pls
do a step by step i dont understand how to do this hw problem
Find the derivative of the trigonometric function f(x) = 7x cos(-x). Answer 2 Points f'(x) =

Answers

Answer 1

Answer:

[tex]f'(x)=7\cos(-x)+7x\sin(-x)[/tex]

Step-by-step explanation:

[tex]f(x)=7x\cos(-x)\\f'(x)=(7x)'\cos(-x)+(-1)(7x)(-\sin(-x))\\f'(x)=7\cos(-x)+7x\sin(-x)[/tex]

Note by the Product Rule, [tex]\frac{d}{dx} f(x)g(x)=f'(x)g(x)+f(x)g'(x)[/tex]

Also, by chain rule, [tex]\cos(-x)=(-x)'(-\sin(-x))=-(-\sin(-x))=\sin(-x)[/tex]

Hopefully you know that the derivative of cos(x) is -sin(x), which is really helpful here.

Hope this was helpful! If it wasn't clear, please comment below and I can clarify anything.


Related Questions

Let z denote a random variable that has a standard normal distribution. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z < 2.36) = (b) P(z 2.36) = (c) P(z < -1.22) = (d) P(1.13 < z < 3.35) = (e) P(-0.77 z -0.55) = (f) P(z > 3) = (g) P(z -3.28) = (h) P(z < 4.98) =

Answers

To determine the probabilities, we can use a standard normal distribution table or a statistical software. Here are the probabilities for each scenario:

(a) P(z < 2.36) = 0.9900

(b) P(z > 2.36) = 1 - P(z < 2.36) = 1 - 0.9900 = 0.0100

(c) P(z < -1.22) = 0.1112

(d) P(1.13 < z < 3.35) = P(z < 3.35) - P(z < 1.13) = 0.9992 - 0.8708 = 0.1284

(e) P(-0.77 < z < -0.55) = P(z < -0.55) - P(z < -0.77) = 0.2912 - 0.2815 = 0.0097

(f) P(z > 3) = 1 - P(z < 3) = 1 - 0.9987 = 0.0013

(g) P(z < -3.28) = 0.0005

(h) P(z < 4.98) = 1 (since the standard normal distribution extends to positive and negative infinity)

The probabilities listed above are determined using the standard normal distribution. The standard normal distribution is a specific case of the normal distribution with a mean of 0 and a standard deviation of 1.

In the standard normal distribution, probabilities are calculated based on the area under the curve. The values in the standard normal distribution table represent the cumulative probabilities up to a certain z-score (standard deviation value).

To calculate the probabilities:

For (a), P(z < 2.36), we look up the z-score 2.36 in the standard normal distribution table and find the corresponding cumulative probability, which is 0.9900.

For (b), P(z > 2.36), we subtract the cumulative probability P(z < 2.36) from 1, as the total area under the curve is equal to 1. Thus, we get 1 - 0.9900 = 0.0100.

For (c), P(z < -1.22), we find the cumulative probability for the z-score -1.22 in the standard normal distribution table, which is 0.1112.

For (d), P(1.13 < z < 3.35), we calculate the cumulative probability for z = 3.35 and subtract the cumulative probability for z = 1.13 from it. This gives us 0.9992 - 0.8708 = 0.1284.

For (e), P(-0.77 < z < -0.55), we find the cumulative probability for z = -0.55 and subtract the cumulative probability for z = -0.77 from it. This yields 0.2912 - 0.2815 = 0.0097.

For (f), P(z > 3), we subtract the cumulative probability P(z < 3) from 1, which results in 1 - 0.9987 = 0.0013.

For (g), P(z < -3.28), we find the cumulative probability for z = -3.28 in the standard normal distribution table, which is 0.0005.

For (h), P(z < 4.98), since the standard normal distribution extends to positive and negative infinity, the probability of any value being less than 4.98 is equal to 1.

The probabilities listed are rounded to four decimal places for simplicity and clarity.

To know more about probabilities,

https://brainly.com/question/29319403

#SPJ11

Find k so that the line through (5,-2) and (k, 1) is a. parallel to 9x + 16y = 32, b. perpendicular to 6x + 13y = 26 a. k = (Type an integer or a simplified fraction.)

Answers

For the line passing through [tex]\((5, -2)\)[/tex] and [tex]\((k, 1)\)[/tex] to be parallel to the line [tex]\(9x + 16y = 32\)[/tex]; [tex]\(k = \frac{1}{3}\)[/tex]

To find the value of [tex]\(k\)\\[/tex] such that the line passing through the points [tex]\((5, -2)\)[/tex] and [tex]\((k, 1)\)[/tex] is parallel to the line [tex]\(9x + 16y = 32\)[/tex], we need to determine the slope of the given line and then find a line with the same slope passing through the point [tex]\((5, -2)\)[/tex].

The given line [tex]\(9x + 16y = 32\)[/tex] can be rewritten in slope-intercept form as [tex]\(y = -\frac{9}{16}[/tex] [tex]\(x + 2[/tex].

The coefficient of [tex]\(x\), \(-\frac{9}{16}\)[/tex] represents the slope of the line.

For the line passing through [tex]\((5, -2)\)[/tex]and[tex]\((k, 1)\)[/tex]to be parallel to the given line, it must have the same slope of [tex]\(\frac{1 - (-2)}{k - 5} = -\frac{9}{16}\)[/tex].

Therefore, we can set up the following equation:

[tex]\(\frac{1 - (-2)}{k - 5} = -\frac{9}{16}\)[/tex]

[tex]\(\frac{3}{k - 5} = -\frac{9}{16}\)[/tex]

To solve for [tex]\(k\)[/tex], we can cross-multiply and solve for [tex]\(k\)[/tex]:

[tex]\(16 \cdot 3 = -9 \cdot (k - 5)\)\(48 = -9k + 45\)\(9k = 48 - 45\)\(9k = 3\)\(k = \frac{3}{9} = \frac{1}{3}\)[/tex]

Therefore, [tex]\(k = \frac{1}{3}\)[/tex] for the line passing through [tex]\((5, -2)\)[/tex] and [tex]\((k, 1)\)[/tex] to be parallel to the line [tex]\(9x + 16y = 32\)[/tex]

To know more about line refer here:

https://brainly.com/question/21298390#

#SPJ11

The mean height for the population of adult American males is 69.0 inches, with a standard deviation of 2.8 inches. A random sample of 100 adult American males is taken.
a) Find the standard error for the sampling distribution of the sample mean. (Round your answer to 3 decimal places.)
b) Find the probability that the sample mean height for this sample of 100 adult American males is less than 68.5 inches. (Round your answer to 4 decimal places

Answers

we are given the mean height and standard deviation for the population of adult American males. We need to calculate the standard error for the sampling distribution of the sample mean and find the probability that the sample mean height is less than a certain value . Therefore, the probability that the sample mean height for this sample of 100 adult American males is less than 68.5 inches is approximately 0.4298 or 42.98%.

a) The standard error (SE) for the sampling distribution of the sample mean can be calculated using the formula: SE = (population standard deviation) / sqrt(sample size).

