Somebody please helppp me!

i)  The Cobb-Douglas production function y = \(Ax^1h^1x^2b^2\) is negatively sloped and convex to the origin. ii) These positive signs ensure that the partial derivatives and second-order partial derivatives are positive or non-negative. iii) This equation represents the isocline defined by RTS = 1 for the given Cobb-Douglas production function.

i) To prove that the Cobb-Douglas production function y = Ax^1h^1x^2b^2 is negatively sloped and convex to the origin, we need to show that the partial derivatives with respect to x1 and x2 are positive, and the second-order partial derivatives are non-negative.

Partial derivatives:

∂y/∂x1 = A *\((1 * x^1 * h^1 * x^2b^2) / x1 = A * h^1 * x^2b^2\)

∂y/∂x2 = A *\((1 * x^1 * h^1 * x^2b^2) / x2 = A * x^1 * h^1 * b^2 * x2(b^2-1)\)

The partial derivatives are positive since A, h^1, and x^1 are assumed to be positive parameters.

Second-order partial derivatives:

∂^2y/∂x\(1^2\) = \(A * h^1 * x^2b^2 > 0\)

∂^2y/∂x\(2^2\) = \(A * x^1 * h^1 * b^2 * (b^2-1) * x2(b^2-2) > 0\)

The second-order partial derivatives are non-negative since A, \(h^1,\) and \(b^2\) are assumed to be positive parameters.

Therefore, the Cobb-Douglas production function y = \(Ax^1h^1x^2b^2\) is negatively sloped and convex to the origin.

ii) For the function to be well-behaved, the parameters A, \(h^1,\) and \(b^2\) should have the following signs:

- A should be positive, as it represents the overall productivity level of the production function.

-\(h^1\) should be positive, as it represents the elasticity of output with respect to the input factor x1.

- \(b^2\) should be positive, as it represents the elasticity of output with respect to the input factor x2.

These positive signs ensure that the partial derivatives and second-order partial derivatives are positive or non-negative, leading to a well-behaved and meaningful production function.

iii) The marginal rate of technical substitution (RTS) for a Cobb-Douglas production function is defined as the ratio of the marginal product of one input to the marginal product of the other input:

RTS = (∂y/∂x1) / (∂y/∂x2)

From the partial derivatives calculated earlier, we have:

RTS = \((A * h^1 * x^2b^2) / (A * x^1 * h^1 * b^2 * x2(b^2-1))\)

    =\((x^2b^2) / (x^1 * b^2 * x2(b^2-1))\)

    = \((x^2b^2) / (x^1 * x2(b^2-1))\)

To find the isocline defined by RTS = 1, we set RTS equal to 1:

1 =\((x^2b^2) / (x^1 * x2(b^2-1))\)

Simplifying, we get:

\(x2(b^2-1) = x^1 * x^2b^2\)

This equation represents the isocline defined by RTS = 1 for the given Cobb-Douglas production function.

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Answer:

\(\boxed {x = 4}\)

\(\boxed {\angle 1 = 41\textdegree}\)

\(\boxed {\angle 2 = 139\textdegree}\)

\(\boxed {\angle 3 = 41\textdegree}\)

\(\boxed {\angle 4 = 139\textdegree}\)

Step-by-step explanation:

Both \(\angle 1\) and \(\angle 3\) are Vertical Angles. So, to the find actual measurement both of angles, you need to write an expression by using the following measurements labeled on both \(\angle 1\) and \(\angle 3\), and solve for \(x\):

\(\angle 1 = 8x + 9\)

\(\angle 3 = 14x - 15\)

\(8x + 9 = 14x - 15\)

-Solve:

\(8x + 9 = 14x - 15\)

\(8x + 9 - 14x = 14x - 14x - 15\)

\(-6x + 9 = -15\)

\(-6x + 9 = -15 - 9\)

\(-6x = -24\)

\(\frac{-6x}{-6} = \frac{-24}{-6}\)

\(\boxed {x = 4}\)

After you have the value of \(x\), use it to find the actual measurement of \(\angle 1\)and \(\angle 3\):

-The value of \(x\):

\(x = 4\)

-Finding the measurement of \(\angle 1\):

\(8x + 9\)

\(8(4) + 9\)

\(32 + 9\)

\(41\)

\(\boxed {\angle 1 = 41\textdegree}\)

-Finding the measurement of \(\angle 3\):

\(14x - 15\)

\(14(4) - 15\)

\(56 - 15\)

\(41\)

