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3 years ago

I dont understand this

Mathematics

1 answer:

kirza4 [7]3 years ago

4 0

Step-by-step explanation:

first u find the angles and then u use some low divide the length of triangle by sin of opposite angles

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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 $).

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

A line has a slope of 2 and passes through the point (3, 9). Which is the equation of the line?

Oxana [17]

We know, y - y1 = m(x - x1)
y - 9 = 2(x - 3)
y - 9 = 2x - 6
y = 2x + 3

In short, Your Answer would be Option B

Hope this helps!

3 0

3 years ago

What is the volume of the square pyramid with base edges 12cm height 10cm

Alina [70]

V=480cm³ . 10 and 12

4 0

3 years ago

What is the slope between (-4,0) and (0,2)

zaharov [31]

The slope is y=1/2x + 2 or y= 0.5x+2

3 0

3 years ago

Read 2 more answers

Please answer this and I’ll make you Brainly

murzikaleks [220]

Answer:

-4 = ?

Step-by-step explanation:

Step 1: Substitute -1 for x

7x^3 + 5x^2 - 2 = ?

7(-1)^3 + 5(-1)^2 - 2 = ?

7(-1) + 5(1) - 2 = ?

-7 + 5 - 2 = ?

-4 = ?

Answer: -4 = ?

3 0

3 years ago