Plugging in the given values, we have:

SE = 2.8 / sqrt(100) = 0.28

Therefore, the standard error for the sampling distribution of the sample mean is 0.28 inches.

b) To find the probability that the sample mean height for the sample of 100 adult American males is less than 68.5 inches, we can use the z-score and the standard normal distribution table.

First, we need to calculate the z-score using the formula: z = (sample mean - population mean) / (standard deviation / sqrt(sample size)).

Plugging in the values, we get:

z = (68.5 - 69) / (2.8 / sqrt(100)) = -0.1786

Next, we can use the z-score to find the corresponding probability using the standard normal distribution table or a calculator. The probability is the area to the left of the z-score.

Looking up the z-score -0.1786 in the standard normal distribution table, we find that the probability is approximately 0.4298.

Therefore, the probability that the sample mean height for this sample of 100 adult American males is less than 68.5 inches is approximately 0.4298 or 42.98%.

Learn more about  sampling distribution here:

https://brainly.com/question/31465269

#SPJ11


A)
Find the point on the curve y= Root x Where the tanget line is
parallel to the line y = x/20
Homework: HW 1.3 Question 17, 1.3.45 Part 1 of 2 HW poin х a) Find the point on the curve y= Vx where the tangent line is parallel to the line y= 20 b) On the same axes, plot the curve y= VX, the lin

Answers

To find the point on the curve y = √x where the

tangent line

is parallel to y = x/20, we equate the derivative of y = √x to the slope of the line, 1/20. Solving this equation gives the

x-coordinate

of the point.

Using the power rule for

differentiation

, we have dy/dx = (1/2) * x^(-1/2). Since we want the tangent line to be

parallel

to y = x/20, which has a slope of 1/20, we set the derivative equal to 1/20 and solve for x:

(1/2) * x^(-1/2) = 1/20.

Simplifying this equation, we get x^(-1/2) = 1/10. Taking the reciprocal of both sides, we have x^(1/2) = 10.

Squaring

both sides, we find x = 100.

Substituting this value of x into the equation y = √x, we get y = √100 = 10.

Therefore, the point on the curve y = √x where the tangent line is parallel to y = x/20 is (100, 10).

On the same axes, we can plot the curve y = √x by plotting points and drawing a smooth

curve

that passes through them. Similarly, we can plot the line y = x/20 by finding two points on the line and connecting them with a straight line.

To learn more about

tangent line

click here :

brainly.com/question/31617205

#SPJ11

11
use L'Hospital to determine the following limit. Use exact values. lim (1 + sin 6x)= 20+

Answers

Using L'Hospital's rule, the limit of (1 + sin 6x) as x approaches infinity is equal to 20.

L'Hospital's rule is used when taking the limit of a function that results in an indeterminate form, such as 0/0 or infinity/infinity. In this case, we have an indeterminate form of 1 + sin(6x) as x approaches infinity.

To use L'Hospital's rule, we take the derivative of both the numerator and denominator of the function and take the limit again. We repeat this process until we have a non-indeterminate form.

Taking the first derivative of 1 + sin(6x) results in 6cos(6x). The denominator remains the same, which is 1. Taking the limit of this new function as x approaches infinity gives us 6(cos infinity), which oscillates between -6 and 6.

Taking the second derivative of the original function yields -36sin(6x). The denominator remains 1. Taking the limit of this new function as x approaches infinity gives us -36(sin infinity), which is zero.

Since we have a non-indeterminate form of (-6/1), we have reached our answer, which is equal to -6. However, since the original expression had a limit of 20, we need to subtract 6 from 20 to get our final answer of 14. Therefore, the limit of (1 + sin(6x)) as x approaches infinity is equal to 14.

Learn more about oscillates here.

https://brainly.com/questions/30111348

#SPJ11








Write the following first-order differential equations in standard form. dy a*y+ cos(82) da

Answers

The given first-order differential equation, dy/dx = a*y + cos(82), can be written in standard form as dy/dx - a*y = cos(82).

To write the given differential equation in standard form, we need to isolate the derivative term on the left side of the equation.

The original equation is dy/dx = a*y + cos(82). To bring the derivative term to the left side, we subtract a*y from both sides:

dy/dx - a*y = cos(82).

Now, the equation is in standard form, where the derivative term is isolated on the left side, and the remaining terms are on the right side. In this form, it is easier to analyze and solve the differential equation using various methods, such as separation of variables, integrating factors, or exact equations.

The standard form of the given differential equation, dy/dx - a*y = cos(82), allows for a clearer representation and facilitates further mathematical manipulation to find a particular solution or explore the behavior of the system.

Learn more about derivative here:

https://brainly.com/question/29020856

#SPJ11

Showing all steps clearly, convert the following second order differential equation into a system of coupled equations. day dy/dt 2 -5y = 9 cos(4t) dx

Answers

We have a system of two coupled first-order differential equations:

dz/dt - 5y = 9cos(4t)

dy/dt = z

To convert the given second-order differential equation into a system of coupled equations, we introduce a new variable z = dy/dt. This allows us to rewrite the equation as a system of two first-order differential equations.

dz/dt = d^2y/dt^2 - 5y = 9cos(4t)

dy/dt = z

In equation (1), we substitute the value of d^2y/dt^2 as dz/dt to obtain:

dz/dt - 5y = 9cos(4t)

Now we have a system of two coupled first-order differential equations:

dz/dt - 5y = 9cos(4t)

dy/dt = z

These coupled equations represent the original second-order differential equation, where the variables y and z are dependent on time t and are related through the equations above. The first equation relates the rate of change of z to the values of y and t, while the second equation expresses the rate of change of y in terms of z.


To learn more about first-order differential click here: brainly.com/question/30645878

#SPJ11

Find all local maxima, local minima, and saddle points for the function given below. Enter your answer in the form (x, y, z). Separate multiple points with a comma (x,y) = 12x - 3xy2 + 4y! Answer m Ta

Answers

The function has one local maximum and two saddle points. The local maximum is located at (1, 1, 13). The saddle points are located at (-1, -1, -3) and (1, -1, -1).