\(\boxed {\angle 3 = 41\textdegree}\)

After you have the actual measurements of \(\angle 1\) and \(\angle 3\), find the actual measurements of \(\angle 2\) and \(\angle 4\).  \(\angle 1\) and \(\angle 2\) are both supplementary (two angle that add up to \(180\textdegree\)), you need to find the measurement of \(\angle 2\) by subtracting the measurement of \(\angle 1\) from \(180\textdegree\). Same thing for \(\angle 3\) and \(\angle 4\):

-Finding the measurement of \(\angle 2\):

\(180\textdegree - \angle 1\)

\(180\textdegree - 41\textdegree\)

\(139\textdegree\)

\(\boxed {\angle 2 = 139\textdegree}\)

-Finding the measurement of \(\angle 4\):

\(180\textdegree - \angle 3\)

\(180\textdegree - 41\textdegree\)

\(139\textdegree\)

\(\boxed {\angle 4 = 139\textdegree}\)

And were done.

Answer:

105 is corresponding to angle B, meaning they are congruent. B and x are supplementry meaning they should add up to equal 180.

Since 180 - 105 = 75, those would be your steps and x is 75

Step-by-step explanation:

Answer:

e=9.14

Step-by-step explanation:

e²=a²+b²-2abcosФ

e²=36+25-2(30)cos112

e=√36+25-2(30)cos112

e=9.14

Answer:

2.Jen's school is farther from home than Paris's school.

Step-by-step explanation:

hyy there ! it may be but not that sure .

The creation story in Christianity exemplifies commitment creativity, obligation, generosity and service.

These values are demonstrated through God's actions and intentions in creating the world and his instructions to humanity to care for it.

Commitment, creativity, obligation, generosity and service are exercised in the creation story of Christianity:

Commitment:

In Christianity, the creation story in Genesis 1 shows God's commitment to creating the world in six days and resting on the seventh day.

This story shows that God was committed to his creation and intended it to be good.

Creativity:

The creation story in Genesis 1 also shows God's creativity in designing and bringing forth the world.

The story describes how God created the heavens and the earth, light, the seas and all living creatures, demonstrating his power and creativity.

Obligation:

In Christianity the creation story also demonstrates God's obligation to care for and provide for his creation.

In Genesis 1:29-30, God gives humans and animals all the plants and fruits on the earth for food showing his obligation to provide for them.

Generosity:

Similarly God's generosity is displayed in the creation story of Christianity.

God creates a world filled with beauty and abundance, with all the resources necessary for life to thrive.

He also gives humans and animals the ability to reproduce and multiply showing his generosity in sustaining life.

Service:

The creation story in Christianity also highlights the importance of service.

In Genesis 2:15 God places Adam in the Garden of Eden and instructs him to work and take care of it.

This shows the value of serving and caring for God's creation.

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When b = 7 and c = 6, the value of a is equal to 3,409.08, given that a is jointly proportional to the square of b and the square of c and a = 371 when b = 5 and c = 3.

We know that a is jointly proportional to b² and c²,

which means that a = k(b²)(c²) for some constant k.

We can use the information given to solve for k:

⇒ a = k(b²)(c²)

⇒ 371 = k(5²)(3²)

⇒ 371 = k(25)(9)

⇒k = 371 / (25)(9)

⇒ k = 1.646

Now that we have k,

We can use it to find the value of a when b = 7 and c = 6:

⇒ a = k(b²)(c²)

⇒ a = 1.646(7²)(6²)

⇒ a = 1.646(49)(36)

⇒ a = 3,409.08

Therefore, when b = 7 and c = 6, a is equal to 3,409.08.

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The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Step-by-step explanation:

-5x+2y= 4         <==== Multiply entire equation by -3 to get:

15x-6y = -12  

2x+3y= 6          <====  Multiply entire equation by 2 to get :

4x+6y = 12    Add the two underlined equations to eliminate 'y'

19x = 0     so x = 0

sub in x = 0 into any of the equations to find:  y = 2

(0,2)

Answer:

13.83

Step-by-step explanation:

\(hf = \sqrt{({6 - 6 })^{2} +( {2 - 5)}^{2} }\)

\( = \sqrt{0 + {( - 3)}^{2} } \)

\( = \sqrt{0 + 9} = \sqrt{9} = 3\)

\(gf = \sqrt{ {(6 - 1)}^{2} + {(2 - 2)}^{2} } \)

\( = \sqrt{ {5}^{2} + {0}^{2} } \)

