A students wants to help her mother in their family store in displaying canned goods. Her mother instructed that the canned should be piled in triangular pile by starting 40 canned goods in the bottom row, 36 in the second row, 32 in the third row, and so on. If the pattern is consistent, how many canned goods will be there in the 7th row?

The number of canned goods in 7th row = 64.

Step-by-step explanation:

The given numbers of canned goods in every row( starting from first ) is represented as

40 , 36, 32, ...

There is a common difference between numbers(d)= 4

∴ Its is an Arithmetic progression.

First term (a) = 40

nth term in A.P. :

7th term in this A.P. = 40+(7-1)(4)=40+(6)(4)=40+24=64

So, the number of canned goods in 7th row = 64.

    for the right-hand side, use cosine double angle identity which states that  cos 2x = cos²x - sin² x    for the left-hand side    we factor using difference of squares.recall difference of squares factoring: a² - b² = (a - b)(a + b)but here we have a⁴ - b⁴, so  a⁴  - b⁴ = (a² - b²)(a²  + b²)note that cos⁴ x is equivalent to (cos x)⁴ and etc.    note that cos²x + sin²x = 1 via the pythagorean identity