To find the local maxima, minima, and saddle points of the given function, we need to analyze its critical points and second-order derivatives. Let's denote the function as f(x, y) = 12x - 3xy^2 + 4y.

To find critical points, we need to solve the partial derivatives with respect to x and y equal to zero:

∂f/∂x = 12 - 3y^2 = 0

∂f/∂y = -6xy + 4 = 0

From the first equation, we can solve for y: y^2 = 4, y = ±2. Substituting these values into the second equation, we find x = ±1.

So, we have two critical points: (1, 2) and (-1, -2). To determine their nature, we calculate the second-order derivatives:

∂²f/∂x² = 0, ∂²f/∂y² = -6x, ∂²f/∂x∂y = -6y.

For the point (1, 2), the second-order derivatives are: ∂²f/∂x² = 0, ∂²f/∂y² = -6, ∂²f/∂x∂y = -12. Since ∂²f/∂x² = 0 and ∂²f/∂y² < 0, we have a saddle point at (1, 2).

Similarly, for the point (-1, -2), the second-order derivatives are: ∂²f/∂x² = 0, ∂²f/∂y² = 6, ∂²f/∂x∂y = 12. Again, ∂²f/∂x² = 0 and ∂²f/∂y² > 0, so we have another saddle point at (-1, -2). To find the local maximum, we examine the point (1, 1). The second-order derivatives are: ∂²f/∂x² = 0, ∂²f/∂y² = -6, ∂²f/∂x∂y = -6. Since ∂²f/∂x² = 0 and ∂²f/∂y² < 0, we conclude that (1, 1) is a local maximum.

In summary, the function has one local maximum at (1, 1, 13) and two saddle points at (-1, -1, -3) and (1, -1, -1).

To learn more about function click here: brainly.com/question/31062578

#SPJ11

Evaluate the following indefinite and definite integrals. Give exact answers, i.e. VTT, not 1.77..., etc. To receive full credit you must state explicitly any substitutions used. 7.[10][(x2 – Vx + 4) dx

Answers

The indefinite integral of[tex]7x^2 – √x + 4 is (7/3)x^3 – (2/3)x^(3/2) + 4x + C[/tex]

To evaluate the indefinite integral, we can use the power rule of integration. For the term[tex]7x^2[/tex], we raise the power by 1 and divide by the new power, giving us [tex](7/3)x^3[/tex]. For the term -√x, we increase the power by 1/2 and divide by the new power, resulting in [tex]-(2/3)x^(3/2)[/tex]. The constant term 4x integrates to [tex]4x^2/2 = 2x^2.[/tex] Adding all these terms together, we get[tex](7/3)x^3 – (2/3)x^(3/2) + 4x + C,[/tex]where C is the constant of integration.

In the definite integral case, we would need to specify the limits of integration to obtain a numeric value.

Learn more about integration here

brainly.com/question/5028068

#SPJ11

5. Determine the Cartesian form of the plane whose equation in vector form is - (-2,2,5)+(2-3,1) +-(-1,4,2), s.1 ER.

Answers

The final Cartesian form of the plane is x + y + z + 5s + 2ER - 8 = 0

To determine the Cartesian form of the plane from the given equation in vector form, we need to simplify the equation and express it in the form Ax + By + Cz + D = 0.

The given equation in vector form is:

-(-2, 2, 5) + (2 - 3, 1) + -(-1, 4, 2) · (s, 1, ER)

Expanding and simplifying the equation, we get:

(2, -2, -5) + (-1, 1) + (1, -4, -2) · (s, 1, ER)

Performing the vector operations:

(2, -2, -5) + (-1, 1) + (s, -4s, -2ER)

Adding the corresponding components:

(2 - 1 + s, -2 + 1 - 4s, -5 - 2ER)

This represents a point on the plane. To express the plane in Cartesian form, we consider the coefficients of x, y, and z in the expression above.

The equation of the plane in Cartesian form is:

(x - 1 + s) + (y - 2 + 4s) + (z + 5 + 2ER) = 0

Simplifying the equation further, we get:

x + y + z + (s + 4s + 2ER) - (1 + 2 + 5) = 0

Combining like terms, we have:

x + y + z + 5s + 2ER - 8 = 0

Rearranging the terms, we obtain the final Cartesian form of the plane:

x + y + z + 5s + 2ER - 8 = 0

Learn more about Cartesian here:

brainly.com/question/28986301

#SPJ11

in a particular calendar year, 10% of the registered voters in a small city are called for jury duty. in this city, people are selected for jury duty at random from all registered voters in the city, and the same individual cannot be called more than once during the calendar year.

Answers

If 10% of the registered voters in a small city are called for jury duty in a particular calendar year, then the probability of any one registered voter being called is 0.1 or 10%.

Since people are selected for jury duty at random, the selection process does not favor any one individual over another. Furthermore, the rule that the same individual cannot be called more than once during the calendar year ensures that everyone has an equal chance of being selected.

Suppose there are 1000 registered voters in the city. Then, 100 of them will be called for jury duty in that calendar year. If a person is not called in a given year, they still have a chance of being called in subsequent years.

Overall, the selection process for jury duty in this city is fair and ensures that all registered voters have an equal opportunity to serve on a jury.

Learn more about probability here,

https://brainly.com/question/10734660

#SPJ11

11. Find the absolute maximum and the absolute minimum, if exists, for each function, 5x3-6x4 A) f(x) = 5x3 – 6x4 B) f(x) = 5x **** 5x - 6x4 5-6x - 5 2+1 4

Answers

The function A) f(x) = 5x^3 – 6x^4 has no absolute maximum or minimum because it is a fourth-degree polynomial with a negative leading coefficient.

In detail, to find the absolute maximum and minimum values of a function, we need to analyze its critical points, endpoints, and behavior at infinity. However, for the function f(x) = 5x^3 – 6x^4, it is evident that as x approaches positive or negative infinity, the value of the function becomes increasingly negative. This indicates that the function has no absolute maximum or minimum.

The graph of f(x) = 5x^3 – 6x^4 is a downward-opening curve that gradually approaches negative infinity. It does not have any peaks or valleys where it reaches a maximum or minimum value.

Consequently, we conclude that this function does not possess an absolute maximum or minimum.

