Whats the most random thing in your gallery

As Earth spins on its axis, producing night and day, it also moves about the Sun in an elliptical orbit that requires about 365

Doss [256]

I think it might be A.) Day. Because when the axis is pointed towards the sun, that shows it is day because that area has sunlight in which you get during the day. It is night when the axis is pointed away from the sun because there is no sunlight in that area which causes darkness in which we get during the night obviously. Winter occurs when the earth is far away from the sun, in which there is no heat, and closest to the sun in which we do get heat, there will be Summer.
Hope this helps some.

7 0

3 years ago

Read 2 more answers

The point of view expressed by the Dutch West India Company’s directors in the letter can best be described as...?

vivado [14]

Explanation:

The Dutch West Corporation's managers' perspective in the document can best be represented as an attempt to persuade the States Government officials to take actions that would support the company economically.

7 0

3 years ago

What is the link between the Enlightenment, the Industrial Revolution and the rise of<br> socialism?

CaHeK987 [17]

Answer:

The Industrial Revolution was the transition to new manufacturing processes in Europe and the United States, in the period from about 1760 to sometime between 1820 and 1840

6 0

3 years ago

What is the area and perimeter of the whole house?

Leni [432]

I don’t have the numbers, but the formula for area is base times height. as long as the house is a square or rectangle which i’m assuming it is. the formula for perimeter is 2L + 2W if it’s a rectangle. for a square it is 4 times the sides of the square. hope that helps.

5 0

3 years ago

A cake has two layers. Each layer is a regular hexagonal prism. You cut and remove a slice that takes away one face of each pris

Ivan

Answer:

Volume of slice is approximately 40 in³

Volume of the remaining cake is 197.014 in³

Explanation:

Here we have two regular hexagons

one top small hexagon cake with side length = 3 in, height = 3 in

One big hexagon cake, side length = 4 in, Height = 4 in

A slice cut such the it removes a side segment is equivalent to an equilateral triangle with side length = length of hexagon side

Also all angles within the equilateral triangle are 60° each

Therefore, the length of the side of the removed equilateral triangle side is given as follows;

Top small cake slice triangle side = 3 in.

Area of surface of small slice = $\frac{1}{2} \times Base \times Height = \frac{1}{2} \times 3 \times 3\times sin(60) = \frac{1}{2} \times 3 \times 3 \times \frac{\sqrt{3} }{2} = \frac{9\sqrt{3} }{4}$

Volume of small slice = Area of surface small slice × Height of small cake

= $\frac{9\sqrt{3} }{4} \times 3 = \frac{27\sqrt{3} }{4} =11.69 \ in^3 \approx 12 \ in^3$

For the big cake, we have;

Big cake slice triangle side = 4 in.

Area of surface of big slice = $\frac{1}{2} \times Base \times Height = \frac{1}{2} \times 4 \times 4\times sin(60) = 8 \times \frac{\sqrt{3} }{2} = 4\sqrt{3}$

Volume of big slice = Area of surface of big slice × Height of big slice

= $4\sqrt{3} \times 4 = 16\sqrt{3} =27.71 \ in^3 \approx 28 \ in^3$

Total volume of slice = Volume of small slice + Volume of big slice

Total volume of slice = 12 in³ +28 in³ = 40 in³

The volume of the remaining cake can be found by noting that there were 6 possible slices of cake based on the 6 sides of the hexagon, since we removed 1 slice, the remaining 5 slices will have a volume given by multiplying the volume of 1 slice by 5 as follows;

For the small cake, the remaining volume = $5 \times \frac{27\sqrt{3} }{4} = 5 \times 11.69 \ in^3 = 58.45 \ in^3$

For the big cake the remaining volume = $5 \times 16\sqrt{3} = 5 \times 27.71 \ in^3 = 138.56 \ in^3$

Total volume remaining cake = 58.45 in³ + 138.56 in³ = 197.014 in³

Together with the above way to find the volume of slice of cake, the volume of the slice can also be found by considering that the cake, with a shape of a regular hexagon is made up of 6 such slices. Therefore, if the volume of a regular hexagon is as follows;

$Volume\, of \, regular \, hexagon, \ A = \frac{3\sqrt{3} }{2} a^2 \times h$

Where:

a = Length of side

h = Height of hexagon

The volume of each slice is therefore,

$\frac{Volume\, of \, regular \, hexagon, \ A }{6} =\frac{ \frac{3\sqrt{3} }{2} a^2 \times h}{6} = a^2 \times h \times \frac{3\sqrt{3} }{12} = a^2 \times h \times \frac{\sqrt{3} }{4}$