given the weekly demand curve of a local wine producer is p= 50-0.1q, and that the total cost function is c= 1500+ 10q, where q bottles are produced each day and sold at a price of $p per unit. a)Express the weekly profit as a function of price.b) at what price must a bottle of wine be sold to realise maximum profit. c) what is the maximum profit that ca be made by the producer

Answer:

x-intercept(s):  (-14,0)

y-intercept(s):  (0,-2)

Step-by-step explanation:

To find the x-intercept, substitute in  0 for yand solve

To find the y-intercept, substitute in  0 for x and solve for y

To calculate the total charge within the cylinder with dimensions r=1.5 and h=3, we use the potential function V = 5r + 4 cos Ø in cylindrical coordinates.

The total charge can be obtained by integrating the charge density over the volume of the cylinder.

The potential V within the cylinder is given by V = 5r + 4 cos Ø, where r represents the radial distance from the axis of the cylinder and Ø represents the angle in the cylindrical coordinate system. To calculate the total charge within the cylinder, we need to integrate the charge density over its volume.

The charge density ρ can be related to the potential by ρ = -∇²V, where ∇² is the Laplacian operator. In cylindrical coordinates, the Laplacian operator takes the form:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز + ∂²/∂z²

Since the potential function V does not depend on the z coordinate, the Laplacian reduces to:

∇² = (1/r) ∂/∂r (r ∂/∂r) + (1/r²) ∂²/∂ز

Applying this operator to the potential function V, we find:

∇²V = (1/r) ∂/∂r (r ∂V/∂r) + (1/r²) ∂²V/∂ز

To find the charge density, we substitute this expression into ρ = -∇²V:

ρ = -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز

To calculate the total charge, we integrate the charge density ρ over the volume of the cylinder:

Q = ∫∫∫ ρ dV = ∫∫∫ -(1/r) ∂/∂r (r ∂V/∂r) - (1/r²) ∂²V/∂ز dV

The integration is performed over the cylindrical coordinates r, Ø, and z, with appropriate limits. Evaluating this integral will give us the total charge within the cylinder.

Learn more about dimensions here:

https://brainly.com/question/31156956

#SPJ11

Answer:

i ussually this answer so yeah but my class is tomorrow

Step-by-step explanation:

Answer:

I believe it is (7, 0)

Step-by-step explanation:

I hope this is right..

Answer:

use slope intercept form to find the x intercept

y = Mx +b

Step-by-step explanation:

x+4y=7

4y= -x+7

y= -1/4x +7/4

so when this line is on the x intercept.. then y =0  soooo plug in zero for y and solve

0= -1/4x + 7/4

-7/4 = -1/4x

7 = x

Answer:

3 and -3

Step-by-step explanation:

For 3  and -3  \(x^{2}\)+ 3  has same answer

Answer:

ididdiiddidkdkdiidkd

Answer:

Slope:3

Step-by-step explanation:

The minimum number of masthead lights for the given vessel is 2.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
A towing vessel 35 meters in length, with a tow 100 meters astern,

Masthead lights = total length of the tow / total length of the vessel
                        = 100 / 35 = 2.85

So, the Number of Masthead lights for the given vessel is 2 ≤ x ≤ 3.
And a minimum number of masthead lights is 2.

Thus, the minimum number of masthead lights for the given vessel is 2.

Learn more about ratios here:

brainly.com/question/13419413

#SPJ2

Answer:

a. sin 300 = -∛3/2, cos 300 = 1/2

b. sin -225 = √2/2, cos -225 = √2/2

c. sin 5π/6 = 1/2, cos 5π/6 = -3√2

d. sin -4π/3 = √3/2, cos -4π/3 = -1/2

Step-by-step explanation:

See unit circle

Sample is subset of population set .It is only a part of population.

For the given statistical study, we have to select the sample and population .

The option ‘The sample is the 50 conference attendees, and the population is all teachers in the state’ is correct.

Population:

The set of all people, items, that are required for a specific study is defined as the population.

Sample:population is a big size data and it is not easy to examine each individual .

Hence, a smaller group of individuals are selected from the population of interest. The small groups are called the sample.

