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KengaRu [80]
2 years ago
11

Gabriel models the volume of a popcorn box as a right rectangular prism and the box can hold 74 cubic inches of popcorn when it

is full. its width is 3 and 1/2 in and its height is 77 in. find the length of the popcorn box in inches. round your answer to the nearest tenth if necessary.
Mathematics
1 answer:
vodka [1.7K]2 years ago
4 0

If the volume of the popcorn box is 74 cubic inches. Then the length of the popcorn box in inches will be 0.3 inches.

<h3>What is a rectangular prism?</h3>

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

Gabriel models the volume of a popcorn box as a right rectangular prism and the box can hold 74 cubic inches of popcorn when it is full.

Its width is 3 and 1/2 in and its height is 77 in.

Then the width of the prism will be

\rm W  = 3 + \dfrac{1}{2}\\\\W = \dfrac{7}{2}

Then the length of the popcorn box in inches will be

\rm V  \ = LWH\\\\\\74= L \times \dfrac{7}{2} \times 77\\\\\\L\ = 0.2745 \approx 0.3

More about the rectangular prism link is given below.

brainly.com/question/12649592

#SPJ1

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7 0
4 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 <em>P</em> is the number of eggs laid, <em>x</em> is the number of workers, and <em>y</em> 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 <em>x</em>. 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<em> </em>the <em>x</em> term to acquire:

\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}

Take the derivative of both sides with respect to <em>x: </em>

\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 <em>x</em> is 30 and when <em>y</em> is $10,000.

First, we will need to find <em>P</em>. Our original equations tells us that:

P=x^{0.3}y^{0.7}

Hence, at <em>x</em> = 30 and at <em>y</em> = 10,000, <em>P </em>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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Answer:

4

Step-by-step explanation:

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