\( = \sqrt{ {5}^{2} } = 5\)

\(gh = \sqrt{ {(6 - 1)}^{2} + {(5 - 2)}^{2} } \)

\( = \sqrt{ {5}^{2} + {3}^{2} } \)

\( \sqrt{25 + 9} \)

\( = \sqrt{34} = 5.83\)

perimeter = 3+5+5.83 = 13.83

Answer:

\(\approx\) -2.195

Step-by-step explanation:

Given the function:

\(d(t)= 12 (.72) ^ t\)

\(d\) is the depth of water in feet and

\(t\) is the amount of time

To find:

The average rate of change for \(t\) in the interval [0, 4].

Solution:

The required rate of change in the time interval [0, 4] can be represented as:

Change in the function over the interval [0, 4] and the change in the interval.

OR

\(\Rightarrow \dfrac{d(4)-d(0)}{4-0}\\\Rightarrow \dfrac{12 (.72) ^ 4-12 (.72) ^ 0}{4-0}\\\Rightarrow \dfrac{3.22-12 \times 1}{4}\\\Rightarrow \dfrac{3.22-12}{4}\\\Rightarrow \dfrac{-8.78}{4}\\\Rightarrow \bold{-2.195}\)

Answer:

1. splitting water into hydrogen and oxygen

Step-by-step explanation:

Answer:

Photosynthesis takes place in two stages: the light-dependent reactions and the Calvin cycle. In the light-dependent reactions, which take place at the thylakoid membrane, chlorophyll absorbs energy from sunlight and then converts it into chemical energy with the use of water.

Step-by-step explanation:

can u pls go answer my question? Thank you and have a nice day :)

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Answer:

15

Step-by-step explanation:

you just put 5/6 x 18 in calculator, please rate 5 stars :)

Answer:

15 pencils.

Step-by-step explanation:

Multiply 18 and 5/6 to find the answer.

\((18)(\frac{5}{6})=15\)

Therefore, she will have given away 15 pencils.

Answer:

In 25 minutes, the monthly phone charges of both companies will be the same.

Step-by-step explanation:

If we allow m to represent the number of minutes, we can create two equations for C, the total cost of phone charges from both companies:

Phoenix equation:  C = 0.5m + 30

Nuphone equation: C - 0.10m + 40

Now, we can set the two equations equal to each other.  Solving for m will show us how many minutes must Abby use for the total cost at both companies to be the same:

0.5m + 30 = 0.10m + 40

Step 1:  Subtract 30 from both sides:

(0.5m + 30 = 0.10m + 40) - 30

0.5m = 0.10m + 10

Step 2:  Subtract 0.10m from both sides:

(0.5m = 0.10m + 10) - 0.10m

0.4m = 10

Step 3:  Divide both sides by 0.4 to solve for m (the number of minutes it takes for the total cost of both companies to be the same)

(0.4m = 10) / 0.4

m = 25

Thus, Abby would need to use 25 minutes for the total cost at both companies to be the same.

Optional Step 4: Check the validity of the answer by plugging in 25 for m in both equations and seeing if we get the same answer:

Checking m = 25 with Phoenix equation:

C = 0.5(25) + 30

C = 12.5 + 30

C = 42.5

Checking m = 25 with Nuphone equation:

C = 0.10(25) + 40

C = 2.5 + 40

C = 42.5

Thus, m = 25 is the correct answer.

Let's simplify step-by-step.

−3x2−5x2(4x3−x2)(2)

Distribute:

=−3x2+−40x5+10x4

Answer:

=−40x5+10x4−3x2

Step-by-step explanation:

f(x) = -x-2

in finding x we need to implies that we already know f(x) = 12

therefore:

f(x) = -12 - 2

we need to know this laws that - × - is = +

this give us to the final answer:

12 + 2 = 14

Answer:

14

Step-by-step explanation:

y = 12

12 = x - 2

14 =x

The completed statements with regards to the compound interest of the amount in the account are;

If the account has a 5% interest rate and is compounded monthly, you have $101.655 million money after 2 years

If the account has a 5% interest rate compounded continuously, you would have $106.096 million money after 2 years

Compound interest is the interest calculated based on the initial amount and the accumulated interests accrued from the periods before the present.

