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2 years ago

14

1/3 - 3 (2/7x - 4) Which of the expressions are equivalent to the expression above? A) 1/3 - (3)(2/7x)-(3)(4) B) 1/3 - 6/7x + 12

C) -11 2/3 - 6/7x D) 12 1/3 - 6/7x E) 1/3 - 6(1/7x - 2) F) 1/3 + (-3)(2/7x) -(3)(4)

1 answer:

KiRa [710]2 years ago

6 0

1/3 - 3 (2/7x - 4)

distribute factor out a 2

1/3 - 3* 2/7 x - 3*(-4) 1/2 - 6 (1/7x-2) Choice E

1/3 - 3* 2/7 x + 12 Choice B

12 1/3 - 6/7 x Choice D

Answers: B,D,E

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Answer:

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The marginal revenue is $MR=580-20x$ .

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Step-by-step explanation:

The Total Revenue ( $TR$ ) received from the sale of $x$ goods at price $p$ is given by

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The Marginal Revenue ( $MR$ ) is the derivative of total revenue with respect to demand and is given by

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From the information given we know that the price they can sell cakes is given by the function $p=580-10x$ , where $x$ is the number of cakes sold per day.

So, the total revenue is

$TR=(580-10x)\cdot x\\TR=580x-10x^2$

And the marginal revenue is

$MR=\frac{d}{dx}(580x-10x^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\MR=\frac{d}{dx}\left(580x\right)-\frac{d}{dx}\left(10x^2\right)\\\\MR=580-20x$

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The Marginal Cost ( $MC$ ) function is the derivative of the cost function and is given by

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We know that the total cost function of the company is given by $C=(30+5x)^2$ , which it is equal to

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a+b\right)^2=a^2+2ab+b^2\\a=30,\:\:b=5x\\\\\left(30+5x\right)^2=30^2+2\cdot \:30\cdot \:5x+\left(5x\right)^2=25x^2+300x+900\\\\C=25x^2+300x+900$

From the total cost function and applying the definition of fixed cost, the fixed cost is $900.

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$MC=\frac{d}{\:dx}\left(25x^2+300x+900\right)\\\\MC=\frac{d}{dx}\left(25x^2\right)+\frac{d}{dx}\left(300x\right)+\frac{d}{dx}\left(900\right)\\\\MC=50x+300+0=50x+300$

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