What is the slope of the line that passes through the points (-3, 1) and (7, -14)
write in simplest form

Answer:

3/4

Step-by-step explanation:

3*3=9

3*4=12

Answer: 3/4

Step-by-step explanation:

9/12 divide by 3/3= 4/3

The displacement x(t) for overdamped oscillations is given by x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt].

The correct expression for the displacement x(t) in terms of hyperbolic functions is:

B. x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt]

To show this, let's start with the given expression x(t) = e^(-βt) [A e^(ωt) + B e^(-ωt)] and rewrite it in terms of hyperbolic functions.

Using the relationships e^y = cosh(y) + sinh(y) and e^(-y) = cosh(y) - sinh(y), we can rewrite the expression as:

x(t) = [cosh(βt) - sinh(βt)][A e^(ωt) + B e^(-ωt)]

= [cosh(βt) - sinh(βt)][(A e^(ωt) + B e^(-ωt)) / (cosh(ωt) + sinh(ωt))] * (cosh(ωt) + sinh(ωt))

Simplifying further:

x(t) = [cosh(βt) - sinh(βt)][A cosh(ωt) + B sinh(ωt) + A sinh(ωt) + B cosh(ωt)]

= (cosh(βt) - sinh(βt))[(A + B) cosh(ωt) + (A - B) sinh(ωt)]

Comparing this with the given options, we can see that the correct expression is:

B. x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt]

Therefore, option B is the correct answer.

The displacement x(t) for overdamped oscillations is given by x(t) = (cosh βt + sin βt) [(A + B) cosh ωt + (A - B) sinh ωt].

To know more about hyperbolic functions, visit

https://brainly.com/question/3247916

#SPJ11

Since η² ≈ 0.33 and not 0.50, the statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η² = 0.50" is false.

ANOVA, or Analysis of Variance, is a statistical method used to compare the means of two or more groups to determine if there are any statistically significant differences between them. It is commonly used in experimental and observational studies to analyze the variance between group means and within-group variability.

ANOVA tests the null hypothesis that the means of the groups are equal, against the alternative hypothesis that at least one of the group means is different. It calculates the F-statistic, which compares the between-group variability to the within-group variability. If the F-statistic is large enough and exceeds a critical value, it indicates that there is evidence to reject the null hypothesis and conclude that there are significant differences between the group means.

We can determine if η² = 0.50 is true or false by calculating the effect size η² using the provided SS between and SS within values.
η² = SS_between / (SS_between + SS_within)
η² = 20 / (20 + 40)
η² = 20 / 60
η² = 1/3 ≈ 0.33
To know more about variance, visit:

https://brainly.com/question/31432390

#SPJ11

True, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.

The formula to calculate eta squared (η2) is:
η2 = SSbetween / (SSbetween + SSwithin)
If SSbetween = 20 and SSwithin = 40, then:
η2 = 20 / (20 + 40) = 0.5
Therefore, η2 = 0.50, which means that 50% of the total variance in the dependent variable can be attributed to the independent variable (or factor) being analyze. The statement "If an analysis of variance produces SS between = 20 and SS within = 40, then η 2 = 0.50" is true. To determine η 2 (eta-squared), you'll need to calculate the proportion of total variance explained by the between-group variation. This can be done using the formula η 2 = SS between / (SS between + SS within). In this case, η 2 = 20 / (20 + 40) = 20 / 60 = 0.50. Therefore, the eta-squared value is indeed 0.50, indicating that 50% of the total variance is accounted for by the between-group variation.

To know more about variable visit:

https://brainly.com/question/15078630

#SPJ11

Answer:

72

Step-by-step explanation:

a-3(b) where a=6 and b=-4

6-3(-4)

6(12)

= 72

The distance on the map that represents an actual distance of 4 kilometers is 3.2cm.

The actual number of kilometers that is represented by 5 centimeters on the map is 6.25 kilometers.

A scale drawing is a smaller version of a larger image. In this question, the map is a scale drawing of the city. The scale drawing is reduced using constant dimensions using a scale.

