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
1 answer:
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
Then the length of the popcorn box in inches will be
More about the rectangular prism link is given below.
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Answer:
Part A)
Part B)
The daily operating cost decreases by about $143 per extra worker.
Step-by-step explanation:
We are given the equation:
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:
Simplify:
Divide both sides by<em> </em>the <em>x</em> term to acquire:
Take the derivative of both sides with respect to <em>x: </em>
Apply power rule. Note that P is simply a constant. Hence:
Simplify. Hence, our derivative is:
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:
Hence, at <em>x</em> = 30 and at <em>y</em> = 10,000, <em>P </em>is:
Therefore, for our derivative, we will have:
Use a calculator. So:
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.
B is the correct answer
good luck
good luck
The answer is m=5 and m=-2. There is no extraneous solution for this equation.