Parameter:

The population parameter is defined as number that describes the population. Also, it can be a numerical value that represents the population.

Statistic:

The statistical measure which is calculated on the basis of sample observations is called Statistic.

Population size is defined as the total number of subjects in any given

statistical study. It is denoted by N.

Sample size is defined as the total number of subjects that are included in sample. It is denoted by n.

From the information, the staff members of a high school newspaper are interested to know the estimate for the average number of years teachers in the state have been teaching. For this a sample of 50 conference attendees of staff members are selected randomly.

The population involves all the units considered in the study. In this study the staff membersof a high school needs to estimates the average number of years value for all the teachers in the state. This indicates that the population in the study is ‘all the teachers in the state'.

So, correct option is option ( A).

To learn more about Population and sample , refer:

https://brainly.com/question/7301139

#SPJ4

Complete question:

Staff members of a high school newspaper want to obtain an estimate of the average number of years teachers inthe state have been teaching. At an educational conference attended by many teachers in the state, the staffmembers randomly selected 50 conference attendees and asked the attendees how long they have been teaching.Which of the following describes the sample and the population to which it would be most reasonable for thestaff members to generalize the results?

(A) The sample is the 50 conference attendees, and the population is all teachers in the state.

(B) The sample is the 50 conference attendees, and the population is all conference attendees.

(C) The sample is all conference attendees, and the population is all teachers in the state.

(D) The sample is all conference attendees, and the population is the 50 conference attendees

(E) The sample is the average number of years that all conference attendees have taught, and the population isall conference attendees.

\(let \: the \: number \: be \: denoted \: by \: p \\ five \: times \: a \: number = 5p \\ square\: of \: a \: number = p {}^{2} \)

\( \gamma - p {}^{2} = 5p - p {}^{2} \)

Answer:

An E

Step-by-step explanation:

Answer:

e comes in every odd number

i.e. one,three,five,seven,nine,eleven......

Step-by-step explanation:

The correct statement is that Ursula has incurred the finance charge of 46.17% about for the loan amounting to $6400. So, the correct option matching the statement is not as quoted in the options above.

Finance charge can be calculated by summarizing and comparing the principal amount with the annuity amount derived by the formula of compound interest.

Hence, the correct option is that Ursula has borne the financial charge as 46.17% of her principal.

To know more about finance charge, click the link below.

https://brainly.com/question/298229

Answer: 39

Step-by-step explanation:

Answer:

um i think  about 39 foot it has been a little scenes i have done this

Step-by-step explanation:

The finite population correction factor is used in computing the standard error of the sample mean when the sample size is smaller than 5% of the population size.

The finite population correction factor is a adjustment made to the standard error of the sample mean when the sample is taken from a finite population, rather than an infinite population.

It accounts for the fact that sampling without replacement affects the variability of the sample mean.

When the sample size is relatively large compared to the population size (more than half), the effect of sampling without replacement becomes negligible, and the finite population correction factor is not necessary.

In this case, the standard error of the sample mean can be estimated using the formula for sampling with replacement.

On the other hand, when the sample size is small relative to the population size (less than 5%), the effect of sampling without replacement becomes more pronounced, and the finite population correction factor should be applied.

This correction adjusts the standard error to account for the finite population size and provides a more accurate estimate of the variability of the sample mean.

Therefore, the correct answer is option 2: the finite population correction factor is used when the sample size is smaller than 5% of the population size.

Learn more about mean here:

https://brainly.com/question/31101410

#SPJ11

Answer:

168

Step-by-step explanation:

21*8=168

Answer:

168 ft ^2

Step-by-step explanation:

Tofind the Area of a rectangle you multiply the Length by the width. By doing this we get the equation Area = 21 * 8. By doing multiplication we get area to be 168.

We have the following:

let x number of dimes

let y number of quarters

Therefore,

Therefore, The quarters can range from 6 coins to 9.6 coins, that is, the maximum can be 10 coins.

Answer:

I think it didnt change

Step-by-step explanation:

Cause both areas from the line are the same and if it were to change the left would be diffrent from the right. So there i think it didnt change.

Answer:

499

Step-by-step explanation:

The Correct answer is option a. 7-9.42, P-value = 0.002 which is derived based on the given data about alcohol consumption.

