the manager of a grovery store asks a store clerk to rearrange a display of canned vegtables in a triangular pyramid. Assume all cans are thr same size and shape.
in the first pyramid their is 1 can in the base, second pyramid has 3 cans in the base and 3rd pyramid shown has 6 cans in the base.
A) if the clerk has 100 cans to use, how many of those can are needed to create the tallest complete pyramid shape?
B) how many can make up the bottom level of the pyramid in part A
c) how many levels is the pyramid in part A
For this question i have no idea where to start or if theirs a formula i can use. thank you for your help
It is always best to start with a diagram. Draw the pyramids and see how many cans are used in each (and the total cans used). You can generate a formula later (if you see the pattern).
Again, draw it out and count cans : )
hi thank you for help but i can’t see the pattern.
To solve this problem, let's start by understanding the pattern in the number of cans needed to create the triangular pyramid.
If we observe closely, the number of cans in each level of the pyramid forms a sequence of triangular numbers:
1, 3, 6, 10, 15, ...
To find the pattern for the number of cans needed to form the pyramid, we use the formula for the nth triangular number:
Tn = (n * (n + 1)) / 2
Where Tn represents the nth triangular number.
A) To determine how many cans are needed to create the tallest complete pyramid shape, we need to find the highest triangular number that is less than or equal to 100.
We can solve this by iterating through the triangular numbers until we find the first one that is greater than 100.
Start with n = 1:
T1 = (1 * (1 + 1)) / 2 = 1
T2 = (2 * (2 + 1)) / 2 = 3
T3 = (3 * (3 + 1)) / 2 = 6
T4 = (4 * (4 + 1)) / 2 = 10
T5 = (5 * (5 + 1)) / 2 = 15
Since T5 is greater than 100, we can conclude that the tallest complete pyramid shape can be created using T4, which is equal to 10 cans.
B) To find the number of cans that make up the bottom level of the pyramid in part A, we can use the formula for the (n - 1)th triangular number. In this case, n = 4.
T(n-1) = ((n - 1) * (n - 1 + 1)) / 2
T(4-1) = ((4 - 1) * (4 - 1 + 1)) / 2 = 3 cans
C) The number of levels in the pyramid can be determined by finding the value of n, where T(n) is the highest triangular number less than or equal to the total number of cans.
In part A, the highest triangular number was T4, which required 10 cans. Therefore, the number of levels is 4.