(c) What is the average rate of change of f(x)=x² - 6x + 8 from 5 to 9?

Answer:

Step-by-step explanation:

If f(x, y, z) = xyzi + yj + zk, the divergence of the curl of the vector field f is zero.

To find the divergence of the curl of the vector field f(x,y,z) = xyzi + yj + zk, we first need to compute the curl of f, which is given by:

curl f = (∇ × f) = ∂(zk)/∂y - ∂(yj)/∂z + (∂(yj)/∂x - ∂(xyzi)/∂y)k + (∂(xyzi)/∂z - ∂(zk)/∂x)j + (∂(zk)/∂x - ∂(yj)/∂y) i

Simplifying this expression, we get:

curl f = (-z)i + xj + yk

Next, we need to find the divergence of the curl of f, which is given by:

div(curl f) = ∇ · (∇ × f) = ∂(∂(zk)/∂y - ∂(yj)/∂z)/∂x + ∂(∂(yj)/∂x - ∂(xyzi)/∂y)/∂y + ∂(∂(xyzi)/∂z - ∂(zk)/∂x)/∂z

Substituting the values from the curl f expression, we get:

div(curl f) = ∂(-z)/∂x + ∂(x)/∂y + ∂(y)/∂z

Simplifying this expression, we get:

div(curl f) = 0

To learn more about vector click on,

https://brainly.com/question/30195131

#SPJ4

\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

The first chart

Step-by-step explanation:

when its set up as y = [5x] is 5 times x equals y, so going through each question, -2 x 5 = -10, -1 x 5 = -5, 0 x 5 = 0, 1 x 5 = 5, and 2 x 5 = 10

The probability of choosing 2 red marbles is 2/11

The probability of selecting a specific color marble is given as

                                           P = \(\frac{n}{N}\)

where, \(n\) =  Number of a specific color marble

and     \(N\)  = Total number of marbles

Now, given an urn containing 6 blue and 5 red marbles

here, n = 5

and   N = 11

Hence the probability of selecting a red marble is given as

                                 P = \(\frac{5}{11}\)

Now grab another red marble without replacing the first one,

then,   n = 4

and     N = 10

Hence the probability of selecting 2nd red marble is given as

                                 P = \(\frac{4}{10}\)

Now, the probability of choosing 2 red marbles is given as

                                 P = \(\frac{5}{11}*\frac{4}{10}\)

=>                             P = \(\frac{2}{11}\)

Read more about probability here:

https://brainly.com/question/30390037

Answer:

D. 125 cm³

Step-by-step explanation:

Volume is how much space an object takes up.

The volume of a cube is denoted by: V = s³, where s is the side length of the cube. Here, we see that s = 5, so plug this into the formula:

V = s³

V = 5³ = 5 * 5 * 5 = 125

The answer is thus D.

Answer:

\(125 {cm}^{3} \)

Step-by-step explanation:

\(volume = b \times h \times l \\ = 5 \times 5 \times 5 \\ = 125 {cm}^{3} \)

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

change time in words 3:45

Answer:

x=-2.6  y=5.2

Step-by-step explanation:

Answer:

25 minutes and 33 seconds

Step-by-step explanation:

please brainiest

Answer:

\( - 3x - 5\)

it should be this answer bcause it has been simplified

The value of x₀ is approximately equal to 24.113.

The formula for the standard normal distribution is given by

=> z = (x - μ) / σ  [ where x is the random variable, μ is the mean, and σ is the standard deviation ]

It also involves using the standard normal distribution table or calculator to find the probability of a value being greater than a given z-score, and solving for the original random variable using the standardized value.

Here we have

Suppose x is a normal distribution random variable with mean 20 and standard deviation 2.5.

We can use the standard normal distribution to solve this problem.

First, we standardize the random variable x by subtracting the mean and dividing by the standard deviation:

=> z = (x - μ) / σ = (x - 20) / 2.5

Now we want to find the value x₀ such that P(x > x₀), which is equivalent to finding the value z such that P(z > (x₀ - 20) / 2.5).

Using a standard normal distribution table or calculator, we can find that the probability of z being greater than 1.645 is approximately 0.05.

So we have:

P(z > 1.645) = P((x - 20) / 2.5 > 1.645)

Simplifying and solving for x₀, we get:

=> (x - 20) / 2.5 > 1.645

=> x - 20 > 4.113

=> x > 24.113

Therefore,

The value of x₀ is approximately equal to 24.113.

