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postnew [5]
3 years ago
9

Driving through the mountains,Dale has to go up and over a high mountain pass. The road has a constant incline for 7 3/4 miles t

o the top of the pass. Dale notices from a road sign that in the first mile he climbs 840 feet. How many feet does he climb in all ?
Mathematics
1 answer:
creativ13 [48]3 years ago
8 0

Answer:

6510

Step-by-step explanation:

7.75 x 840 = 6510

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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
Answers please!!!!!!!!!!
Julli [10]

Answer:

X=8, each side is=27

Step-by-step explanation:

Equilateral triangle, each side has the same lenght

5x-13=11x-61

61-13=11x-5x

48=6x

x=8

5(8)-13=27

7 0
3 years ago
If three-quarters of the pizza provided 12 pieces on the table, how many pieces were in the pizza when it was full?
Anna71 [15]
Take 12 and divide it by 3 to get the number of slices per quarter. Then multiply the answer you got by four. The answer is 16.
8 0
3 years ago
Collin Buys a TV for £720 depreciate at a rate of 4% per year how much will it be worth in three years
belka [17]

Answer:

The worth of the TV after 3 years is £809.90208

Step-by-step explanation:

The answer to given question can be found from the anual depreciation formula and solving for the Future Value (F. V.) of the machine

The given parameters of the TV are;

The amount at which Collin buys the TV, P = £720

The rate at which the TV depreciates at, R = 4%

The number of years the depreciation is applied, T = 3 years

The amount the TV is worth after three years, 'A', is given as follows;

A = P \cdot \left(1 + \dfrac{R}{100} \right )^T

By plugging in the known values, we have;

A = 720 \cdot \left(1 + \dfrac{4}{100} \right )^3 = 809.90208

The amount the TV is worth after three years, A = £809.90208

8 0
3 years ago
What is the general form of the equation of the line shown?
Lyrx [107]

Answer:

  B)  x - y = 0

Step-by-step explanation:

The equation for the line shown is y=x. This can be written in general form by subtracting y:

  x - y = 0

_____

General form for the equation of a line is ...

  ax +by +c = 0

where a, b, c are preferred to be mutually prime integers and a ≥ 0. If a = 0, then b ≥ 0.

6 0
3 years ago
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