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4 years ago

X+4(2+3) < 5x is there a solution??

Mathematics

1 answer:

zavuch27 [327]4 years ago

5 0

Answer:

$\Huge\boxed{\mathsf{\longrightarrow X>5}}$

Step-by-step explanation:

Isolate x on one side of the equation.

First, do parenthesis.

4(2+3)

Add.

3+2=5

Multiply.

4*5=20

Rewrite the equation problem.

x+20<5x

Secondly, subtract 20 from both sides.

x+20-20<5x-20

Solve.

x<5x-20

Thirdly, subtract 5x from both sides.

x-5x<5x-20-5x

Solve.

5-1=4

-4x<-20

Then, multiply -1 from both sides.

(-4x)(-1)>(-20)(-1)

Solve.

(-4x)(-1)=4x

(-20)(-1)=20

4x>20

Divide by 4 from both sides.

4x/4>20/4

Solve.

20/4=5

x>5

$\Large\boxed{\mathsf{\Rightarrow X>5}}}$

The solutions is 5, therefore, the correct answer is x>5.

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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.

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3 years ago

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dezoksy [38]

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Hope this helps! :)

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Step-by-step explanation:

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3 years ago

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Vilka [71]

Answer:

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