Learn more about fourth-degree polynomial:

https://brainly.com/question/25827330

#SPJ11

In 19 years, Oscar Willow is to receive $100,000 under the terms of a trust established by his grandparents. Assuming an interest rate of 5.3%, compounded continuously, what is the present value of Oscar's legacy?
The present value of the legacy is $____________. (Round to the nearest cent as needed.)

Answers

Answer:

 $36,531.33

Step-by-step explanation:

You want to know the present value of $100,000 in 19 years at an interest rate of 5.3% compounded continuously.

Future value

The future value will be ...

  FV = P·e^(rt) . . . . . . . . principal p invested at annual rate r for t years

  100,000 = P·e^(0.053·19) . . . . . . . substituting given numbers

  P = 100,000·e^(-0.053·19) ≈ 36,531.33

The present value of the legacy is $36,531.33.

<95141404393>

Alebra, pick all the equations that represent the graph below, there is 3 answers

Answers

There are a few ways to work this one.  

The first thing to know is that if (1,0) is an x-intercept, then (x-1) will be a factor in the factored version.  So this makes the first answer correct and the second one not:

Yes: y = 3(x-1)(x-3)

No:  y = 3(x+1)(x+3)

The second thing to know is that if (h,k) is the vertex, then equation in vertex form will be y = a (x-h)^2 + k.

Since (2,-3) is the vertex, then the equation would be y = a (x-2)^2 -3.

This makes the third answer correct and the fourth not:

Yes: y = 3(x-2)^2 - 3

No: y = 3(x+2)^2 + 3

By default, this means that the last answer must work, since you said there are 3 answers.

We can confirm it is correct (and not a trick question) by factoring the last answer:

   y = 3x^2 - 12x +9

     = 3 (x^2 -4x +3)

     = 3 (x-3)(x-1)

And this matches our first answer.

a survey was given to a random sample of 70 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. of those surveyed, 70% of the people said they were in favor of the plan. determine a 95% confidence interval for the percentage of people who favor the tax plan, rounding values to the nearest tenth

Answers

Rounding to the nearest tenth, the 95% confidence interval for the percentage of people who favor the tax plan is (56.8%, 83.2%).

determine a 95% confidence interval for the percentage of people who favor the tax plan, use the formula for calculating the confidence interval for a proportion. The formula is:

Confidence Interval = Sample Proportion ± Margin of Error

Step 1: Calculate the sample proportion:

The sample proportion is the percentage of people in favor of the tax plan, which is given as 70%. We convert this to a decimal: 70% = 0.7.

Step 2: Calculate the margin of error:

The margin of error depends on the sample size and the desired confidence level. For a 95% confidence interval, we use a z-value of 1.96.

Margin of Error = z * sqrt((p * (1-p)) / n)

p is the sample proportion, and n is the sample size.

Margin of Error = 1.96 * sqrt((0.7 * (1-0.7)) / 70)

Step 3: Calculate the confidence interval:

Confidence Interval = Sample Proportion ± Margin of Error

Confidence Interval = 0.7 ± Margin of Error

Substituting the calculated value for the margin of error:

Confidence Interval = 0.7 ± (1.96 * sqrt((0.7 * (1-0.7)) / 70))

Calculating the values:

Confidence Interval = 0.7 ± (1.96 * sqrt(0.21 / 70))

Confidence Interval = 0.7 ± (1.96 * 0.0674)

Confidence Interval = 0.7 ± 0.1321

Confidence Interval = (0.568, 0.832)

Rounding to the nearest tenth, the 95% confidence interval for the percentage of people who favor the tax plan is (56.8%, 83.2%).

For more such questions on tax plan

https://brainly.com/question/1775528

#SPJ8

4. Suppose the temperature at a point (x,y:=) in the lab of one defined by TlX.X.2)=y22+y2+xz2 If one scientist standing at the position (1,1,1) 4.1. find the rate of change of temperature at the poin

Answers

To find the rate of change of temperature at the point (1, 1, 1), we need to calculate the gradient vector of the temperature function and evaluate it at the given point.

The gradient vector of a function f(x, y, z) is given by ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z). In this case, the temperature function is T(x, y, z) = y^2 + y^2 + x*z^2.

Step 1: Calculate the partial derivatives: ∂T/∂x = 0 (since there is no x term in the temperature function). ∂T/∂y = 2y + 2y = 4y. ∂T/∂z = 2xz^2

Step 2: Evaluate the gradient vector at the point (1, 1, 1):

∇T(1, 1, 1) = (∂T/∂x, ∂T/∂y, ∂T/∂z) = (0, 4(1), 2(1)(1)^2) = (0, 4, 2)

Therefore, the gradient vector at the point (1, 1, 1) is (0, 4, 2). The rate of change of temperature at the point (1, 1, 1) is given by the magnitude of the gradient vector: Rate of change of temperature = |∇T(1, 1, 1)| = √(0^2 + 4^2 + 2^2) = √20 = 2√5. Hence, the rate of change of temperature at the point (1, 1, 1) is 2√5.

To learn more about   gradient vector click here: brainly.com/question/29751488

#SPJ11

Initial population in a city was recorded as 4000 persons. Ten years later, this population increased to 8000. Assuming that population grew according to P(t) « ekt, the city population in twenty years turned = (A) 16,000 (B) 12,000 (C) 18,600 (D) 20,000 (E) 14, 680

Answers

The city population in twenty years is 16,000 persons.

To determine the city's population after twenty years, we can use the growth model equation [tex]P(t) = P(0) * e^(kt)[/tex], where P(t) is the population at time t, P(0) is the initial population, e is the base of the natural logarithm, k is the growth rate constant, and t is the time in years.

Given that the initial population was 4000 persons, we have P(0) = 4000. We can use the information that the population increased to 8000 persons after ten years to find the growth rate constant, k.

Using the formula[tex]P(10) = P(0) * e^(10k)[/tex] and substituting the values, we get [tex]8000 = 4000 * e^(10k).[/tex] Dividing both sides by 4000 gives us [tex]e^(10k) = 2.[/tex]

Taking the natural logarithm of both sides, we have 10k = ln(2), and solving for k gives us k ≈ 0.0693.

Now, we can find the population after twenty years by plugging in the values into the growth model equation: [tex]P(20) = 4000 * e^(0.0693 * 20) ≈[/tex] 16,000 persons.

Therefore, the city population in twenty years will be approximately 16,000 persons.

Learn more about population here

brainly.com/question/27779235

#SPJ11

For what values of k does the function y = cos(kt) satisfy the differential equation 64y" = -81y? k= X (smaller value) k= (larger value)

Answers

The values of k that satisfy the differential equation 64y" = -81y for the function y = cos(kt) are k = -4/3 and k = 4/3.

