Answer:
the 3rd one
Step-by-step explanation:
I just think
Producing 73.8 units gives the lowest possible average cost.
The average cost (AC) is the ratio of the total cost to the number of units produced. It is given by:
AC = C(x) / x
AC = (0.2x³ – 24x² + 1514x +30064) / x
AC = 0.2x² - 24x + 1514 + 30064/x
The lowest possible average cost is at AC' = 0. Hence differentiating the average cost, gives:
AC' = 0.4x - 24 - 30064/x²
0.4x - 24 - 30064/x² = 0
0.4x³ - 24x² - 30064 = 0
Solving the cubic polynomial gives:
x = 73.8 units
Therefore the lowest possible average cost is when 73.8 units are produced.
Find out more at: brainly.com/question/20346871
Answer:
<h3>Question 1</h3>
<u>Function given:</u>
<u>In the vertex form:</u>
- y = x² + 4x + 4 - 8 = (x + 2)² - 8
Axis of symmetry is the vertical line passing through the vertex.
<u>The vertex is</u>
<u>Axis of symmetry is </u>
<u>y- intercept is </u>
- x = 0 ⇒ y = -4, so the point (0, -4)
<u>Two other points are</u>
- x = 1 ⇒ y = (1 + 2)² - 8 = 9 - 8 = 1, the point is (1, 1)
- x = -1 ⇒ y = (-1 + 2)² - 8 = 1 - 8 = -7, the point is (-1, -7)
<em>See the graph with all the points plotted</em>
<h3>Question 2</h3>
<u>Function given:</u>
<u>In standard form:</u>
<u>In vertex form:</u>
- y = - 2x² + 4x - 2 + 8 = -2(x - 1)² + 8
<u>The vertex:</u>
<u>Axis of symmetry is </u>
<u>y - intercept </u>
- x = 0 ⇒ y = -2(-1)² + 8 = -2 + 8 = 6, the point is (0, 6)
<u>Two other pints:</u>
- x = -1 ⇒ y = -2(-1 - 1)² + 8 = -8 + 8 = 0, the point is (-1, 0)
- x = 2 ⇒ y = -2(2 - 1)² + 8 = -2 + 8 = 6, the point is (2, 6)
<em>The graph is attached with the points plotted.</em>
The equation that can be paired with x + 2y = 5 to create an inconsistent system is given by:
2x + 4y = 3.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
An inconsistent system is a system that has no solutions, and it happens when the coefficients of x and y are multiples, and the independent terms are not.
Hence:
x + 2y = 5.
2x + 4y = 3.
Is inconsistent, as the variables are each multiplied by 2, but the independent term is not.
More can be learned about a system of equations at brainly.com/question/24342899
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