The chi-square test of homogeneity is a statistical test used to determine whether there is a significant difference between the observed frequencies of two categorical variables.

In this case, the test statistic would be the chi-square value calculated using the observed frequencies of alcohol consumption in the sample of smokers and non-smokers, and the P-value would be the probability of obtaining a chi-square value as extreme or more extreme than the calculated value under the assumption that the null hypothesis is true (i.e. no difference in alcohol consumption between smokers and non-smokers).

In this case, the test statistic would be 7.942 and the P-value would be 0.002 which implies that there is a significant difference in alcohol consumption between smokers and non-smokers.

Learn more about Chi-Square Test here:

https://brainly.com/question/29850910

#SPJ4

Answer:

B is correct

Step-by-step explanation:

The solution of the quadratic equation is x = (-1/2) + (i√3)/2 and x = (-1/2) - (i√3)/2. If the sum of the reciprocals of the roots of the quadratic equation is one, then the equation can be expressed in the form ax²+bx+c=0.


Given, the quadratic equation is

a*x² + b*x + c = 0

The sum and product of roots of a quadratic equation are given by:

Sum of roots = - b/a

Product of roots = c/a

Let α and β be the roots of the quadratic equation.

Sum of reciprocals of the roots is given by:

α⁻¹ + β⁻¹ = αβ / α + β

Given that the sum of the reciprocals of the roots is one.

α⁻¹ + β⁻¹ = 1

αβ = α + β

αβ - α - β + 1 = 1

α(β - 1) - (β - 1) = 0

(α - 1)(β - 1) = 1

α - 1 = 1/β - 1

α = 1/β

Substitute α = 1/β in the quadratic equation.

a*(1/β)² + b*(1/β) + c = 0

a/β² + b/β + c = 0

Multiply the equation by β².

a + bβ + cβ² = 0

The equation can be expressed in the form ax²+bx+c=0.

a = c, b = 1, c = 1

Now, solve the quadratic equation by substituting the values of a, b, and c.

x² + x + 1 = 0

The roots of the equation can be found using the quadratic formula.

x = [-b ± √(b²-4ac)]/2a

Substitute a, b, and c in the formula.

x = [-1 ± √(-3)]/2

The roots of the equation are:

x = (-1/2) + (i√3)/2 and x = (-1/2) - (i√3)/2

Thus, the solution of the quadratic equation is x = (-1/2) + (i√3)/2 and x = (-1/2) - (i√3)/2.

To know more about quadratic equation refer here:

https://brainly.com/question/29269455

#SPJ11

To show that β=3α, where β represents the volumetric thermal expansion coefficient and α represents the linear thermal expansion coefficient, we can calculate the infinitesimal change in volume (dv) of a cube with sides of length l when the temperature changes by dt.

The linear thermal expansion coefficient α is defined as the fractional change in length per unit change in temperature. Similarly, the volumetric thermal expansion coefficient β is defined as the fractional change in volume per unit change in temperature.

Let's consider a cube with sides of length l. The initial volume of the cube is \(V = l^3\). Now, when the temperature changes by dt, the sides of the cube will also change. Let dl be the infinitesimal change in length due to the temperature change.

The infinitesimal change in volume, dv, can be calculated using the formula for differential calculus:

\(\[dv = \frac{{\partial V}}{{\partial l}} dl = \frac{{dV}}{{dl}} dl\]\)

Since \(V = l^3,\) we can differentiate both sides of the equation with respect to l:

\(\[dV = 3l^2 dl\]\)

Substituting this back into the previous equation, we get:

\(\[dv = 3l^2 dl\]\)

Now, we can express dl in terms of dt using the linear thermal expansion coefficient α:

\(\[dl = \alpha l dt\]\)

Substituting this into the equation for dv, we have:

\(\[dv = 3l^2 \alpha l dt = 3\alpha l^3 dt\]\)

Comparing this with the definition of β (fractional change in volume per unit change in temperature), we find that:

\(\[\beta = \frac{{dv}}{{V dt}} = \frac{{3\alpha l^3 dt}}{{l^3 dt}} = 3\alpha\]\)

Therefore, we have shown that β = 3α, indicating that the volumetric thermal expansion coefficient is three times the linear thermal expansion coefficient for a cube.