To determine the values of k that satisfy the given differential equation, we need to substitute the function y = cos(kt) into the equation and solve for k.

First, we find the second derivative of y with respect to t. Taking the derivative of y = cos(kt) twice, we obtain y" = -k^2 * cos(kt).

Next, we substitute the expressions for y" and y into the differential equation 64y" = -81y:

64(-k^2 * cos(kt)) = -81*cos(kt).

Simplifying the equation, we get -64k^2 * cos(kt) = -81*cos(kt).

We can divide both sides of the equation by cos(kt) since it is nonzero for all values of t. This gives us -64k^2 = -81.

Finally, solving for k, we find two possible values: k = -4/3 and k = 4/3.

Therefore, the smaller value of k is -4/3 and the larger value of k is 4/3, which satisfy the given differential equation for the function y = cos(kt).

Learn more about differential equation here:

https://brainly.com/question/25731911

#SPJ11

In the following exercises, use appropriate substitutions to write down the Maclaurin series for the given binomial.
N -1/3
177. (1-2x)2/3

Answers

The Maclaurin series for the binomial (1-2x)^(2/3) can be expressed as the sum of terms with coefficients determined by the binomial theorem. Each term is obtained by substituting values into the binomial series formula and simplifying the expression. The resulting Maclaurin series expansion can be used to approximate the function within a certain range.

To find the Maclaurin series for (1-2x)^(2/3), we can use the binomial series formula, which states that for any real number r and x satisfying |x| < 1, (1+x)^r can be expanded as a power series:

(1+x)^r = C(0,r) + C(1,r)x + C(2,r)x^2 + C(3,r)x^3 + ...

where C(n,r) is the binomial coefficient given by:

C(n,r) = r(r-1)(r-2)...(r-n+1) / n!

In our case, r = 2/3 and x = -2x. Plugging these values into the formula, we get:

(1-2x)^(2/3) = C(0,2/3) + C(1,2/3)(-2x) + C(2,2/3)(-2x)^2 + C(3,2/3)(-2x)^3 + ...

Let's calculate the first few terms:

C(0,2/3) = 1

C(1,2/3) = (2/3)

C(2,2/3) = (2/3)(2/3 - 1) = (-2/9)

C(3,2/3) = (2/3)(2/3 - 1)(2/3 - 2) = (4/27)

Substituting these values back into the series expansion, we have:

(1-2x)^(2/3) = 1 - (2/3)(-2x) - (2/9)(-2x)^2 + (4/27)(-2x)^3 + ...

Simplifying further:

(1-2x)^(2/3) = 1 + (4/3)x + (4/9)x^2 - (32/27)x^3 + ...

Therefore, the Maclaurin series for (1-2x)^(2/3) is given by the expression:

1 + (4/3)x + (4/9)x^2 - (32/27)x^3 + ...

This series can be used to approximate the function (1-2x)^(2/3) for values of x within the convergence radius of the series, which is |x| < 1.

Learn more about binomial theorem here:

brainly.com/question/30095070

#SPJ11

The Maclaurin series for the given binomial function is 1 - (4/3)x - (4/9)x²- (32/27)x³ +...

What is the  Maclaurin series?

The Maclaurin series is a power series that uses the function's successive derivatives and the values of these derivatives when the input is zero.

Here, we have

Given: ([tex](1-2x)^{2/3}[/tex],

We have to find  the Maclaurin series

We use the binomial series formula, which states that any real number r and x satisfying |x| < 1, [tex](1+x)^{r}[/tex] can be expanded as a power series:

[tex](1+x)^{r}[/tex]= C(0,r) + C(1,r)x + C(2,r)x² + C(3,r)x³+ ...

where C(n,r) is the binomial coefficient given by:

C(n,r) = r(r-1)(r-2)...(r-n+1) / n!

In our case, r = 2/3 and x = -2x. Plugging these values into the formula, we get:

[tex](1-2x)^{2/3}[/tex] = C(0,2/3) + C(1,2/3)(-2x) + C(2,2/3)(-2x)² + C(3,2/3)(-2x)³ + ...

Let's calculate the first few terms:

C(0,2/3) = 1

C(1,2/3) = (2/3)

C(2,2/3) = (2/3)(2/3 - 1) = (-2/9)

C(3,2/3) = (2/3)(2/3 - 1)(2/3 - 2) = (4/27)

Substituting these values back into the series expansion, we have:

[tex](1-2x)^{2/3}[/tex] = 1 - (2/3)(-2x) - (2/9)(-2x)² + (4/27)(-2x)³ + ...

Simplifying further:

[tex](1-2x)^{2/3}[/tex] = 1 + (4/3)x + (4/9)x² - (32/27)x³ + ...

Hence, the Maclaurin series for (1-2x)^(2/3) is given by the expression:

1 - (4/3)x - (4/9)x²- (32/27)x³ +...

To learn more about the Maclaurin series from the given link

https://brainly.com/question/31965660

#SPJ4

Find the area of the surface generated by revolving the given curve about the y-axis. x = 2/6 – y, -15y

Answers

To find the area of the surface generated by revolving the curve x = 2/6 - y about the y-axis, we can use the method of cylindrical shells.  To find the total area, we integrate 2πy dy from -∞ to 2/6: ∫(from -∞ to 2/6) 2πy dy

In this case, the curve x = 2/6 - y represents a straight line in the xy-plane. When revolved about the y-axis, it creates a cylindrical surface. The equation x = 2/6 - y can be rewritten as y = 2/6 - x, which represents the same line.

To find the limits of integration, we need to determine the range of y-values that the curve covers. From the equation y = 2/6 - x, we can see that y ranges from -∞ to 2/6.

The circumference of each cylindrical shell is given by 2πy, and the height of each shell is given by the differential dy. Therefore, the area of each shell is 2πy dy.

To find the total area, we integrate 2πy dy from -∞ to 2/6:

∫(from -∞ to 2/6) 2πy dy

Evaluating this integral gives us the area of the surface generated by revolving the curve x = 2/6 - y about the y-axis.

To learn more about cylindrical click here, brainly.com/question/30627634

#SPJ11

I
WILL THUMBS UP YOUR POST
Find the critical point of the function f(x, y) = 1 + 2x - 6x² - 7y + 6y² This critical point is a: Maximum

Answers

To find the critical point of the function f(x, y) = 1 + 2x - 6x² - 7y + 6y², we need to find the values of x and y where the gradient of the function is equal to zero.