Learn more about Normal distribution at

https://brainly.com/question/29509087

#SPJ4

Answer:

I think 48

Step-by-step explanation:

multiply the bottom numbers

Answer:

i think is 44

Step-by-step explanation:

Answer:

( 4 ,− 13 )

Step-by-step explanation:

Therefore, the position of the mass after t seconds is given by: y(t) = (1/2)e^((-1 + (1/2)sqrt(13))t) + (1/2)e^((-1 - (1/2)sqrt(13))t)

We are given:

mass (m) = 4 kg

damping constant (c) = 8 Ns/m

stretch distance at force of 1.5 N beyond natural length (x) = 0.5 m

stretch distance at release (y) = 1 m

initial velocity (v) = 0 m/s

We can find the spring constant (k) using Hooke's law: F = -kx, where F is the force applied, and x is the displacement from the equilibrium position. At x = 0.5 m and F = 1.5 N, we have:

1.5 N = -k(0.5 m)

k = -3 N/m

We can then find c2 - 4mk:

c2 - 4mk = c - 4mωn

where c is the damping constant, m is the mass, and ωn is the natural frequency.

The natural frequency ωn is given by:

ωn = sqrt(k/m)

Substituting the given values, we get:

ωn = sqrt(-3/4) = sqrt(3)/2

Therefore, c2 - 4mk = 8 - 4(4)(3/2) = -16

So, c2 - 4mk = -16 m^2kg^2/sec^2.

Next, to find the position of the mass after t seconds, we can use the following formula:

y(t) = c1e^(αt) + c2e^(βt)

where α and β are the roots of the characteristic equation, and c1 and c2 are constants to be determined based on initial conditions.

The characteristic equation is given by:

mλ^2 + cλ + k = 0

Substituting the given values, we get:

4λ^2 + 8λ - 3 = 0

Solving this quadratic equation, we get:

λ = (-8 ± sqrt(64 + 48))/8

λ = -1 ± (1/2)sqrt(13)

Therefore, the larger root is α = -1 + (1/2)sqrt(13), and the smaller root is β = -1 - (1/2)sqrt(13).

To determine the constants c1 and c2, we need to use the initial conditions. At t = 0, the spring is released from a stretched position of 1 m with zero initial velocity. Therefore, we have:

y(0) = c1 + c2 = 1 ...(1)

and

y'(0) = αc1 + βc2 = 0 ...(2)

Substituting the values of α and β, we get:

(-1 + (1/2)sqrt(13))c1 + (-1 - (1/2)sqrt(13))c2 = 0

Simplifying, we get:

sqrt(13)c1 - sqrt(13)c2 = 0

or, c1 = c2

Substituting this into equation (1), we get:

2c1 = 1

or, c1 = c2 = 1/2

Therefore, the position of the mass after t seconds is given by:

y(t) = (1/2)e^((-1 + (1/2)sqrt(13))t) + (1/2)e^((-1 - (1/2)sqrt(13))t)

Visit here to learn more about damping constant brainly.com/question/12975843

#SPJ11

Answer:

30 seconds

Step-by-step explanation:

→ Work out how many floors it's going to travel

15 - 3 = 12 floors

→ Work out how many meters 12 floors is

12 × 5 = 60 meters

→ Work out how long that will take

60 ÷ 2 = 30 seconds

Answer:

9 I THINK SO YEA TRUST ME I GOT BIG BRAINS

Step-by-step explanation:

Answer:

tenth place value.

Step-by-step explanation:

Note the placement of the 9. It is directly after the decimal point:

...

0 tens

2 ones

.

9 tenths

.. hundredths

...

In this case, note where the decimal point is, the next digit will be in the tenths place value.

