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2 years ago

Find all numbers whose absolute value is 6.

Mathematics

1 answer:

posledela2 years ago

4 0

Answer:

6 and -6

Absolute value mans the distance a number is away from 0.

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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

2 years ago

PLEASE HELP GIVE YOU BRAINLYEST

Harrizon [31]

Answer:

(-6,0)

Step-by-step explanation:

the y-axis is any (x number, 0)

8 0

2 years ago

Six less than the product of 7 and a number equals 5.

VARVARA [1.3K]

Answer:

x = 11/7 or 1.57

Step-by-step explanation:

let the number be x

now :

=》the product of 7 and the number

7 × x = 7x

=》6 less than the product

7x - 6

=》now, we know :

7x - 6 = 5

7x = 6 + 5

7x = 11

x = 11 / 7

7 0

2 years ago

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The double box plot shows the test scores for Miss Robinson's second and fourth period

Afina-wow [57]

Answer: The second period class has the greater first quartile.

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3 years ago

Which equation represents the graphed function?

inessss [21]

Answer:

mathmiticians: impossible

Step-by-step explanation:

some random kid: the answer is approxamatly 47.7

3 0

2 years ago