The gradient of the function is given by ∇f(x, y) = (∂f/∂x, ∂f/∂y), where ∂f/∂x and ∂f/∂y are the partial derivatives of f with respect to x and y, respectively. Taking the partial derivative of f with respect to x, we have ∂f/∂x = 2 - 12x. Taking the partial derivative of f with respect to y, we have ∂f/∂y = -7 + 12y. To find the critical point, we set both partial derivatives equal to zero and solve the system of equations:

2 - 12x = 0

-7 + 12y = 0

Solving the first equation, we have 2 - 12x = 0, which gives x = 2/12 = 1/6. Solving the second equation, we have -7 + 12y = 0, which gives y = 7/12. Therefore, the critical point of the function f(x, y) = 1 + 2x - 6x² - 7y + 6y² is (1/6, 7/12). To determine the nature of this critical point, we need to analyze the second-order partial derivatives or use the Hessian matrix.

Learn more about Hessian matrix here:

https://brainly.com/question/32250866

#SPJ11

Use the given sample data to find the p-value for the hypotheses, and interpret the p-value. Assume all conditions for inference are met, and use the hypotheses given here:
H_0\:\:p_1=p_2H0p1=p2
H_A\:\:p_1\ne p_2HAp1?p2
A poll reported that 41 of 100 men surveyed were in favor of increased security at airports, while 35 of 140 women were in favor of increased security.
P-value = 0.0086; If there is no difference in the proportions, there is about a 0.86% chance of seeing the observed difference or larger by natural sampling variation.
P-value = 0.0512; If there is no difference in the proportions, there is about a 5.12% chance of seeing the observed difference or larger by natural sampling variation.
P-value = 0.0086; There is about a 0.86% chance that the two proportions are equal.
P-value = 0.0512; There is about a 5.12% chance that the two proportions are equal.
P-value = 0.4211; If there is no difference in the prop

Answers

based on the small p-value, we have evidence to reject the null hypothesis in favor of the alternative hypothesis, suggesting that there is a significant difference in the proportions of men and women favoring increased security at airports.

What is Hypothesis?

A hypothesis is an educated guess while using reasonable thinking, about the answer to a scientific question. Although it is not proof in an experiment, it is the predicted outcome of the experimentation. It can either be supported or not supported at all, but it depends on the data gathered.

Based on the provided information, the correct interpretation of the p-value would be:

P-value = 0.0086; If there is no difference in the proportions, there is about a 0.86% chance of seeing the observed difference or larger by natural sampling variation.

The p-value of 0.0086 indicates that the probability of observing the difference in proportions (favoring increased security at airports) as extreme as or larger than the one observed in the sample, assuming there is no difference in the population proportions, is approximately 0.86%.

In other words, if the null hypothesis were true (i.e., there is no difference in proportions between men and women favoring increased security at airports), there is a very low probability of obtaining the observed difference or a larger difference due to natural sampling variation.

Therefore, based on the small p-value, we have evidence to reject the null hypothesis in favor of the alternative hypothesis, suggesting that there is a significant difference in the proportions of men and women favoring increased security at airports.

To learn more about Hypothesis from the given link

https://brainly.com/question/606806

#SPJ4

Use the integral Test to determine whether the series is convergent or divergent. R-1 Evaluate the following integral. dx Since the integral Select-finite, the series is -Select

Answers

The integral of dx from 1 to infinity is finite. Therefore, the series is convergent.

The integral test states that if a series ∑(n=1 to infinity) an converges, then the corresponding integral ∫(1 to infinity) an dx also converges. In this case, the integral ∫(1 to infinity) dx is simply x evaluated from 1 to infinity, which is infinite. Since the integral is finite, the series must be convergent.

The integral test is a method used to determine whether an infinite series converges or diverges by comparing it to a corresponding improper integral. In this case, we are considering the series with terms given by an = 1/n.

The integral we need to evaluate is ∫(1 to infinity) dx. Integrating dx gives us x, and evaluating this integral from 1 to infinity, we get infinity.

According to the integral test, if the integral is finite (i.e., it converges), then the corresponding series also converges. Conversely, if the integral is infinite (i.e., it diverges), then the series also diverges. since the integral is infinite, we conclude that the series ∑(n=1 to infinity) 1/n diverges.

Learn more about convergent here:

https://brainly.com/question/29258536

#SPJ11

Calculate the following limit using the factorization formula x^ − a^ = (x − a) (x^− ¹ + x^ 1 - xn-2a+xn-3a? + ... + Xô where n is a positive integer and a is a real number. 4 X - 1296 lim X-6

Answers

The limit using the factorization formula is 0.

[tex]lim(x→6) (x^4 - 1296) = 0 * 72 = 0.[/tex]

To calculate the limit using the factorization formula, we can rewrite the expression as follows:

[tex]lim(x→6) (x^4 - 1296) = lim(x→6) [(x^2)^2 - 36^2][/tex]

Now, we can apply the factorization formula:

[tex](x^2)^2 - 36^2 = (x^2 - 36) (x^2 + 36)[/tex]

So, the expression can be rewritten as:

[tex]lim(x→6) (x^4 - 1296) = lim(x→6) (x^2 - 36) (x^2 + 36)[/tex]

Now, we can evaluate the limit term by term:

[tex]lim(x→6) (x^2 - 36) = (6^2 - 36) = 0lim(x→6) (x^2 + 36) = (6^2 + 36) = 72[/tex]

Therefore, the overall limit is:

[tex]lim(x→6) (x^4 - 1296) = 0 * 72 = 0[/tex]

learn more about the limit here:
https://brainly.com/question/12211820

#SPJ11

express the confidence interval .222 < p < .888 in the form p - e

Answers

The confidence interval .222 < p < .888 can be expressed as p - e, where p = 0.555 and e = 0.333.

In a confidence interval, the point estimate represents the best estimate of the true population parameter, and the margin of error represents the range of uncertainty around the point estimate.

To express the given confidence interval in the form p - e, we need to find the point estimate and the margin of error.

The point estimate is the midpoint of the interval, which is the average of the upper and lower bounds. In this case, the point estimate is (0.222 + 0.888) / 2 = 0.555.

To find the margin of error, we need to consider the distance between the point estimate and each bound of the interval.

Since the interval is symmetrical, the margin of error is half of the range.

Therefore, the margin of error is (0.888 - 0.222) / 2 = 0.333.

Now we can express the confidence interval .222 < p < .888 as the point estimate minus the margin of error, which is 0.555 - 0.333 = 0.222.

