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3 years ago

Find the value of c so that (x+2) is a factor of the polynomial p(x). p(x)=4x^3+cx^2+x+2

Mathematics

1 answer:

Wittaler [7]3 years ago

6 0

Answer:

c = 8

Step-by-step explanation:

Use synthetic division here; it's the fastest approach.

Given that (x + 2) is a factor, take -2 and use this as the divisor in synthetic division:

-2 4 c 1 2

-8 (-2c+ 16) (4c-34)

---------------------------------------------

4 (c - 8) (-2c + 17) 4c - 32

The remainder, 4c - 32, must equal zero if (x + 2) is a factor.

Then 4c - 32 = 0, and c = 8

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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

I need help with a b c d

Lady_Fox [76]

Answer:

Step-by-step explanation: 2 is the real population

7 0

3 years ago

What is -32 divided by 9

soldier1979 [14.2K]

The answer is −3.555555555555556 but you can just put -3.55

8 0

3 years ago

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A doctor can complete 3 examinations in 2 hours. How many examinations can the doctor complete in 5 hours?

Levart [38]

I believe it to be six but than again I could be sadly wrong

3 0

3 years ago

Read 2 more answers

A copy machine makes

IrinaK [193]

This problem can be represented in a formula with fractions. To make it more simple, we are converting 5m30s to just pure seconds, which = 154 copies in 330 seconds.

You set up the formula like this: 154/330 = x/60. (it is x/60 because you want to know the x amount of copies per 60 seconds)

Cross multiply, you get 330x = 9240. Divide both sides by 330, you get:

x = 28 copies.

The final answer is 28 copies per minute

7 0

3 years ago