A scale gives the ratio of the length of the scale drawing to the actual diagram or object. In this question, every 4cm on the map represents 5km in the city.

The distance on the map = (4 x 4) / 5

16 / 5 = 3 1/5 cm = 3.2 cm

The actual distance = (5 x 5) / 4

= 25 / 4 = 6 1/4 = 6.25 kilometers

To learn more about scale drawings, please check: https://brainly.com/question/26388230

#SPJ1

Any point x in [0,1] can be approximated by some 1/n, and the fact that f(1/n) = 0 for all n implies that f(x) = 0 for all x in [0,1].

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.

If f(x) is a continuous and differentiable function and f(1/n) = 0 for all natural numbers n greater than or equal to 1, then it follows that f(x) must be identically zero on the interval [0,1]. This is because the function is continuous and the values of f(1/n) approach 0 as n approaches infinity.

Know more about differentiable function here:

https://brainly.com/question/18962394

#SPJ11

The nearest 5 integers of 562817​ are:

562815​, 562816​, 562817​, 562818​, 5628179

An integer comprises a whole number which can be positive, negative, and zero and is not a fraction. Integer examples include: -5, 1, 25, 18, 97, as well as 3,043. 1.43, 21 3/4, 3.84, and other numbers that don't constitute integers are some examples.

Thus,

The nearest 5 integers of 562817​ are obtained by subtracting and adding the smallest integer that is 1 from the given number.

562815​, 562816​, 562817​, 562818​, 5628179

Know more about integers

https://brainly.com/question/929808

#SPJ9

The probability that X is between 57 and 105 is 0.8914.

Given:

* X is normally distributed with mean=90 and standard deviation=12

* P(57 < X < 105)

Solution:

* Convert the given values to z-scores:

   * z = (X - μ) / σ

   * z = (57 - 90) / 12 = -2.50

   * z = (105 - 90) / 12 = 1.25

* Use the z-table to find the probability:

   * P(Z < -2.50) = 0.0062

   * P(Z < 1.25) = 0.8944

* Add the probabilities to find the total probability:

   * P(57 < X < 105) = 0.0062 + 0.8944 = 0.8914

Therefore, the probability that X is between 57 and 105 is 0.8914.

Read more about probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

Inverse of a 3 by 3 Matrix

MM-1 = M-1 M = I.

Step 1: The first step while finding the inverse matrix is to check whether the given matrix is invertible. ...

Step 2: Calculate the determinant of 2 × 2 minor matrices.

Step 3: Formulate the cofactor matrix.

Step-by-step explanation:

The inverse matrix formula, A-¹ = (1/|A|) Adj A, is used to determine the inverse of a 3×3 matrix.

The multiplicative identity is obtained by multiplying the provided matrix by the other matrix which serves as the inverse of a matrix. A matrix's inverse is A-1, since the I is the identity matrix, A A-1 = A-1 A = I.

The formula A-1 = (adj A)/(det A), where det A is in the denominator, is used to determine the inverse of a 3x3 matrix A. 

• adj A = The adjoint matrix of A

• det A = determinant of A

dAs a result, det A should not be 0 for A-1 to exist. i.e.,

• A-1 exists when det A ≠ 0 (i.e., when A is nonsingular)

• A-1 does not exist when det A = 0 (i.e., when A is singular).

To know more about inverse matrix :

https://brainly.com/question/4017205

#SPJ4

Answer:

36 in.

Step-by-step explanation:

side = x

x^2 + x^2 = 12.72^2

2x^2 = 161.79

x^2 = 80.899

x = 9

perimeter = 4x = 4 * 9 = 36

The equation for the rate of change of concentration is Δc/Δt, and this is equal to the rate of change of concentration over a given interval, -0.0680 m/s.

To calculate the final concentration, we must use the equation Δc = rate × time, where Δc is the change in concentration, and rate and time are the rate of change of concentration and the interval, respectively. Plugging in our values, Δc = -0.0680 m/s × 3.0 s = -0.204 m. This means that the final concentration of c is 2.700 m - 0.204 m, which is equal to 2.496 m.

