2)

Thus, 8x³ + 9(3x²) + 3³x(3²x + 2) ≥ 18x√[2x]

The minimum value of 18x√[2x] is when 2x is equal to 1.

This is because when 2x is equal to 1,

we have: 18x√[2x] = 18(1/2)√1 = 9.

Now, 8x³ + 9(3x²) + 3³x(3²x + 2) ≥ 9.

In other words,8x³ + 54x + 27³x + 36x ≥ 9

This implies: 8x³ + 54x + 27³x + 36x + 81³x ≥ 9 + 81³x = 81(1 + 3³x)

The above inequality can be written as: (1 + 3³x)(8x³ + 54x + 27³x + 36x) ≥ 81

Therefore, 8x³ + 54x + 27³x + 36x ≥ 81/(1 + 3³x)

This implies: 8x³ + 54x + 27³x + 36x ≥ 81/28

The above inequality can be written as: 8x³ + 54x + 27³x + 36x ≥ 81√6/14

This implies: 8x³ + 54x + 27³x + 36x ≥ 81√6/7.

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The determinant of the upper triangular matrix R is equal to the determinant of the square matrix A.

Hence prove det ( det(A) det(D) . D

QR decomposition QR decomposition is a technique of expressing a matrix as a product of an orthogonal matrix and an upper triangular matrix.

Here, any real square matrix can be decomposed as A QR where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning Tq = QQ" =I) and R is an upper triangular matrix.

The factorization is unique if A is invertible. In that case, the determinant of A can be written as a product of the determinants of Q and R.

For a triangular matrix, the determinant is the product of the diagonal elements.

That is, if A is an n × n matrix, then A = QR

where Q is an orthogonal matrix of size n × n and R is an upper triangular matrix of size n × n.

The determinant of A can be written as the product of the determinants of Q and R.

That is, |A| = |Q| |R|

Since Q is orthogonal, |Q| = ±1

Also, since R is upper triangular, |R| = Product of diagonal elements of R

Now, for an invertible matrix A|A| ≠ 0So,|Q| |R| ≠ 0|Q| ≠ 0 and |R| ≠ 0So,|A| ≠ 0

Therefore, det(A) det(D) .

D200 can be written as |A| = |Q| |R| |D|200

Now, |R| is the product of diagonal elements of R.

Therefore, |D|200 = 1.So, |A| = |Q| |R|

Now, the determinant of Q is ±1.

Therefore, |A| = ± |R|

Therefore, |R| = |A|

This completes the proof.

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Yes, the function y(t)=cos(t) is a solution to the differential equation d2y/dt2 = 2y3 - y.

To prove this, we will use the method of substitution. First, we plug y(t)=cos(t) into the differential equation, giving us:
d2y/dt2 = cos(t)3 - cos(t)

We can rewrite this as:
d2y/dt2 = cos3(t) - 1

We can now use the identity cos2(t) = 1 - sin2(t) to rewrite the equation as:
d2y/dt2 = (1 - sin2(t))3 - 1

Next, we take the derivative of both sides of the equation:
d3y/dt3 = -3(1 - sin2(t))2 * (2*sin(t)*cos(t))

Finally, we use the identity sin2(t) + cos2(t) = 1 and rewrite the equation as:
d3y/dt3 = -3(2*sin(t)*cos(t))

Since the right hand side of the equation is 0, this proves that the function y(t)=cos(t) is a solution to the differential equation d2y/dt2 = 2y3 - y.

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The equation of a sphere with endpoints (5,0,5) and (7,4,7) is (x - 6)^2 + (y - 2)^2 + (z - 6)^2 = 13 .


To derive this equation, we can calculate the radius of the sphere. The midpoint of the diameter is (6,2,6) and the distance between the two points is:

√[(7 - 5)^2 + (4 - 0)^2 + (7 - 5)^2] = √26 = 5.1


Therefore, the equation of the sphere with radius 5.1 and midpoint (6,2,6) is:

(x - 6)^2 + (y - 2)^2 + (z - 6)^2 = 5.1^2 = 26.01.

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value of missing angle x in the triangle is 66.6°

Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three main trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:

Given;

Height of triangle=123 units

Base of triangle=284 units

Using trigonometric function

tanx° =p/b

tanx° =284/123 =2.30894

Taking the inverse, we get

x°=66.6°

Hence, value of missing angle x in the triangle is 66.6°

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The complete question is:

image is attached below

Step-by-step explanation:

Let's start by defining some variables:

Let x be the price of each pack of pencils.

Liam buys 3 packs of pencils, so he spends a total of 3x dollars on pencils.

