If s varies inversely as
t^2, and s = 10 when t=2, find s when t is 10.​

$13.35 rougly around that

The text discusses a production function and addresses various aspects of a firm's decision-making. It covers profit maximization, factor demand functions, supply function, profit function, Hotelling's lemma, cost minimization, conditional factor demand functions, and the cost function. These concepts are derived using mathematical calculations and formulas. Hotelling's lemma is verified, and the cost function is determined.

(a) The firm's profit maximization problem can be stated as follows: Maximize profits (π) by choosing the optimal levels of inputs (z and zo) that maximize the output (y) given the prices of output (p) and inputs (w, w₂).

(b) To derive the firm's factor demand functions, we need to find the conditions that maximize profits.

The first-order condition for input z is given by:

∂π/∂z = p * (∂f/∂z) - w = 0

Substituting the production function f(z) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/4 * z^(-3/4) / z^(1/2)) - w = 0

Simplifying, we get:

p * (1/4 * z^(-7/4)) - w = 0

Solving for z, we find:

z = (4w/p)^(4/7)

Similarly, for input zo, the first-order condition is:

∂π/∂zo = p * (∂f/∂zo) - w₂ = 0

Substituting the production function f(zo) = z^(1/4) / z^(1/2) into the above equation, we have:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Simplifying, we get:

p * (1/2 * z^(1/4) * zo^(-3/2)) - w₂ = 0

Solving for zo, we find:

zo = (2w₂ / (pz^(1/4)))^(2/3)

(c) To derive the firm's supply function, we need to find the level of output (y) that maximizes profits.

Using the production function f(z), we can express y as a function of z:

y = z^(1/4) / z^(1/2)

Given the factor demand functions for z and zo, we can substitute them into the production function to obtain the supply function for y:

y = (4w/p)^(4/7)^(1/4) / (4w/p)^(4/7)^(1/2)

Simplifying, we get:

y = (4w/p)^(1/7)

(d) The firm's profit function is given by:

π = p * y - w * z - w₂ * zo

Substituting the expressions for y, z, and zo derived earlier, we have:

π = p * ((4w/p)^(1/7)) - w * ((4w/p)^(4/7)) - w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

(e) To verify Hotelling's lemma, we need to calculate the partial derivatives of the profit function with respect to the prices of output (p), input z (z₁), and input zo (z₂).

Hotelling's lemma states that the partial derivatives of the profit function with respect to the prices are equal to the respective factor demands:

∂π/∂p = y - z * (∂y/∂z) - zo * (∂y/∂zo) = 0

∂π/∂z₁ = -w + p * (∂y/∂z₁) = 0

∂π/∂z₂ = -w₂ + p * (∂y/∂z₂) = 0

By calculating these partial derivatives and equating them to zero, we can verify Hotelling's lemma.

(f) The firm's cost minimization problem can be stated as follows: Minimize the cost of production (C) given the level of output (y), prices of inputs (w, w₂), and factor demand functions for inputs (z, zo).

(g) To derive the firm's conditional factor demand functions, we need to find the conditions that minimize costs. We can express the cost function as follows:

C = w * z + w₂ * zo

Taking the derivative of the cost function with respect to z and setting it to zero, we get:

∂C/∂z = w - p * (∂y/∂z) = 0

Simplifying, we have:

w = p * (1/4 * z^(-3/4) / z^(1/2))

Solving for z, we find the conditional factor demand for z.

Similarly, taking the derivative of the cost function with respect to zo and setting it to zero, we get:

∂C/∂zo = w₂ - p * (∂y/∂zo) = 0

Simplifying, we have:

w₂ = p * (1/2 * z^(1/4) * zo^(-3/2))

Solving for zo, we find the conditional factor demand for zo.

(h) The firm's cost function is given by:

C = w * z + w₂ * zo

Substituting the expressions for z and zo derived earlier, we have:

C = w * ((4w/p)^(4/7)) + w₂ * ((2w₂ / (pz^(1/4)))^(2/3))

This represents the firm's cost function.

To know more about profit maximization problem, refer here:

https://brainly.com/question/29787532#

#SPJ11

Answer:

The factored form is,

\((4a^2+2a+1)(4a^2-2a-1)\)

Step-by-step explanation:

We have,

\(16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\\)

Using the difference of square formula,

\(x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)\)

Which is the factored form,

In linear equation, £ 8.4 much does a ticket cost.