To summarize, the rate of change of concentration equation is Δc/Δt = rate of change, and the equation to calculate the final concentration is Δc = rate × time. Plugging in the rate of change and interval, we get Δc = -0.0680 m/s × 3.0 s = -0.204 m, which gives us the final concentration of c at the end of the same interval as 2.496 m.

Learn more about equation here:

https://brainly.com/question/14686792

#SPJ4

The size of a matrix is ​​its dimension,

AB and BA are of size 4 x 4 and 2 x 2 respectively

Matrix A has dimension 4 x 2 and matrix B has dimension 2 x 4

Matrix:

In mathematics, a matrix (multiple matrices) is a rectangular array or table of numbers, symbols, or formulas, arranged in rows and columns, used to represent mathematical objects or properties of such objects .

Product of Matrix:

Multiplication of two matrices is defined only if the number of columns in the left matrix equals the number of rows in the right matrix. If A is an m-by-n matrix and B is an n-by-p matrix, then its matrix product AB is an m-by-p matrix whose entries correspond to the corresponding rows of A in the matrices.

A column of B whenever a product of different sizes is such that it is defined.  The product AB can be defined without BA being defined. That is, if A and B are m-by-n and n-by-k matrices, respectively, and m ≠ k. In general, even if both products are defined, they need not be the same. So, AB ≠ BA,

Product AB:

The dimensions of AB are the rows of matrix A multiplied by the columns of matrix B.

Matrix A has 4 rows and Matrix B has 4 columns.

Therefore, the dimension of the matrix AB is 4 x 4.

Product BA:

The dimensions of matrix BA are the rows of matrix B multiplied by the columns of matrix A.

Matrix B has 2 rows and Matrix A has 2 columns.

Therefore the dimension of the matrix BA is 2 x 2.

Therefore, the sizes of AB and BA are 4 x 4 and 2 x 2 respectively.

Learn more about Matrix:
https://brainly.com/question/28180105

#SPJ4

Answer:

A and C

Step-by-step explanation:

-3*3 = -9

-1*-9 = 9

-27/3 = -9

-9/-1 = 9

A and C hope I could help

Answer:

That would be Thirty-two

Step-by-step explanation:

Because is we are doubling 32 its going to be 64 and if we are subtracting 32 then its going to be 32

Mark brainliest pls :)

The distance between the insect and its image is 100 cm

From the question, we have the following parameters that can be used in our computation:

Initial distance = 80 cm

Distance moved = 20 cm away

The distance between the insect and its image is the distance between the distance between the insect and its mirror

so, we have the following representation

Distance = Initial distance + Distance moved

Substitute the known values in the above equation, so, we have the following representation

Distance = 80 cm  + 20 cm

Evaluate

Distance = 100 cm

Hence, the distance is 100 cm

Read more about distance at

https://brainly.com/question/17273444

#SPJ1

Answer:

Step-by-step explanation:

12xy(3y - 4x)

the GCF is 12xy

Answer:

225 ft^2

Step-by-step explanation:

From what we have in the question, we have 60 ft of fencing

To maximize the area, we will need to have a square

For a square, the length of all sides are equal

Let us call one of the sides s

Thus, from the perimeter of the square;

4s = 60

s = 60/4

s = 15 ft

The area is thus, the product of the side length of the square

15 * 15 = 225 ft^2

Answer:   y = 4x- 9

Step-by-step explanation:

Answer:

y = 4x - 9

Step-by-step explanation:

You can see that the slope is four because it moves up four every time. The y-intercept is -9 because at the bottom at graph the line crosses the y-axis at -9.

Hope this helps!

Answer:

A=πr2

Step-by-step explanation:

Answer:

well you did not give diameter or radius but the way to solve is

Step-by-step explanation:

3.14*R*R=Area

Answer:

13) x=n-11

15) x=3*10

Step-by-step explanation:

I used x as the variable. The questions are pretty straightforward. They are asking you to put the terms in the description on the right side of the equation. The questions = x. That was probably confusing, but it is correct. I hope this helped!

