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Doss [256]
3 years ago
7

10 POINTS!!! FULL ANSWER WITH FULL STEP BY STEP SOLUTION PLEASE

Mathematics
1 answer:
Inga [223]3 years ago
3 0
A) Profit is the difference between revenue an cost. The profit per widget is
  m(x) = p(x) - c(x)
  m(x) = 60x -3x^2 -(1800 - 183x)
  m(x) = -3x^2 +243x -1800
Then the profit function for the company will be the excess of this per-widget profit multiplied by the number of widgets over the fixed costs.
  P(x) = x×m(x) -50,000
  P(x) = -3x^3 +243x^2 -1800x -50000

b) The marginal profit function is the derivative of the profit function.
  P'(x) = -9x^2 +486x -1800

c) P'(40) = -9(40 -4)(40 -50) = 3240
  Yes, more widgets should be built. The positive marginal profit indicates that building another widget will increase profit.

d) P'(50) = -9(50 -4)(50 -50) = 0
  No, more widgets should not be built. The zero marginal profit indicates there is no profit to be made by building more widgets.

_____
On the face of it, this problem seems fairly straightforward, and the above "step-by-step" seems to give fairly reasonable answers. However, if you look at the function p(x), you find the "best price per widget" is negatve for more than 20 widgets. Similarly, the "cost per widget" is negative for more than 9.8 widgets. Thus, the only reason there is any profit at all for any number of widgets is that the negative costs are more negative than the negative revenue. This does not begin to model any real application of these ideas. It is yet another instance of failed math curriculum material.

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1/2 yard is equal to 18 inches

Step-by-step explanation:

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2 years ago
Consider the function h(x) =x2 – 12x + 58.
alekssr [168]

Answer:

The correct option is;

x ≥ 6; h⁻¹(x) = 6 +√(x - 22)

Step-by-step explanation:

Given the function, h(x) = x² - 12·x + 58

We can write, for simplification;

y = x² - 12·x + 58

Therefore;

When we put x as y to find the inverse in terms of x, we get;

x = y² - 12·y + 58

Which gives;

x - x = y² - 12·y + 58 - x

0 = y² - 12·y + (58 - x)

Solving the above equation with the quadratic formula, we get;

0 = y² - 12·y + (58 - x)

x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}

a = 1, b = -12, c = 58 - x

Therefore;

x = \dfrac{-(-12)\pm \sqrt{(-12)^{2}-4\times (1)\times (58 - x)}}{2\times (1)}= \dfrac{12\pm \sqrt{144-232 + 4 \times x)}}{2}

x =  \dfrac{12\pm \sqrt{4 \times x - 88}}{2} =  \dfrac{12\pm \sqrt{4 \times (x - 22)}}{2}  = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2}

x = \dfrac{12\pm 2 \times \sqrt{ (x - 22)}}{2} = {6 \pm  \sqrt{ (x - 22)}}

We note that for the function, h(x) = x² - 12·x + 58, has no real roots and the real minimum value of y is at x = 6, where y = 22 by differentiation as follows;

At minimum, h'(x) = 0 = 2·x - 12

x = 12/2 = 6

Therefore;

h(6) = 6² - 12×6 + 58 = 22

Which gives the coordinate of the minimum point as (6, 22) whereby the minimum value of y = 22 which gives √(x - 22) is always increasing

Therefore, for x ≥ 6, y or h⁻¹(x) = 6 +√(x - 22)  and not 6 -√(x - 22) because 6 -√(x - 22) is less than 6

The correct option is  x ≥ 6; h⁻¹(x) = 6 +√(x - 22).

7 0
3 years ago
HELP PLS I NEED IN 5 MINUTES
Westkost [7]

Answer:

x = 8

Step-by-step explanation:

Triangle OBC is congruent to triangle OBA (SAS  ----  side angle side)

5 0
3 years ago
1/2 sq. unit 1/2 sq. unit 1 sq. unit 1/2 sq. unit 1/2 sq. unit What is the area of the entire rectangle in square units? Explain
neonofarm [45]

Answer:

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Step-by-step explanation:

<u>Entire area is the sum of areas of sections:</u>

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3 years ago
Can you please help me?​
yan [13]

Answer:

-3, -4, -4, 0, 16, 64, 192.

Step-by-step explanation:

I don't know for sure if this is correct, but when i did it theses are the answers i got. You do y=8*2^x. Meaning you substitute the x for the x values such as -3, -2, and -1.  

Also if you have one there's a setting you can go to on an actual calculator and type in this on a Y/X chart. I didn't use one this time because i don't have one, but thought you'd find that information useful.

6 0
3 years ago
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