What are a definition and an example of a linear equation?

They each pay £ 6.30

the total they pay is

6.3 × 4 = £ 25.2

buy three tickets and get a free ticket

3 tickets is £ 25.2

25.2/3 = £ 8.4

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

Answer: x-int: (-4, 0), y-int: (0, 1/2)

Step-by-step explanation:

x-int: when y = 0

-x + 8*0 = 4

-x = 4

x = -4

(-4, 0)

y-int: when x = 0

0 + 8y = 4

8y = 4

y = 1/2

(0, 1/2)

Answer:

The next 3 numbers will be 1 3/4, 2, and 2 1/4

Step-by-step explanation:

The numbers in the sequence are increase by 1/4. So to find the next number in the sequence and 1/4 to the previous number. Don't foget to simplify your answers. Ex.) Rather than saying 2 2/4 you would say 2 1/2.

The solution to the equation √(2 + 2x) - 6 = 2 when evaluated is x = 31

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

√(2 + 2x) - 6 = 2

So, we have

√(2 + 2x) = 8

Take the square of both sides

so, we have the following representation

2 + 2x = 64

Evalyate the like terms

2x = 62

Divide by 2

This means that

x = 31

Hence, the solution is x = 31

Read more about equations at

https://brainly.com/question/18831322

#SPJ1

Complete question

What is √(2 + 2x) - 6 = 2

Scale factor of given equation is 64 : 1

initial volume = 13  cubic feet

final volume = 832 cubic feet

scale factor = 832 / 13

                    = 64 : 1

learn more about scale factor here :

brainly.com/question/22312172

#SPJ1

a).  2^38 bytes of memory

b). 12 bits

c). The maximum number of entries in the single-level page table would be 2^38.

d). The size would be 2^38 * 4KB, which equals 2^20 pages.

e). The maximum number of entries it can have depends on the remaining bits of the logical address.

f). The amount of bits required to denote an index into the inner page table is obtained by subtracting the offset and outer page index bits from the logical address.

a. To address a physical memory size of 128GB (2^37 bytes), a 64-bit architecture would require 38 bits for the logical address, allowing access to a maximum of 2^38 bytes of memory.

b. Given that the page size is 4KB (2^12 bytes), 12 bits would be needed to specify the displacement into a page. This means that the lower 12 bits of the logical address would be used for page offset or displacement.

c. With a single-level page table, the maximum number of entries would be equal to the number of possible logical addresses. In this case, since the logical address requires 38 bits, the maximum number of entries in the single-level page table would be 2^38.

d. The size of the single-level page table is determined by the number of entries it contains. Since each entry maps to a page of size 4KB, the size of the single-level page table can be calculated by multiplying the number of entries by the size of each entry. In this case, the size would be 2^38 * 4KB, which equals 2^20 pages.

e. For a two-level page table, the size of the outer page table is determined by the number of entries it can contain. Since the outer page table uses 4KB pages, the maximum number of entries it can have depends on the remaining bits of the logical address. The number of bits used for the index into the outer page table is determined by subtracting the bits used for the inner page index and the offset from the total number of bits in the logical address.

f. The number of bits used to specify an index into the inner page table can be determined by subtracting the bits used for the offset and the bits used for the outer page index from the total number of bits in the logical address. The remaining bits are then used to specify the index into the inner page table.

Learn more about bytes here:

https://brainly.com/question/15166519

#SPJ11

Answer:

2√6cm

Step-by-step explanation:

Area = L×L

A=L2

24 =L2

√24 =√L2

2√6= L

:.L =2√6.cm.

Answer: Samantha is 13 years old and Jennifer’s age is 10 years old.

Because it said she was 3 years older, which means 13 +10 = 23.

Step-by-step explanation:

I think.

Samantha age is 7 years and Jennifer age is 4 years.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Samantha is 3 years older than Jennifer.

let Jennifer age be x.

So, Samantha age= x + 3

Now, The square of Jennifer's age plus Samantha's age is equal to 23.

x²+ (x+ 3) = 23

x² + x + 3 = 23

x² + x - 20 = 0

(x- 4) ( x + 5) = 0

x= 4, -5

Hence, Samantha age is 7 years and Jennifer age is 4 years.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ2

Based on the data in the tables, which conjecture about inscribed and central angles is true include the following: B. If an inscribed angle and a central angle intercept arcs with equal measures, the inscribed angle is half the measure of the central angle.