~

The probability that the sample proportion will differ from the population proportion by more than 0.03 is 0.9476

To determine the probability

The given parameters are:

True proportion and the mean (p) = 0.06

The samples size (n) = 235

Start by calculating the standard deviation using

\(\sigma = \sqrt{\frac{p(1-p)}{n} }\)

This gives

\(\sigma = \sqrt{\frac{0.06\;*\;(1-0.06)}{235} }\)

\(\sigma = \sqrt{\frac{0.06\;*\;(0.94)}{235} }\)

\(\sigma = \sqrt{\frac{0.0564}{235} }\)

\(\sigma = \sqrt{0.00024 }\)

\(\sigma = 0.01549\)

Next, we calculate the x values

\(x = x_{1} \pm x_{2}\)

where x₁ = 0.06 and x₂ = 0.03

x = x₁ + x₂ , x₁ - x₂

x = 0.06 + 0.03, 0.06 - 0.03

x = 0.09, 0.03

Calculate the z score for both x values

\(z = \frac{x\; - \; \mu}{\sigma}\)

\(z = \frac{0.09\; - \; 0.06}{0.01549}, \frac{0.03\; - \; 0.06}{0.01549}\)

\(z = \frac{0.03}{0.01549}, \frac{-0.03}{0.01549}\)

\(z = 1.94, -1.94\)

The p values at the z scores are:

p = 0.9738, 0.0262

Note: refer to z tables to find the p values

Calculate the difference

p = 0.9738 - 0.0262

p = 0.9476

Hence, the probability that the sample proportion will differ from the population proportion by less than 0.03 is 0.9476

Visit the link below to learn more about probabilities:

brainly.com/question/25870256

#SPJ4

The parametric inferential statistical test for a single sample with a known population variance is the one-sample z-test.The null hypothesis in this test is that the sample mean is equal to the population mean.

The one-sample z-test is a parametric test used to determine whether a sample mean is significantly different from a known population mean when the population variance is also known. This test assumes that the data are normally distributed and the sample is a random sample from the population.

The one-sample z-test is a statistical test used to test a hypothesis about a population mean when the population variance is known. It is a parametric test, which means that it makes assumptions about the population distribution and sample size. Specifically, it assumes that the data are normally distributed and that the sample is a random sample from the population. The test is called a z-test because it uses the standard normal distribution to calculate the test statistic. The test statistic is calculated by taking the difference between the sample mean and the population mean, and dividing it by the standard error of the mean. The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size.

To know more than statistical visit :-

https://brainly.com/question/32201536

#SPJ11

Answer:

Tonicity is a measure of the concentration of solute particles in a solution compared to another solution. It is used to describe the effects of a solution on a cell.

If a cell is placed in a 15% solute solution and the cell shrinks, it means that the solution is hypertonic to the cell. Hypertonic solutions have a higher concentration of solute particles than the inside of the cell, which causes water to move out of the cell by osmosis. As water leaves the cell, it shrinks.

So, in this case, the tonicity of the 15% solution is hypertonic.

Answer:

i cant do dat because im broke sorry

Step-by-step explanation:

The solution to the systems of equations graphically is (2, 4)

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

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

Read more about equations at

brainly.com/question/148035

#SPJ1

3 3/5 x (-5 1/3)

18/5 x (-16/3)

-288/15

-96/5 or -19.2

Hope this helps! :)

Answer:

I think the value of x= 45°

Answer:

(-1,-6)

Step-by-step explanation:

1. Translation 4 units to the left - (-1,4)

2. Reflection across the x axis - (-1,-4)

3. Translation 2 units down - (-1,-6)

Answer:

-512

Step-by-step explanation:

The common ratio is multiplying by 4, therefore 4 muliplyed by -128 is -512

Just substitute the given values of 'y' in the equation to find 'x'.

1) y = 150

=》y = 250 - 20x

=》150 = 250 - 20x

=》150 - 250 = -20x

=》-100 = -20x

=》-100/-20 = x

=》5 = x

2) y = -1150

=》y = 250 - 20x

=》-1150 = 250 - 20x

=》-1150 - 250 = -20x

=》 -1400 = -2px

=》-1400/-20 = x

=》70 = x

______

RainbowSalt2222 ☔

Answer:

1) y=250-20x

150=250-20x

150-250= -20x

-100= -20x

-100/-20= -20x/-20

5= x

x=5

2) y=-1150

-1150=250-20x

-1150-250= -20x

-1400= -20x

-1400/-20= -20x/20

70= x

or x=70

Answer:

Here is the image you need to replicated

(っ◔◡◔)っ ♥ Hope It Helps ♥

Answer:

9/4x + y = -18

General Formulas and Concepts:

Pre-Algebra

Algebra I

Standard Form: Ax + By = C

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

Slope-Intercept Form:   y = -9/4x - 18

Step 2: Rewrite

Step 3: Identify

Standard Form:   9/4x + y = -18

Answer:

check the length and the angles and check the height of it