Find the missing side. Round to the nearest tenth

Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers

lora16 [44]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

$\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}$

Where P is the number of eggs laid, x is the number of workers, and y is the daily operating budget (assuming in US dollars $).

A)

We want to find dy/dx.

So, let’s find our equation in terms of x. We can raise both sides to 10/7. Hence:

$\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}$

Simplify:

$\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y$

Divide both sides by the x term to acquire:

$\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}$

Take the derivative of both sides with respect to x:

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]$

Apply power rule. Note that P is simply a constant. Hence:

$\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})$

Simplify. Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

We want to evaluate the derivative when x is 30 and when y is $10,000.

First, we will need to find P. Our original equations tells us that:

$P=x^{0.3}y^{0.7}$

Hence, at x = 30 and at y = 10,000, P is:

$P=(30)^{0.3}(10000)^{0.7}$

Therefore, for our derivative, we will have:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)$

Use a calculator. So:

$\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143$

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0

3 years ago

What value of x is in the solution set of 3(x – 4) > 5x + 2?

bonufazy [111]

We have to simplify and get the value of x from this inequality given:

Given inequality,

$3(x - 4) > 5x + 2$

Now let's simplify by using distributive property,

$3x - 12 > 5x + 2$

We need to find x, so let's isolate x to the letter side of the inequality for calculation at ease.

$3x - 12 - 5x - 2 > 0$

$- 2x - 14 > 0$

Now, dividing -2 from both sides.

Note : As we are dividing a negative number from both sides, the sign of the inequality will be reversed.

$\dfrac{ - 2x - 14}{ - 2} > \dfrac{0}{ - 2}$

$x + 7 < 0$

Now subtracting -7 from both sides,

$x + 7 - 7 < 0 - 7$

$x < - 7$

Or, Interval of the equal $(- \infin, -7 ]$

#CarryOnLearning

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3 0

3 years ago

PLEASE HELP! I AM CONFUSED! Explain your answer, thank you so much! (I will give brainlyest)

antiseptic1488 [7]

Answer:

y+3 = 2(x-4)

Step-by-step explanation:

If we have a slope and a point, we can use the point slope form for an equation of a line

y -y1= m(x-x1)

where m is the slope and (x1,y1) is the point

y--3 = 2(x-4)

y+3 = 2(x-4)

8 0

3 years ago

Read 2 more answers

2. What is the solution of (-8x)= 32?

raketka [301]

Answer:

x=-4

Step-by-step explanation:

divide 32 by 8 and move the negative sign to the result.

6 0

3 years ago

What is the domain of the function on the graph?

MA_775_DIABLO [31]

Answer:

Option 2

Step-by-step explanation:

4 0

3 years ago