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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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Plsss help I will mark brainlist
givi [52]

Answer:

38 deg

Step-by-step explanation:

Angles A and M are corresponding angles of congruent triangles, so they are congruent.

m<A = m<M = 38 deg

6 0
2 years ago
Steve invests in a circus production. The cost includes an overhead of $84,000, plus production costs of $2000 per performance.
Dima020 [189]

Answer:

14

Step-by-step explanation:

Given that Steve  invests in a circus production. The cost includes an overhead of $84,000, plus production costs of $2000 per performance. A sold-out performance brings in $8000.

Sales per performance =8000

Production cost per performance =2000

Contribution per performance = 8000-2000=6000

Overhead costs = 84000

Break even units = overhead cost/contribution per performance

= \frac{84000}{6000} \\=14

14 performances should be done to break even

3 0
3 years ago
Sabina bought a samsung mobile set for rs.15750 after getting the discount of 10%. Find the price of mobile set before discount.
Elanso [62]

Answer:

Step-by-step explanation:

90/100 * x = 15750

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x = 15750/0.9

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Now check this by taking 10% off. Do you get 15750?

Let's see

10/100 of 17500 = 1750

Subtract that from 17500

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7 0
3 years ago
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zavuch27 [327]

Answer:

0.35

Explanation:

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<u>Follow the branch B and then branch D</u>

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6 0
2 years ago
Read 2 more answers
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Stells [14]
Answer is 20 cm i guess

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