In Geometry, an arc is a trajectory that is generally formed when the distance from a given point has a fixed numerical value. Generally speaking, the degree measure of an arc in a circle is always equal to the central angle that is present in the included arc.

Additionally, the inscribed angle of a circle is equal to half of the central angle of a circle. Mathematically, this is given by this mathematical expression:

m∠A = 1/2(C)

m∠A = 1/2(100)

m∠A = 50°.

Read more on intersecting chords here: https://brainly.com/question/27251228

#SPJ1

Answer:

4 buses

Step-by-step explanation:

There are 173 basketball fans

one bus can hold 46 fans

Hence the number of buses needed can be calculated as follows

= 173/46

= 3.76

= 4

Hence 4 buses are needed

Answer:

-1(-4)=-5

Step-by-step explanation:

as h = -1

There is no real solution of the equation.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given is an equation x = 2 / (x-2) we need to find the solution,

x = 2 / (x-2)

x(x-2) = 2

x²-2x = 2

x²-2x-2 = 0

Using the quadratic formula, we get the solution of this equation,

x = 1±√3

Hence, there is no real solution of the equation.

Learn more about equation, click;

https://brainly.com/question/29657992

#SPJ7

a standard wooden pencil typically measures around 7 inches to 7.5 inches in length.

The average length of a pencil can vary depending on factors such as the type of pencil, region, and manufacturer. However, a standard wooden pencil typically measures around 7 inches to 7.5 inches in length. This range encompasses the most common lengths found in the market.

It's important to note that there may be slight variations in length between different pencil brands and styles. Additionally, specialty or novelty pencils may have different lengths based on their design or intended purpose.

To obtain a more accurate average length for a specific set of pencils or a particular region, you would need to measure a representative sample of pencils and calculate the average length based on the measurements obtained.

Learn more about Measurement here

https://brainly.com/question/28983562

#SPJ4

The equation of the tangent plane to the surface z = ln(x - 3y) at the point (4, 1, 0) is x - 3y - 1 = 0.

To find the equation of the tangent plane to the surface given by z = ln(x - 3y) at the point (4, 1, 0), we can use the gradient.

The gradient of a function gives the direction of the steepest ascent at any point on the surface. The gradient vector at a point (x, y, z) is given by:

∇f(x, y, z) = (∂f/∂x, ∂f/∂y, ∂f/∂z)

In this case, the function is f(x, y, z) = ln(x - 3y). Taking partial derivatives:

∂f/∂x = 1 / (x - 3y)

∂f/∂y = -3 / (x - 3y)

∂f/∂z = 0

Evaluating the partial derivatives at the point (4, 1, 0):

∂f/∂x = 1 / (4 - 3(1)) = 1 / 1 = 1

∂f/∂y = -3 / (4 - 3(1)) = -3 / 1 = -3

∂f/∂z = 0

Therefore, the gradient vector at the point (4, 1, 0) is ∇f(4, 1, 0) = (1, -3, 0).

Now, we can find the equation of the tangent plane using the point-normal form of a plane. The equation of the plane is:

(x - x0, y - y0, z - z0) · ∇f(x0, y0, z0) = 0

Substituting the values, we have:

(x - 4, y - 1, z - 0) · (1, -3, 0) = 0

Simplifying this equation, we get:

(x - 4) - 3(y - 1) = 0

x - 4 - 3y + 3 = 0

x - 3y - 1 = 0

Therefore, the equation of the tangent plane to the surface z = ln(x - 3y) at the point (4, 1, 0) is x - 3y - 1 = 0.

Learn more about tangent here:

https://brainly.com/question/27021216

#SPJ11

Answer:

You count the cat's ears as the area of a right triangle, the middle as the area of a rectangle, and the cat's chin as the area of a semi-ellipse.

Answer:

C. 35 degrees

Step-by-step explanation:

Answer:

35 is your answer 21 plus 51 plus 73 plus 35

Step-by-step explanation:

ab=CD________given

∆abc=∆acd

Therefore <DAC=<BAC opposite equal sides

Ad||Bc________given

alternative angles are equal

Answer:

the answer is 88

Step-by-step explanation:

so what you have to do is multiply the sum of the length and width by 2

20+24=44          44 times 2 = 88

Step-by-step explanation:

a²+ab+b²

(0)^2 + (0)(1) + (1^2)

  0    +    0    +    1        = 1  

The expression is written as 2x + 2

Algebraic expressions are widely described as those mathematical expressions that are composed of coefficients of variables, then variables, constant values, factors and terms.

