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Lisa [10]
3 years ago
10

The average cost per unit for the production of a certain brand of DVD is given by C=\frac{500+60c+0.01x^2}{x} , where x is the

number of units produced.
The is a line _ over the C, don't know what that means.

A. What is the average cost per unit when 500 units are produced? 60 units? 100 units?

B. Is it reasonable to say that the average cost continues to fall as the number of units produced rises?

Mathematics
1 answer:
Ganezh [65]3 years ago
7 0

Answer:

  A: for 500: 66; for 60: 68.9; for 100: 66

  B: no

Step-by-step explanation:

We assume your average cost function is ...

  \overline{C}=\dfrac{0.01x^2+60x+500}{x}

A. The overline over the C indicates it is an average value.

Evaluating the cost function at the different production levels, we find the average cost per unit to be ...

<u>500 units</u>

  c = ((0.01·500)+60)500 +500)/500 = 65 +1 = 66

<u>60 units</u>

  c = ((0.01·60 +60)·60 +500)/60 = 60.6 +500/60 ≈ 68.93

<u>100 units</u>

  c = ((0.01·100 +60)·100 +500)/100 = 61 +5 = 66

__

B. Dividing out the fraction, we find that the cost per unit is ...

  0.01x +60 +500/x

As x gets large, this approaches the linear function c = 0.01x +60. This <em>increases</em> as the number of units produced rises. (The minimum average cost is at a production level of about 224 units.)

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zysi [14]

Considering the definition of zeros of a function, the zeros of the quadratic function f(x) = x² + 4x +9 do not exist.

<h3>Zeros of a function</h3>

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

In summary, the roots or zeros of the quadratic function are those values ​​of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

In a quadratic function that has the form:

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the zeros or roots are calculated by:

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<h3>This case</h3>

The quadratic function is f(x) = x² + 4x +9

Being:

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the zeros or roots are calculated as:

x1=\frac{-4+\sqrt{4^{2}-4x1x9 } }{2x1}

x1=\frac{-4+\sqrt{16-36 } }{2x1}

x1=\frac{-4+\sqrt{-20 } }{2x1}

and

x2=\frac{-4-\sqrt{4^{2}-4x1x9 } }{2x1}

x2=\frac{-4-\sqrt{16-36 } }{2x1}

x2=\frac{-4-\sqrt{-20} }{2x1}

If the content of the root is negative, the root will have no solution within the set of real numbers. Then \sqrt{-20} has no solution.

Finally, the zeros of the quadratic function f(x) = x² + 4x +9 do not exist.

Learn more about the zeros of a quadratic function:

brainly.com/question/842305

brainly.com/question/14477557

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