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Karo-lina-s [1.5K]
3 years ago
7

Profit, P(x), is the difference between revenue, R(x), and cost, C(x), so P(x) = R(x) - C(x). Which expression represents P(x),

if R(x) = 2x^4 – 3x^3 + 2x – 1 and C(x) = x^4 – x^2 + 2x + 3?
Mathematics
2 answers:
harkovskaia [24]3 years ago
5 0

Answer:

x^4-3x^3+x^2-4

Step-by-step explanation:

Given the following functions

R(x) = 2x^4 – 3x^3 + 2x – 1 and

C(x) = x^4 – x^2 + 2x + 3

We are to find the profit function P(x)

P(x) = R(x) - C(x)

P(x) = 2x^4 – 3x^3 + 2x – 1 - ( x^4 – x^2 + 2x + 3)

P(x) = 2x^4 – 3x^3 + 2x – 1 - x^4 + x^2 - 2x - 3

Collect the like terms

P(x) = 2x^4-x^4-3x^3+x^2+2x-2x-1-3

P(x) = x^4-3x^3+x^2+0-4

P(x) = x^4-3x^3+x^2-4

Hence the required profit function P(x) is x^4-3x^3+x^2-4

Brums [2.3K]3 years ago
3 0

Answer:

x^4-3x^3+x^2-4

Step-by-step explanation:

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The change in the stock market from the beginning of the day to the end of the day is 29 3/4

<h3>How to determine the change in the stock market from the beginning of the day to the end of the day?</h3>

The given parameters are:

Beginning = 60 3/4

End = 90 1/2

The change in the stock market from the beginning of the day to the end of the day is calculated as;

Change = End  - Beginning

So, we have

Change = 90 1/2 - 60 3/4

Evaluate

Change = 29 3/4

Hence, the change in the stock market from the beginning of the day to the end of the day is 29 3/4

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Type the missing numbers in this sequence:<br> -101, -105,<br> -109,<br> -117
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Answer:

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2 years ago
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A figure is translated using the rule (x, y) - (x - 3, y + 6).
Strike441 [17]

Answer:

Left 3 units and up 6 units

Step-by-step explanation:

6 0
3 years ago
4.06 Question 9
Jlenok [28]

Answer: B. Graph of 2 lines that intersect at one point. Both lines are solid. One line passes through (-2,2) and (0,3) and is shaded below the line.

y < = 1/2x + 3...(-2,2)                y < = 1/2x + 3....(0,3)

2 < = 1/2(-2) + 3                        3 < = 1/2(0) + 3

2 < = -1 + 3                                3 < = 0 + 3

2 < = 2 (correct)                        3 < = 3 (correct)

The other line passes through points (0,1) and (1,-2) and is shaded above the line.

y > = -3x + 1...(0,1)            y > = -3x + 1...(1,-2)

1 > = -3(0) + 1                   -2 > = -3(1) + 1

1 > = 0 + 1                         -2 > = -3 + 1

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4 0
2 years ago
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A 11 inch by 8 inch piece of cardboard squares cut out of the corners and is folded up to make up an open-top-box. If the volume
Arada [10]
<h3>Answer:  b. either 2.5 inches or about .716 inches</h3>

=====================================================

Work Shown:

I have attached two images below. The first shows figures 1 through 4. The second image shows figure 5.

Start with figure 1. Work your way left to right, top to bottom til you get to figure 4. This is the basic process to turn a flat piece of cardboard into a 3D folded box.

The dashed lines in figure 1 are x inches long.

Figure 2 is the result of cutting out the dashed lines you see in figure 1.

When you fold along the dashed lines in figure 2, you'll end up with something similar to figure 3.

Figure 4 is the completed open-top-box. In other words, this box does not have a lid.

The green portions in figures 3 and 4 indicate where the flaps used to be in reference to figure 2.

-------------------

Since those dashed lines in figure 1 were x inches long, this means that the distance from A to B is 11-x-x = 11-2x inches long.

This makes segment BD to be 8-2x inches long. We are subtracting off 2 copies of x each time for each dimension.

------------------

length = AB = 11-2x

width = BD = 8-2x

Since we want the length to be positive, this means 11-2x > 0 which solves to x < 5.5

Since we want the width to be positive, this means 8-2x > 0 which solves to x < 4

Overall, we must make x < 4 to make both inequalities 11-2x > 0 and 8-2x > 0 to be true at the same time.

Furthermore, x is some length itself, so it cannot be negative either. Therefore x > 0 or 0 < x

Combine 0 < x and x < 4 to get 0 < x < 4

The restriction 0 < x < 4 will be used later.

------------------

For now, let's compute the volume.

Volume = Length*Width*Height

Volume = (AB)*(BD)*x

Volume = (11-2x)*(8-2x)*x

Volume = (88-22x-16x+4x^2)*x

Volume = (88-38x+4x^2)*x

Volume = 88x-38x^2+4x^3

This is the algebraic way of representing the volume in terms of the cut length x

We want this volume to be 45 cubic inches. We set  88x-38x^2+4x^3 equal to 45 and solve for x

88x-38x^2+4x^3 = 45

4x^3-38x^2+88x-45 = 0

At this point we try to factor by grouping or we turn to a calculator. Cubics are often very difficult to solve by hand, so I recommend using a calculator (unless you can quickly spot how to factor by grouping, but I don't see a quick way of doing that). Note: based on the answer choices that aren't whole numbers (assuming choice C is a non-answer), this heavily implies we do not have rational roots, and therefore factoring over the rationals will be impossible. In other words, the answer choices tell us to immediately use a graphing calculator to find the roots.

Using geogebra (see figure 5), I find the three approximate roots to be

x = 0.716 (shown as point A)

x = 2.5 (point B)

x = 6.284 (point C)

Recall that earlier we made 0 < x < 4. The first two roots satisfy this inequality, but x = 6.284 is outside this range. So we ignore it. It looks like your teacher put 6.284 as a trick answer in choice A.

5 0
3 years ago
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