These mathematical expressions are also known to be composed of certain arithmetic or mathematical operations.

These operations are listed thus;

From the information given;

Let the number be x

Then, we have that;

x + 1

Double the expression

2(x + 1)

2x + 2

Learn more about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

Thus, the volume of the given oblique pyramid is found as 230 cu. ft.

A pyramid is a 3D polyhedron having three maybe more triangle-shaped surfaces that meet above the base and a polygonal base.

Volume of a Pyramid = 1/3 × Base Area × Height

Base Area = 1/2 * base * height

Base Area = 1/2 *12*5

Base Area = 30 sq. ft

Volume of a Pyramid = 1/3 × 30 × 23

Volume of a Pyramid = 230 cu. ft.

Thus, the volume of the given oblique pyramid is found as 230 cu. ft.

Know more about the pyramid

https://brainly.com/question/13649951

#SPJ1

By simplifying  45y/30y (7x+49)  this  we get 3 / 2(7x + 49).

45y/30y (7x+49)

45y / 30y(7x +49) : 3 / 2(7x + 49)

45y / 30y(7x + 49)

45y / 30(7x + 49)

Factor the number :45 = 15 . 3

=15.3 / 30(7x + 49)

Factor the Number : 30 = 15 . 2

15.3 / 15.2(7x + 49)

Cancel the common factor : 15

= 3 / 2(7x + 49).

To Learn more About simplifying refer to:

https://brainly.com/question/28036586

#SPJ1

First, find the cost of how much fence Mary needs per side.

10 * 5 = 50

10 * 5 = 50

6 * 5 = 30

6 * 5 = 30

Second, add all together.

50 + 50 + 30 + 30 = 160

Therefore, the total cost of the fence will be $160.

Best of Luck!

Answer:

f(x) = |x + 2| + 1

Step-by-step explanation:

The graph of f(x) is translated 2 units to the left and 1 unit up

A horizontal translation of 2 units results in the original function being f(x +2)

A vertical translation of 1 unit happens at f(x) + 1

Horizontal translation of 2 units left of f(x) = |x| is f(x+2) = |x + 2|

Vertical translation of 2 units up : f(x) = |x| + 1

Combined we get g(x) = |x + 2| + 1

In statistics, the estimation of a population parameter based on the statistics of a sample is known as a point estimate.

A point estimate is an estimation of a population parameter based on a single statistic obtained from a sample. The formula for a point estimate is given as:Point estimate = Sample statisticIn the given question, the department store manager wants to estimate the mean amount spent by all customers at this store at a 97% confidence level, and the manager knows that the standard deviation  of amounts spent by all customers at this store is $59. The minimum sample size should be chosen so that the estimate is within $5 of the population mean.

The formula for calculating the minimum sample size required to estimate the population mean with a certain level of confidence is given as: n = (z^2 * σ^2) / E^2Where,n = the minimum sample size required to estimate the population meanz = the z-value for the desired level of confidenceσ = the population standard deviationE = the maximum allowable errorSo, the first step is to find the value of z at the 97% confidence level using the z-table.The z-value for the 97% confidence level is 1.8808 approximately.

To know more about deviation visit:

https://brainly.com/question/29758680

#SPJ11

\(\qquad\qquad\huge\underline{{\sf Answer}}\)

Here we go ~

Slope of the graph can be expressed as :

\(\qquad \sf  \dashrightarrow \:slope = \tan( \theta) = \dfrac{4}{5}\)

\(\qquad \sf  \dashrightarrow \: \dfrac{x}{30} = \dfrac{4}{5} \)

\(\qquad \sf  \dashrightarrow \: x = \dfrac{4}{5} \times 30\)

\(\qquad \sf  \dashrightarrow \: x = {4}{} \times 6\)

\(\qquad \sf  \dashrightarrow \: x = 24 \: units\)

So, the value of x is 24 units

Answer:

10π

Step-by-step explanation:

First, remember the formula for the circumference of a circle is C= 2πr. Then remember that the diameter is twice the radius.

So here, when we have a diameter of 10ft, and we see the formula for circumference is C= 2πr, and because a Diameter is equal to 2 radii, I can also say C= Dπ. So in your case C= 10ft×π = 10ftπ