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3 years ago

What is the y-intercept? y-3=1\2(x+2)

1 answer:

6 0

Y-3=1/2(x+2)

To find the y-intercept, we must first get the equation in slope intercept form. Start off by distributing 1/2 into the parentheses.

y-3= 1/2x+1
Add 3 to both sides

y= 1/2x+4

The slope is whatever is in front of x, in this case, 1/2. The y-intercept is the number after that which would be 4

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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

What is the value of y?

scZoUnD [109]

All angles in triangle inside add up to 180
so

the angles are y, 79,37
therefor
y+79+37=180
solvde for y
y+79+37=180
add
y+116=180
subtract 116 from ot hsides
y=64

angle y=64 degrees

7 0

3 years ago

(-4k4 + 14 + 3k?) + (-364 - 14k - 8)

zepelin [54]

Answer:

it equals 38 because eit makes alot of sense and I e it with

5 0

3 years ago

What is 4,000,275,000 in word form?

castortr0y [4]

Answer:

Four billion, two-hundred seventy five thousand.

4 0

3 years ago

Read 2 more answers

Zach only wants to plant a group of ten flowers in each box is there any way that Zach could plant all 53 flowers using only box

Sveta_85 [38]

Answer:

5.3

Step-by-step explanation:

first u have to get ur numbers then divide 53 by 10

4 0

3 years ago