For a display, identical cubic boxes are stacked in square layers. each layer consists of cubic boxes arranged in rows that form a square, and each layer has 1 fewer row and 1st fewer box in each remaining row than the layer directly below it. if the bottom layer has 81 boxes and the top layer has only 1 box, how many boxes are in the display?

285 boxes

Step-by-step explanation:

High School Mathematics 10+5 pts

For a display, identical cubic boxes are stacked in square layers. Each layer consists of cubic boxes arranged in rows that form a square, and each layer has 1 fewer row and 1 fewer box in each remaining row than the layer directly below it. If the bottom layer has 81 boxes and the taop layer has only 1 box, how many boxes are in the display?

Report by Annamaecoleman9007 23.07.2019

Answers

MrRoyal

MrRoyalAmbitious

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DeniceSandidgeAmbitious

285 boxes are in the display

Step-by-step explanation:

Given

Top layer box = 1

Last row box = 81

From the question, every row is a square and the bottom layer has 81 squares.

And 81 = 9²

The next row has 1 less than the previous row and that is 8²

Then, 7², 6² till 1²

So we can say that cubes in the rows as that

Sum of all Squares = 9² + 8² + 7² + 6² + 5² + 4² + 3² + 2² + 1²

Sum of all Square = 81 + 64 + 49 + 36 + 25 + 16 + 9 + 4 +1 = 285

So, the total number of boxes in display are 285 boxes

hello from mrbilldoesmath!

answer:   x (x+6)^2, choice b

discussion:

factor x out of the equation:

x^3 + 12x^2 + 36x = x (x^2 + 12x + 36).

note that 6+6 = 12 and 6*6 = 36 so the above factors into:

x (x+6)^2

which is choice b

you,

mrb