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Mekhanik [1.2K]
3 years ago
7

Which of the following examples could correctly show the mean density of lunar soil?

Mathematics
2 answers:
viva [34]3 years ago
7 0
<span>The correct answer is 3.24 grams per cubic centimetre. As a matter of fact, the lunar soil’s mean density may range from 2.90 to 3.24 g cm-3 which highly depends on the type of ingredients present in its resource materials.</span>
alex41 [277]3 years ago
5 0
I just did this assignment, the correct answer from the following is <span>3.24 grams per cubic centimeter.</span>
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A piece of wire of length 6363 is​ cut, and the resulting two pieces are formed to make a circle and a square. Where should the
Lerok [7]

Answer:

a.

35.2792 cm from one end (The square)

And 27.7208 cm from the other end (The circle)

b. See (b) explanation below

Step-by-step explanation:

Given

Length of Wire ,= 63cm

Let L be the length of one side of the square

Circumference of a circle = 2πr

Perimeter of a square = 4L

a. To minimise

4L + 2πr = 63 ----- make r the subject of formula

2πr = 63 - 4L

r = (63 - 4L)/2π

r = (31.5 - 2L)/π

Let X = Area of the Square. + Area of the circle

X = L² + πr²

Substitute (31.5 - 2L)/π for r

So,

X² = L² + π((31.5 - 2L)/π)²

X² = L² + π(31.5 - 2L)²/π²

X² = L² + (31.5 - 2L)²/π

X² = L² + (992.25 - 126L + 4L²)/π

X² = L² + 992.25/π - 126L/π +4L²/π ------ Collect Like Terms

X² = 992.25/π - 126L/π + 4L²/π + L²

X² = 992.25/π - 126L/π (4/π + 1)L² ---- Arrange in descending order of power

X² = (4/π + 1)L² - 126L/π + 992.25/π

The coefficient of L² is positive so this represents a parabola that opens upward, so its vertex will be at a minimum

To find the x-cordinate of the vertex, we use the vertex formula

i.e

L = -b/2a

L = - (-126/π) / (2 * (4/π + 1)

L = (126/π) / ( 2 * (4 + π)/π)

L = (126/π) /( (8 + 2π)/π)

L = 126/π * π/(8 + 2π)

L = (126)/(8 + 2π)

L = 63/(4 + π)

So, for the minimum area, the side of a square will be 63/(4 + π)

= 8.8198 cm ---- Approximated

We will need to cut the wire at 4 times the side of the square. (i.e. the four sides of the square)

I.e.

4 * (63/(4 + π)) cm

Or

35.2792 cm from one end.

Subtract this result from 63, we'll get the other end.

i.e. 63 - 35.2792

= 27.7208 cm from the other end

b. To maximize

Now for the maximum area.

The problem is only defined for 0 ≤ L ≤ 63/4 which gives

0 ≤ L ≤ 15.75

When L=0, the square shrinks to 0 and the whole 63 cm wire is made into a circle.

Similarly, when L =15.75 cm, the whole 63 cm wire is made into a square, the circle shrinks to 0.

Since the parabola opens upward, the maximum value is at one endpoint of the interval, either when

L=0 or when L = 15.75.

It is well known that if a piece of wire is bent into a circle or a square, the circle will have more area, so we will assume that the maximum area would be when we "cut" the wire 0, or no, centimeters from the

end, and bend the whole wire into a circle. That is we don't cut the wire at

all.

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2 years ago
I need help on what to write exactly
Naily [24]

Answer:

Step-by-step explanation:

the equation could model a scenario determining the number of players on each team in a league of five teams, if 2 players have to be taken out of the possible players to be referees and to keep score. there will be 11 on each team

7 0
3 years ago
Read 2 more answers
What is the 100th term of 6,10,14,18
Usimov [2.4K]

Answer:

406

Step-by-step explanation:

6+(4x100)

3 0
2 years ago
The radius of a circle is 8 feet. What is the area of sector bounded by a 90° arc?
Lera25 [3.4K]

Since 90 degree is 1/4 of a circle, the area will be 1/4 th area of the full circle.

The radius is given by, r = 8 ft, therefore, the area of the full circle is,

\begin{gathered} A=\pi\times r^2 \\ A=3.14\times8^2=200.96ft^2 \end{gathered}

Therefore, the area of the sector is,

A^{\prime}=\frac{1}{4}\times200.96ft^2=50.24ft^2\begin{gathered} A^{\prime}=\frac{\theta}{360}\times\pi\times r^2 \\ \text{ =}\frac{\text{90}}{360}\times\pi\times8^2 \\ \text{ =}\frac{1}{4}\pi\times64=16\pi \end{gathered}

4 0
1 year ago
Fidel has $217.18 and his checking account until the end of the month Fidel writes a check for $357.42 how much money does Fidel
Alenkasestr [34]

Answer:

the amount that Fidel now have in his checking account is $140.24

Step-by-step explanation:

The computation of the amount that Fidel now have in his checking account is shown below:

= Ending balance  - Opening balance

= $357.42 - $217.18

= $140.24

Hence, the amount that Fidel now have in his checking account is $140.24

We simply applied the above formula so that the correct value could come

And, the same is to be considered

7 0
2 years ago
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