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Mariana [72]
2 years ago
12

Corry collects cube containers. She fills them with water and pours them into a rectangular prism. She was playing with them and

discovered something interesting. She had three cube containers. One cube was 1 inch by 1 inch by 1 inch. A second cube was 2 inches by 2 inches by 2 inches and a third cube was 3 inches by 3 inches by 3 inches.She filled all three with water. Then Corry poured all three cubes into a rectangular prism filling it exactly! The rectangular prism has a square base with a side length (1+2+3 = 6) inches and the height is 1 inch.Corry wonders whether she has found a pattern. Investigate using more cube containers to fill square base prisms with heights of 1 in. Describe any conjectures you discover.
Mathematics
1 answer:
Alinara [238K]2 years ago
3 0

Answer:

  \displaystyle\sum_{i=1}^n{i^3}=\left(\sum_{i=1}^n{i}\right)^2

Step-by-step explanation:

The only sum of three cubes that has a total equal to the square of the sum of their dimensions is the one Corry found.

However, we notice that ...

  1³ +2³ +3³ +4³ = (1 +2 +3 +4)² = 100

If we add the next number in sequence, we get ...

  100 +5³ = 225 = (10 +5)²

  225 +6³ = 441 = (15 +6)²

So, it seems that the sum of the first n cubes is equal to the square of the sum of the first n natural numbers.

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just olya [345]

Answer:

This is called a <u><em>parallelogram</em></u>

<u><em>Now, Area:</em></u>

Area = base * Height

Area = 4 * 3

Area = 12 cm²

3 0
3 years ago
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An airline charges 150 for a ticket and 20 for each bag.
Scorpion4ik [409]

it will be C

Answer:

C = 20b + 150

Step-by-step explanation:

because it's 150 for a ticket for each 20 bags. depending on how many bags there are, it wi give you the answer of the cost.

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2 years ago
Any help would be appreciated. (Check the picture)
White raven [17]

the answer would be 0.800375 but when you round it to the nearest tenth it would be 0.8

4 0
3 years ago
-5n-20=-20-10(n-2) (please help)
k0ka [10]

Answer:

n=4

Step-by-step explanation:

First use distributive property to expand -10(n-2)

-5n-20=-20-10n+20

Simplify

-5n-20=-10n

Combine Like Terms

-20=-5n

Divide both sides by -5 to isolate "n"

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5 0
3 years ago
A circle has a circumfernce of 13 it has a arc length of 11. What is the central angle of the arc in degrees
tatiyna

Answer: 304.6°

Step-by-step explanation:

First of all, using the circumference of the circle formula to find the radius of the circle.

Circumference of the circle = 13, ie

2πr = 13,

r = 13/2π ---------------------------- 1

Now getting the radius of the circle now, you now substitute for this in the formula for finding the length of an arc to get the central angle.

Arc length = 11 , ( 2πr0°/360) or (πr0°/180), so

πr0°/180 = 11 ------------------------ 2

Now solve for 0°, the central angle of the angle by making it the subject of the formula.

πr0° = 180 x 11

0° = 180 x 11

----------- ----------------- 3

πr

Now, put equation 1 in equation 3 and solve.

0° = 1980

--------

π x 13/2π

= 1980 x 2π

-----------

π.x. 13

= 1980 x 2

----------

13

= 3960/13

= 304.6°

Therefore, the central angle of the arc is 304.6°

Please be meticulous and understand the way I change the r in the denominator. It was the rule in fraction when dividing.

5 0
3 years ago
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