Arrange the following<br> weights in descending<br> order<br> 50 mg, 35 hg, 500g, 14 KG

You have been asked to design a rectangular box with a square base and an open top. The volume of the box must be 1536cm3. Deter

Katen [24]

Answer:

The dimensions of the box are:

Length = 11.53cm

Breadth = 11.53cm

Height = 11.53cm

Step-by-step explanation:

The volume of the box can be calculated with this formula:

The volume of the box = area of square base X height of the box.

We are given that the length of one side of the square base is = x cm, and its height is h cm.

Area of square base = $x^{2}cm^{2}$

The surface area of the box will be minimized if the height of the box, is the same as its length. hence, we can take the height of the box to be x cm also.

In this case, the volume of the box will be $x^{3}=1536cm^{3}$

from this, $x =3\sqrt{1536}= 11.53cm$

There fore, the box has its length, height, and width all having the same values.

The dimensions of the box are:

Length = 11.53cm

Breadth = 11.53cm

Height = 11.53cm

8 0

3 years ago

Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally

DiKsa [7]

Answer:

65,280

Step-by-step explanation:

Consider the 4×4 grid ...

$\left[\begin{array}{cc}a&b\\d&c\end{array}\right]$

where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.

The same will be true of 270° rotational symmetry, for the same reason.

__

For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)

__

The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...

65,536 -256 = 65,280 . . . . colorings not rotationally symmetric

8 0

3 years ago

Assume that f(x)=ln(1+x) is the given function and that Pn represents the nth Taylor Polynomial centered at x=0. Find the least

WINSTONCH [101]

Answer:

the least integer for n is 2

Step-by-step explanation:

We are given;

f(x) = ln(1+x)

centered at x=0

Pn(0.2)

Error < 0.01

We will use the format;

[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01

So;

f(x) = ln(1+x)

First derivative: f'(x) = 1/(x + 1) < 0! = 1

2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1

3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2

4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6

This follows that;

Max|f^(n+1) (c)| < n!

Thus, error is;

(n!/(n + 1)!) × 0.2^(n + 1) < 0.01

This gives;

(1/(n + 1)) × 0.2^(n + 1) < 0.01

Let's try n = 1

(1/(1 + 1)) × 0.2^(1 + 1) = 0.02

This is greater than 0.01 and so it will not work.

Let's try n = 2

(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267

This is less than 0.01.

So,the least integer for n is 2

7 0

4 years ago

PLEAS HELP I REALLY NEED HELP

blsea [12.9K]

Answer:

the first one in the picture

Step-by-step explanation:

8x8x8x8=4096

9x9x9x9=6561

4096x6561=26873856

72x72x72x72=26873856

5 0

2 years ago

What do landforms include

olganol [36]

Answer:

A landform is a feature on the Earth's surface that is part of the terrain. Mountains, hills, plateaus, and plains are the four major types of landforms. Minor landforms include buttes, canyons, valleys, and basins. Tectonic plate movement under the Earth can create landforms by pushing up mountains and hills.

7 0

3 years ago

Arrange the following weights in descending order 50 mg, 35 hg, 500g, 14 KG