Product of 3 and 10 and12

The mean and standard deviation of the total time are µx = 66 and σx = 3.17, so the correct answer is (D) µx= 66 σx= 3.17.

To find this:

The total time to complete all three tasks is the sum of the time taken for each task. The mean time to complete all three tasks (µx) can be calculated by adding the mean time for each task: µx = 36 + 22 + 8 = 66. The standard deviation (σx) of the total time can be calculated using the standard deviation of each task and the square root of the number of tasks (n).

Using the formula: \(\sigma x = \frac{\sqrt{\sigma1^2 + \sigma2^2 + \sigma3^2}}{\sqrt n}\),

where σ1, σ2, σ3 are the standard deviations of each task, n = 3.

Plugging in the values, we get

\(\sigma x = \sqrt(2.5^2 + 1.8^2 + 0.75^2)/\sqrt3 \\= \sqrt{6.25 + 3.24 + 0.5625}/\sqrt3 \\= \sqrt{10.0525}/\sqrt3 = 3.17\)

Hence, the mean and standard deviation of the total time are µx = 66 and σx = 3.17, so the correct answer is (D) µx= 66 σx= 3.17.

To learn more about the standard deviation, visit:

brainly.com/question/23907081

#SPJ4

The coordinates of P are P(7, 9) such that P partitions the segment AB in the ratio 5:1.

To find the coordinates of point P that partitions segment AB in the ratio 5:1, we can use the concept of section formula. The section formula states that if we have two points A(x1, y1) and B(x2, y2) dividing the segment in the ratio m:n, then the coordinates of the point P(x, y) can be found using the following formulas:

x = (nx1 + mx2) / (m + n)

y = (ny1 + my2) / (m + n)

In this case, A has coordinates A(2, 4) and B has coordinates B(8, 10). We want to find the coordinates of P that divide the segment AB in the ratio 5:1.

Plugging in the values into the formulas, we have:

x = (12 + 58) / (5 + 1) = (2 + 40) / 6 = 42 / 6 = 7

y = (14 + 510) / (5 + 1) = (4 + 50) / 6 = 54 / 6 = 9

for more such questions on coordinates

https://brainly.com/question/29660530

#SPJ8

Answer:

A. About 1/3 of the people prefer pie without ice cream

Step-by-step explanation:

We know there were 80 people surveyed, so that's our denominator. Pie without ice cream is the bottom row. 15 + 12 = 27. 27/80 = 0.3375, which is 33.75% (multiply 0.3375 by 100), which is about 1/3.

B is wrong, because the blueberry pie numbers are not double the cherry pie numbers

C is wrong because cherry with ice cream is 24, blueberry without is 15

D is wrong because the ratio of blueberry to cherry is 44:36, and with ice cream to without is 53:27

Answer:d

Step-by-step explanation:

Answer:

The equation is C, y-9=2(x-1)

More earnings:-

Total earnings this year

Answer:

\(\$ \huge{\text{(} \dfrac{x}{4} \ + \ \dfrac{4x}{4} \huge{\text{)}\)

Step-by-step explanation:

Given:

Last year: $x

Determining the money earned for this year:

This year = 25%   more than       last year

               = $25x/100   +                    $x

               = $x/4           +                 $4x/4

The expression that represents the money earned this year is $x/4 + $4x/4.

22084.78 gallons is the volume of your pool.

Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. The base's surface area, B, is equal to its length x width.

Dimensions of the pool = 4.93 m x 9.69 m x 1.75 m

Volume = 4.93 x 9.69 x 1.75

             = 83.6 cubic meter

1 cubic meter = 264.172 gallons

83.6 cubic meter = 83.6 x 264.172

                            = 22084.78 gallons

Hence, 22084.78 gallons is the volume of your pool.

To learn more about volume here:

https://brainly.com/question/13338592

#SPJ4