The compound interest formula indicates that we get;

\(A = P\cdot (1 + \frac{r}{n}) ^{n\cdot t}\)

Where;

P = The principal amount invested = $92 million

r = The interest rate = 5% monthly

n = The number of times the interest is compounded per annum = 12

t = The number of years = 2 years

Therefore; \(A = 92\cdot (1 + \frac{0.05}{12}) ^{12\times 2}\approx 101.655\)

The amount in the account after 2 years is therefore about $101.655 million

The formula for the amount in the account if the principal is compounded continuously, we get;

A = \(P\cdot e^{(r\cdot t)}\)

Therefore, we get;

\(A = 96 \times e^{0.05 \times 2} \approx 106.096\)

The amount in the account after 2 years, compounded continuously therefore, is about $106.096 million

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Circumference of a circle with equation \((x+2)^{2}+(y-3)^{2}\) = 9 is 6pi.

To find the circumference of a circle with equation  \((x+2)^{2}+(y-3)^{2}\) = 9, we first need to identify its radius, which is the square root of the constant term 9. The radius is therefore 3 units.

The formula for the circumference of a circle is C = 2πr, where C is the circumference, r is the radius, and π is a mathematical constant approximately equal to 3.14159.

Using this formula, we can calculate the circumference of the given circle as:

C = 2πr = 2π(3) = 6π

Therefore, the circumference of the circle with equation  \((x+2)^{2}+(y-3)^{2}\) = 9 is 6π units.

It's important to note that the circumference of a circle is the distance around the edge of the circle. It is an important parameter for many applications in geometry, physics, and engineering, among others. Being able to calculate the circumference of a circle given its equation is a fundamental skill in mathematics and is essential for solving many problems in different fields.

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Grayce has 0.825 g of diamonds and Morgan has 0.824 g of diamonds. Grayce has more grams of diamonds

From the question, we are to determine the person that has more grams of diamonds

From the given information,

"Grayce has three diamonds that weigh 0.275 g each"

and

"Morgan has two diamonds that weigh 0.412 g each"

Thus,

The total mass of Grayce's diamonds is 3 × 0.275 g

3 × 0.275 g = 0.825 g

Also,

The total mass of Morgan's diamonds is 2 × 0.412 g

2 × 0.412 g = 0.824 g

Since 0.825 is greater than 0.824,

Then,

Grayce has more grams of diamonds.

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3) The extra number of feet of coiled tubing Tom needs to run into the well is: 5445 ft

4) The total length of coiled tubing Brendan ran in the wellbore is: 994 ft

5) The distance that the coiled tubing has reached after the first four hours is:  a depth of 16,776 feet in the well.

3) Initial amount of coiled tubing he had after 81 minutes = 9,153 feet

Amount of tubing after another 10 minutes = 10,283 feet

The total tubing required = 15,728 feet.

The extra number of feet of coiled tubing Tom needs to run into the well is: Needed tubing length - Current tubing length

15,728 feet - 10,283 feet = 5,445 feet

4) Speed at which Brendan is running coiled tubing = 99.4 feet per minute.

Coiled tubing inside the wellbore after 8 minutes is: 795.2 feet

Coiled tubing inside the wellbore after 2 more minutes is: 198.8 feet

The total length of coiled tubing Brendan ran in the wellbore is:

Total length = Initial length + Additional length

Total length =  795.2 feet + 198.8 feet

Total Length = 994 feet

5) Rate at which coiled tubing is being run into a 22,000-foot wellbore = 69.9 feet per minute. After the first four hours, we need to determine how deep the coiled tubing has reached.

A time of 4 hours is same as 240 minutes

Thus, the distance covered in the first four hours is:

Distance = Rate * Time

Distance = 69.9 feet/minute * 240 minutes

Distance = 16,776 feet

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Answer:

The height above ground when the ride stops is 96 feet

Step-by-step explanation:

The given diameter of the carnival ride, d = 120 ft.

The height of the ride above the ground, h = 6 ft.

The angle through which the ride is rotated, θ = 240° counterclockwise

Therefore, we have;

The radius of the ride, r = d/2

∴ r = 120 ft./2 = 60 ft.

We note that at 180° rotation, the ride is at the highest point, \(h_{max}\) = 6 ft. + 120 ft. = 126 ft.

When the ride rotates a further 240° - 180° = 60° the height drops from the maximum point by y = 60 ft. × cos (60°) = 30 ft., such that the final height above ground is therefore;

h = 126 ft. - 30 ft. = 96 ft.

The height above ground when the ride stops, h = 96 ft.

Answer:is there more info

Step-by-step explanation:

Answer:

c^2 - b

Step-by-step explanation:

There are no like terms.