Therefore, the confidence interval .222 < p < .888 can be expressed as p - e, where p = 0.555 and e = 0.333.

Learn more about confidence interval here:

https://brainly.com/question/31748686

#SPJ11




4 4 4 11. Let f(x)={{ı – x)* +%*$*+x*}" = - x Determine f'(0) 1 2 12. If h(x)= f(g(x)) such that f(1)= = = f"(i)==ş, 8(2) = 1 and g'(2) = 3 then find h' (2) 22 = = 2 1 13. Find the equation of the

Answers

1-The value of f'(0) is -1 ,

2- the value of h'(2) is 24

3-the equation of the line passing through (3, 5) and (7, 9) is y = x + 2.

1. Calculation of f'(0):

f(x) = (√(1 - x²)) / (-x)

Apply the quotient rule:

f'(x) = [(-x)(1 - x²)(-1/2) - (√(1 - x²))(-1)] / (-x)²

Simplify the expression:

f'(x) = (x - √(1 - x²)) / (x²(1 - x²)(-1/2))

Evaluate f'(0):

f'(0) = (0 - √(1 - 0²)) / (0²(1 - 0²)(-1/2))

= (-√1) / (0²(1)(-1/2))

= -1

Therefore, f'(0) = -1.

2. Calculation of h'(2):

h(x) = f(g(x))

Apply the chain rule:

h'(x) = f'(g(x)) * g'(x)

Given values: f(1) = 4, f'(1) = 8, g(2) = 1, and g'(2) = 3.

h'(2) = f'(g(2)) * g'(2)

= f'(1) * g'(2)

= 8 * 3

= 24

Therefore, h'(2) = 24.

3. Calculation of the equation of the line passing through (3, 5) and (7, 9):

Use the slope-intercept form: y = mx + b

Calculate the slope (m):

m = (y2 - y1) / (x2 - x1)

= (9 - 5) / (7 - 3)

= 4 / 4

= 1

Choose one point (x, y) = (3, 5)

Substitute the values into the slope-intercept dorm:

5 = 1(3) + b

Solve for b:

5 = 3 + b

b = 5 - 3

b = 2

which makes the equation y = x + 2.

learn more about Chain rule here:

https://brainly.com/question/28972262

#SPJ4

The complete question is:

1. Let's consider the function f(x) = (√(1 - x²)) / (-x). Find the value of f'(0).

2. Suppose we have two functions f(x) and g(x). If h(x) is defined as h(x) = f(g(x)) and we know that f(1) = 4, f'(1) = 8, g(2) = 1, and g'(2) = 3, find the value of h'(2).

3. Determine the equation of the line passing through two points, (x1, y1) = (3, 5) and (x2, y2) = (7, 9).

2. The solution of the differential equation dy = (x + y + 1)2 da is given by (a) y=-1-1+tan(x + c) (b) y = x - 1+tan(x+c) (c) y=2. - 1+tan: + c) y = -2:0 +1+tan(x+c) y=x+1-tan(2x + c) do 4- & $ 4 26

Answers

The solution of the given differential equation dy = (x + y + 1)^2 dx is given by (c) y = -2x + 1 + tan(x + c).

To solve the differential equation dy = (x + y + 1)^2 dx, we can separate the variables and integrate both sides.

Starting with the original equation, we have dy/(x + y + 1)^2 = dx.

Integrating both sides, we get ∫dy/(x + y + 1)^2 = ∫dx.

The integral on the left side can be evaluated using the substitution method, where we let u = x + y + 1.

Differentiating u with respect to x, we have du/dx = 1 + dy/dx. Rearranging this equation, we have dy/dx = du/dx - 1.

Substituting these values back into the integral, we have ∫1/u^2 * (du/dx - 1) dx = ∫(1/u^2)(du - dx) = ∫(1/u^2) du - ∫(1/u^2) dx.

Integrating, we obtain -1/u - x + c = -1/(x + y + 1) - x + c.

Rearranging, we have y = -2x + 1 + tan(x + c), which matches option (c).

Learn more about differential equation here:

https://brainly.com/question/25731911

#SPJ11

geometry a square has a side length of x inches. the difference between the area of the square and the perimeter of the square is 18. write an equation to represent the situation.

Answers

The required equation is:[tex]x^2 - 4x = 18.[/tex]

State the formula for a square's area?

The area of a square is:

Area = (side length) *( side length)

Alternatively, it can also be written as:

[tex]Area =( side\ length)^2[/tex]

In both cases, the area of a square is calculated by multiplying the length of one side by itself, since all sides of a square are equal in length.

Let's start by finding the area and perimeter of the square.

By the formula,the area of a square is :

Area = (side length)*( side length) =[tex]x^2.[/tex]

The perimeter of a square is:

Perimeter = 4(side length)

Perimeter= 4x

Now, we can write the equation that represents the given situation:

Area of the square - Perimeter of the square = 18

Substituting the formulas for area and perimeter:

[tex]x^2 - 4x = 18[/tex]

So, the equation to represents the situation is:

[tex]x^2 - 4x = 18.[/tex]

To learn more about the area of a square from the given link

brainly.com/question/25092270

#SPJ4

please answer this question.

Answers

The area of a triangle ABC is 6.8 square centimeter.

In the given triangle ABC, ∠BAC=80°, AC=4.9 cm and BC=5.6 cm.

In the given parallelogram STUV, SV=4 cm and VU=5 cm.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Now, sin80°/5.6 = sinB/4.9

sinB/4.9 = 0.9848/5.6

sinB/4.9 = 0.1758

sinB = 0.1758×4.9

sinB = 0.86142

sinB = 59°

Here, ∠C=180-80-59

∠C=41°

Now, sin80°/5.6 = sin41°/AB

0.9848/5.6 = 0.6560/AB

0.1758 = 0.6560/AB

AB = 0.6560/0.1758

AB = 3.7 cm

We know that, Area of a triangle = 1/2 ab sin(C)

Area of a triangle = 1/2 ×3.7×5.6 sin41°

= 1/2 ×3.7×5.6×0.6560

= 3.7×2.8×0.6560

= 6.8 square centimeter

Therefore, the area of a triangle ABC is 6.8 square centimeter.

To learn more about the area of a triangle visit:

brainly.com/question/27701864.

#SPJ1

Which symmetric matrices S are also orthogonal ? Then ST = S-1 (a) Show how symmetry and orthogonality lead to S2 = I. (b) What are the possible eigenvalues of this S? (c) What are the possible eigenv

Answers

(a) Symmetric and orthogonal matrices have the property S^2 = I, where I is the identity matrix.