To learn more about coefficient refer:

https://brainly.com/question/24068089

#SPJ11

This expression gives:

(f+g)(3) = 21

To find (f+g)(x), we first substitute the expressions for f(x) and g(x) into the equation:

(f+g)(x) = f(x) + g(x) = (x - 9) + 3x^2

Next, we simplify the expression by combining like terms:

(f+g)(x) = 3x^2 + x - 9

This is the simplified expression for (f+g)(x).

Now, to find (f+g)(3), we substitute x=3 into the expression:

(f+g)(3) = 3(3)^2 + 3 - 9

We simplify the expression further using the order of operations (exponentiation before multiplication and addition/subtraction):

(f+g)(3) = 3(9) + 3 - 9

(f+g)(3) = 27 + 3 - 9

(f+g)(3) = 30 - 9

(f+g)(3) = 21

Therefore, when x=3, (f+g)(3) equals 21.

Learn more about  expression from

brainly.com/question/1859113

#SPJ11

If y=-2x+6 were changed to y= 3x+2, how would the graph of the new line compare with the first one: A. The new graph would be steeper than the original-graph, and the y-intercept would shift down 4 units.

In Mathematics and Geometry, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In this context, we can reasonably infer and logically deduce that the graph of the new line would be steeper than the original graph because a slope of 3 is greater than a slope of -2.

Also, the y-intercept would shift down 4 units;

y-intercept = 6 - 2

y-intercept = 4 units.

Read more on slope here: brainly.com/question/3493733

#SPJ1

These constants can be determined by applying initial conditions or boundary conditions specific to the problem. Once the values of C1 and C2 are determined, the general solution becomes a particular solution that satisfies the given conditions.

To find the general solution, we assume a solution of the form y(t) = e^(rt) and substitute it into the differential equation. This leads to the characteristic equation r^2 + 11r - 12 = 0.

Solving the quadratic equation, we find two roots: r1 = -12 and r2 = 1. These roots correspond to the exponential terms e^(-12t) and e^(t) in the general solution.

Since the equation is linear, the general solution is the linear combination of the individual solutions associated with the roots. Therefore, the general solution is y(t) = C1e^(-12t) + C2e^(t), where C1 and C2 are constants of integration.

Learn more about general here:

https://brainly.com/question/32062078

#SPJ11

Answer:

Tr2

Step-by-step explanation:

pie * radius * radius

Answer:

Step-by-step explanation:

The circumference of a circle is given to be 2πr, and its radius to be r.

9514 1404 393

Answer:

  m∠c = 52°

Step-by-step explanation:

Corresponding angles are congruent:

  13x +11° = 15x -7° . . . . . the corresponding angles have equal measures

  18° = 2x . . . . . . . . . . . . add 7° -13x to both sides

  9° = x . . . . . . . . . . divide by 2

Now, we can find c. It is supplementary to the corresponding angles.

  c = 180° -(15x -7°) = 180° -15(9°) +7° . . . . . substitute for x

  m∠c = 52°

Answer:

The equivalent expression for this equation is x²¹ × y⁻²¹

Step-by-step explanation:

When you are multiplying exponents that are in parentheses, you multiply the exponential numbers together. So, for this problem, we will multiply the exponents together so we can get our final equivalent expression.

(x⁻³ × y³)⁻⁷

So, we will multiply -3 by -7 and we will also multiply 3 by -7 because those are our exponential numbers.

x²¹ × y⁻²¹

So, this is the final expression that is equivalent to our equation.

The expression (x⁻³.y³)⁻⁷ is equivalent to x ²¹ . y ⁻²¹.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

The given expression is,

(x⁻³.y³)⁻⁷

To find the solution for the expression,

Simplify the power terms,

x⁽⁻³ˣ⁻⁷⁾ . y ³ˣ⁻⁷

x ²¹ . y ⁻²¹

The simplified form of the expression (x⁻³.y³)⁻⁷ is x ²¹ . y ⁻²¹.

Hence, option (A) is correct.

To know more about Algebra on:

https://brainly.com/question/24875240

#SPJ2