By working with the exponential equation we will get:

i) N = 1000

ii) k = -0.02

iii) t = 34.66 seconds

Here we know that the equation:

\(N = 1000*e^{-k*t}\)

models the population at a time t.

i) When t = 0, we have:

\(N = 1000*e^{-k*0}\\N = 1000*1\\N = 1000\)

That is the initial population of bacteria.

ii) at t = 0, the rate of decay is -20 /min

the differentiation of the exponential gives:

\(N' = -k*1000*e^{-k*t}\)

And evaluating that in t = 0 should give -20., then:

\(-20 = -k*1000*e^{-k*t}\\\\-20 = -k*1000\\-20/1000 = -k\\-0.02 = -k\\0.02 = k\)

That is the value of k.

iii) Here we need to solve the equation:

\(500= 1000*e^{-0.02*t}\\\\0.5 = e^{-0.02*t}\\\\ln(0.5) = ln(e^{-0.02*t})\\\\ln(0.5) = -0.02*t\\\\ln(0.5)/ -0.02 = t\\ \\34.66 = t\)

So it will take 34.66 seconds to reach half of the initial population.

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Given:

Step by step solution:

We need to comment on the number of solutions of the equation:

From here we can say that y will have only one solution, which is equal to y = 15.

Answer:

2 miles per hours

Step-by-step explanation:

You divide 1/3 mile by 1/6 hour

Use the reciprocal.

1/3 x 6/1 = 2/1

Simplify

2/1 = 2

You can also solve it this way:

If 1/6 hour is 10 minutes, and it takes 10 minutes to walk 1/3 a mile, then it would take 30 minutes to walk a mile.

30 x 2 = 60

Either way, Richard walks 2 miles per hour.

Richard is walking at an average speed of 2 miles per hour which is the correct answer would be option (B).

Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.

To determine how fast is Richard walking, in miles per hour

We have to calculate the average speed which is the ratio of the total distance traveled by a body to the total time

Total distance traveled by Richard = 1/3 mile

The total time taken = 1/6 hour

Average speed = the total distance / the total time

Average speed = (1/3) / (1/6)

Reciprocal the denominator term, and we get

Average speed = (1/3) × 6

Average speed = 2 miles per hour

Therefore, he is at an average speed of 2 miles per hour

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Answer:

Answer. circumference = 151 m ( appr.) Ans :- The cost of fencing is Rs 604 .

x = 5pi/6 is not in the interval [0, pi/2]

Starting with the given equation:

4 cos x - 8 sin x cos x = 0

We can factor out 4 cos x:

4 cos x (1 - 2 sin x) = 0

So either cos x = 0 or (1 - 2 sin x) = 0.

If cos x = 0, then x = pi/2 since we're only considering the interval [0, pi/2].

If 1 - 2 sin x = 0, then sin x = 1/2, which means x = pi/6 or x = 5pi/6 in the interval [0, pi/2].

So the two solutions in the interval [0, pi/2] are x = pi/2 and x = pi/6.

That x = 5pi/6 is not in the interval [0, pi/2].

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The given equation is 4 cos x - 8 sin x cos x = 0. To find the solutions in the interval [0, pi/2], we need to solve for x.
Find the solutions within the given interval. Equation: 4 cos x - 8 sin x cos x = 0

First, let's factor out the common term, which is cos x:

cos x (4 - 8 sin x) = 0

Now, we have two cases to find the solutions:

Case 1: cos x = 0
In the interval [0, π/2], cos x is never equal to 0, so there is no solution for this case.

Case 2: 4 - 8 sin x = 0
Now, we'll solve for sin x:

8 sin x = 4
sin x = 4/8
sin x = 1/2

We know that in the interval [0, π/2], sin x = 1/2 has one solution, which is x = π/6.

So, in the given interval [0, π/2], the equation has only one solution: x = π/6.

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Answer:

18

Step-by-step explanation:

We can rewrite the question into mathematical forms, such as:

\(\frac{3}{1} =\frac{x}{6}\)

solve for x:

\(\frac{3}{1} =\frac{x}{6} \\\\3*6=\frac{x}{6}*6\\\\18=x\)

Answer:

0.2 lb of ham in decimal digits

Step-by-step explanation:

At a grocery store, you want to buy 2/1/10 lb of ham

2 / 1 divided by 10

2/1 = 2 so now

2/ 10 = 1/ 5

Hence, 0.2lb of ham in decimal digits

Answer: May

Step-by-step explanation: