Which of these ordered pairs is a solution to the linear inequality 3y – 2x ≥ 8? (1, 3) (3, 1) (–4, 2) (2,

Artist 52 [7]

the 20x(8+2) is just two times greater as its 200 instead of 100 which is the other answer

4 0

2 years ago

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

2 years ago

21x =7? A. x=3 B. None of these C. x=147 D. x=28

Varvara68 [4.7K]

Answer: B

Step-by-step explanation:

To isolate x, you divide both sides by 21

21x=7

$\frac{21x}{21}=\frac{7}{21}$

x = 7/21

Simplify by dividing both the numerator and denominator by 7

x = 1/3

Since, 1/3 is not an option, B is the correct answer

6 0

1 year ago

How to simplify -3 (4×-5y-5×)

Phoenix [80]

-12x + 15y + 15x
3x + 15y

4 0

2 years ago

If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dx/dt

valina [46]

The area of a circle in terms of the circle's radius $r$ is

$A=\pi r^2$

Differentiating both sides with respect to $t$ , you get

$\dfrac{\mathrm dA}{\mathrm dt}=2\pi r\dfrac{\mathrm dr}{\mathrm dt}$

3 0

3 years ago

Which of these ordered pairs is a solution to the linear inequality 3y – 2x ≥ 8? (1, 3) (3, 1) (–4, 2) (2, –4)