(b) The possible eigenvalues of such a matrix S are ±1.

(c) The possible eigenvectors of S correspond to the eigenvalues ±1.

(a) Symmetric matrices have the property that they are equal to their transpose: S = ST. Orthogonal matrices have the property that their transpose is equal to their inverse: ST = S^(-1). Combining these two properties, we have S = ST = S^(-1). Multiplying both sides by S, we get S^2 = I.

(b) The eigenvalues of a symmetric matrix S are always real. In the case of an orthogonal matrix that is also symmetric, the possible eigenvalues are ±1. This is because the eigenvalues represent the scaling factors of the eigenvectors, and for an orthogonal matrix, the eigenvectors remain the same length after transformation.

(c) The eigenvectors of an orthogonal matrix that is also symmetric correspond to the eigenvalues ±1. The eigenvectors associated with eigenvalue 1 are the vectors that remain unchanged or only get scaled, while the eigenvectors associated with eigenvalue -1 get inverted or flipped. These eigenvectors form a basis for the vector space spanned by the matrix S.

By examining the properties of symmetry and orthogonality in matrices, we can deduce important relationships between their powers, eigenvalues, and eigenvectors. These properties have applications in various areas, such as linear algebra, geometry, and data analysis, allowing us to understand and manipulate matrices effectively.

Learn more about Matrices : brainly.com/question/29024761

#SPJ11

Other Questions
A nurse is initiating a peripheral IV infusion punctures the skin and selected vein and observes blood return in the flashback chamber of the IV catheter. Which of the following actions should the nurse perform next?a. secure the catheter to the skin with a transparent dressingb. lover the catheter until it is almost flush with the skinc. advance the catheter about 1/4 inch into the veind. remove the stylet slowly from the lumen of the catheter when one nucleotide contains cytosine, what type of base is the cytosine attached to on the opposite nucleotide strand? Complete the following steps for the given function, interval, and value of n a. Sketch the graph of the function on the given interval b. Calculate Ax and the grid points x X. x c. Illustrate the left and right Riemann sums, and determine which Riemann sum underestimates and which sum overestimates the area under the curve. d. Calculate the left and right Riemann sums. f(x) -2x2+5 on [1,6]: n5 a. Sketch the graph of f(x) 2x2 +5 on the interval [1, 6]. The Endangered Species Act has been described as "the most powerful environmental law on the books," yet the ESA has numerous substantive and procedural problems. Identify and discuss one of each type of problem. if jews and romans had a low view of women during the first-century, and they typically weren't viewed as credible sources, why would the gospel writers say that a group of women found the tomb of jesus empty? I would like you to critique a translated text using one of the models of Peter Newmark, Raymond van den Broeck, Katharina Reiss, John M. Dodds, and Antoine Berman. The text should be written in English and in accordance with academic writing rules. It should consist of at least 750 words. Suppose that a coin flipping four times, and let X represent the number of head that cancome up. Find:1. probability function corresponding to the random variable X.2. Find the cumulative distribution function for the random variable X. Triangle ABC, with vertices A(-9,-8), B(-2,-9), and C(-8,-5), is drawn inside a rectangle. What is the area, in square units, of triangle ABC? Which of the following best describes the artists likely purpose in painting this particular subject?Group of answer choicesa) To advocate for violent rebellion against British colonial authoritiesb) To call for greater emigration by Europeans to the West Indiesc) To argue for the respectability of free people of colord) To demonstrate the racial oppression suffered by free people of color in the West Indies Which of the following risks is most difficult to measure and mange? Select one: O a. Credit risk, because returns are not normally distributed O b. Market risk, because of the optionality of many positions Oc. Interest rate risk, because no one can consistently predict directional changes O d. Operational risk, because sufficient data does not exist Sam I Am invests $108,000 today at 8% per annum, compounded quarterly. What will the balance of Sam's investment be in 6 years? (Round your answer to the nearest penny.) Lois thinks that people living in a rural environment have a healthier lifestyle than other people. She believes the average lifespan in the USA is 77 years. A random sample of 20 obituaries from newspapers from rural towns in Idaho give x = 80.63 and s = 1.87. Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? Assume normality. (a) State the null and alternative hypotheses: (Type "mu" for the symbol mu > e.g. mu >|1 for the mean is greater than 1. mu Globalisation is hailed as a driver of economic growth but yet there are strong anti-globalisation movements across the world."" Discuss the economic and technological impact of globalisation in any less developed country (Nigeria) of your choice You took a(n) 8000, 5-year loan. Payments at the end of each year are flat (equal in every year) at an interest rate of 16 percent. Calculate the appropriate loan table, showing the breakdown in each year between principal and interest. important contributors to niacin intake in the american diet are an increase in the price of a product leads to * an increase in the marginal utility per dollar (mu?p) of that product, which leads to an increase in the quantity purchased. an increase in the marginal utility per dollar (mu/p) of that product, which leads to a decrease in the quantity purchased. a decrease in the marginal utility per dollar (mu/p) of that product, which leads to an increase in the quantity purchased. a decrease in the marginal utility per dollar (mu/p) of that product, which leads to a decrease in the quantity purchased. Use a triple integral to compute the exact volume of the solld enclosed by y = 93?, y=6, 2=0, x=0, and z = 10 - y in the first octant Volume = (Give an exact answer.) Consider the process of manufacturing Tesla cars. Name one financial metric, one external metric, and one internal metric for this process Working Dog Inc. sells equipment for search and rescue dogs. Relevant data on its best-selling working harness are below. Assume 365 working days per year. If Working Dog decided to produce the rescue dog harness in-house rather than order from an external vendor, and the production rate per day was 100 units, what would be the optimal production quantity? Assume the machine setup cost will be the same as the procurement (order) cost, and all other data are the same. Forecasted daily demand50 units Forecast error standard deviation15 units Lead time7 days Annual holding rate30% Procurement cost per order$50 Product value$45 In-stock probability85% a. 520 b. 368 c. 493 d. 27 e. 38 You decided to award a 10% discount to a valuable customer and in D2 you calculated the discount amount that will appear on their monthly invoices using the 10% typed into A2. Because the % symbol is a mathematical operator, when you multiplied the figure in C2 by this cell, Excel worked out the 10 percent. You then used a Dollar sign in D2 so that you could use Autofill to correctly copy this formula down as far as D5. You would like to use Copy and Paste to copy this block of formulas to the cells H2 to H5. If you copy and paste without any further adjustment, will they work correctly in the new location?The Discount amount values are selected.