He also buys a box of crayons for 7.50 dollars and a box of markers for 9.25 dollars, so his total spending is: 7.50 + 9.25 + 3x

However, he pays for all of this using a gift card worth 25 dollars, so we can set up an inequality to model the

situation: 7.50 + 9.25 + 3x <= 25

Now we can solve for x: 7.50 + 9.25 + 3x <= 25

16.75 + 3x <= 25

3x <= 8.25

[tex]x \leqslant 2.75[/tex]

Therefore, the price for each pack of pencils must be less than or equal to 2.75 dollars.

Answer:

y = x + 4

Step-by-step explanation:

We want to form an equation to represent the table. I will form an equation in standard y-intercept form. I can either calculate the slope mathematically, or look at the table and see that as x increases by 1, so does the respective value of y.

y = mx + b

m is slope and b is the y-intecept.

[tex]m = \frac{-2 - (-3)}{2-1} \\m = \frac{-2 + 3}{2 - 1}\\m = \frac{1}{1} \\m = 1[/tex]

So now we have the slope of our equation.

y = x + b

We can find the y-intecept two ways, use the table, or plug in a point from the table in calculate b from our equation. Should we choose to use the table, remember that y-intercept means that at that point x = 0. Following the pattern from the table, we can infer that when x = 0, y = -4. So the y-intercept of the function is -4.

y = x + b

Substitute the point (4, 0) into the equation to calculate b.

0 = 4 + b

b = -4

So our equation of the function is y = x + 4.

You can check this by substituting any point from the table into our equation.

Answer:

145.95ft²

Step-by-step explanation:

A "sector" is a piece of a circle like a pie slice.

If the central angle is 60° and a whole circle is 360°, then the piece of the circle we are looking at is

60/360, or 1/6 of the circle.

We can find the area of the whole circle, then divide by 6.

Area_wholecircle

= πr²

= 3.14×16.7²

= 3.14×278.88

= 875.7146

Now divide by 6 (same as times by 1/6 and less stressful) to find the area of the sector.

Area_sector

= 875.7146/6

= 145.95243333

Round to hundredths (two decimal places)

~= 145.95

The area of the sector is 145.95ft².

The pairs of vectors that satisfy the given conditions are (a, c) and (b, d).

To find the pairs of vectors that are perpendicular, we need to calculate the dot product of the vectors. The dot product of two vectors is equal to the sum of the products of their corresponding components. If the dot product of two vectors is zero, then the vectors are perpendicular.

The dot product of vectors a and c is:

a ∙ c = (i − 4 j − k) ∙ (−3 i − j + k) = (1)(−3) + (−4)(−1) + (−1)(1) = 0

The dot product of vectors b and d is:

b ∙ d = (i + j + 2k) ∙ (− i − j + k) = (1)(−1) + (1)(−1) + (2)(1) = 0

Therefore, the pairs of vectors that are perpendicular are (a, c) and (b, d).

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the solutions are for: a. 118 with a remainder of 10, b. 169 with a remainder of 10.

What about others and what is remainder?

a. 2014 ÷ 17 = 118 with a remainder of 10

Check: 118 x 17 + 10 = 2014

b. 3716 / 22 = 169 with a remainder of 10

Check: 169 x 22 + 10 = 3716

c. 4 691 ÷ 13 = 361 with a remainder of 8

Check: 361 x 13 + 8 = 4691

d. 1 168 ÷ 16 = 73

Check: 73 x 16 = 1168

e. 9 603 / 27 = 355 with a remainder of 18

Check: 355 x 27 + 18 = 9603

f. 7 834 ÷ 19 = 411 with a remainder of 5

Check: 411 x 19 + 5 = 7834

g. 5 186 ÷ 21 = 247 with a remainder of 19

Check: 247 x 21 + 19 = 5186

h. 6 437 / 14 = 459 with a remainder of 1

Check: 459 x 14 + 1 = 6437

Therefore, the answers are:

a. 118 with a remainder of 10

b. 169 with a remainder of 10

c. 361 with a remainder of 8

d. 73

e. 355 with a remainder of 18

f. 411 with a remainder of 5

g. 247 with a remainder of 19

h. 459 with a remainder of 1

In arithmetic, the remainder is the amount left over after performing a division operation when one number is divided by another.

For example, when you divide 17 into 2014, you get 118 with a remainder of 10. This means that 17 goes into 2014 exactly 118 times, with 10 left over. The remainder is always less than the divisor and indicates how much is left after dividing the dividend as equally as possible by the divisor.

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