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ycow [4]
3 years ago
12

The revenue equation (in hundreds of millions of dollars) for barley production in a certain country is approximated by R(x) = 0

.0613x​2 +​ 1.1584x + 2.4813 where x is in hundreds of millions of bushels. Find the marginal-revenue equation and use it to find the marginal revenue for the production of the given number of bushels.1) The marginal-revenue equation is R' (x) = _______2) Find the marginal revenue for the production of 200,000,000 bushels______3) Find the marginal revenue for the production of 650,000,000______ ​
Mathematics
1 answer:
STatiana [176]3 years ago
3 0

Answer:

The marginal-revenue equation is R'(x)=0.1226x+1.1584.

The marginal revenue for the production of 200,000,000 bushels is R'(x)=1.4036.

The marginal revenue for the production of 650,000,000 bushels is R'(x)=9.1274.

Step-by-step explanation:

The derivative R'(x) of the revenue function is called the marginal revenue function and is the rate of change of revenue with respect to the number of units sold.

We know the revenue function, R(x) = 0.0613x^{2} +1.1584x+2.4813. Therefore, the marginal revenue function is

R'(x)=\frac{d}{dx}R(x) = \frac{d}{dx}(0.0613x^{2} +1.1584x+2.4813)\\\\=\frac{d}{dx}\left(0.0613x^2\right)+\frac{d}{dx}\left(1.1584x\right)+\frac{d}{dx}\left(2.4813\right)\\\\R'(x)=0.1226x+1.1584

To find the marginal revenue for the production of:

200,000,000 bushels we use x = 2, since x is in units of hundreds of million of dollars.

R'(x)=0.1226\cdot \:2+1.1584\\\\R'(x)=0.2452+1.1584\\\\R'(x)=1.4036

650,000,000 bushels we use x = 65, since x is in units of hundreds of million of dollars.

R'(x)=0.1226\cdot \:65+1.1584\\\\R'(x)=7.969+1.1584\\\\R'(x)=9.1274

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What is the slope of the line? <br>y = -2/7x<br><br>A. -2<br>B. -2/7<br>C. 0<br>D. 2/7​
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4 0
3 years ago
1) -24, -4, 16, 36, ...<br> Find a23
viktelen [127]

We're given the Arithmetic Progression <em>-24, -4, 16, 36 ...</em> .

We know that a term in an AP is generally represented as:

\bf a_n\ =\ a\ +\ (n\ -\ 1)d

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We need to find \sf a_2_3.

From the given progression, we have:

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Using these in the formula,

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Therefore, the 23rd term in the AP is -464.

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