Step-by-step explanation: Given that a stack of logs has 32 logs on the bottom layer. Each subsequent layer has 6 fewer logs than the previous layer and the top layer has two logs.

We are to find the total number of logs in the pile.

Let n represents the total number of logs in the pile.

Since each subsequent layer has 6 fewer logs then the previous layer, so the number of logs in each layer will become an ARITHMETIC sequence with

first term, a = 32 and common difference, d = -6.

We know that

the n-th term of an arithmetic sequence with first term a and common difference d is

$a_n=a+(n-10)d.$

Since there are n logs in the pile, so we get

$a+(n-1)d=2\\\\\Rightarrow 32+(n-1)(-6)=2\\\\\Rightarrow 32-6n+6=2\\\\\Rightarrow 6n=36\\\\\Rightarrow n=6.$

Thus, the total number of logs in the pile is 6.

6 0

3 years ago

Complete the table of ordered pairs for the given linear equation

nika2105 [10]

Answer:

First blank= -1

Second blank= 14

Step-by-step explanation:

Plug in x to the equation. 1/7 x (-7)= -7/7=-1

2=1/7(x) to divide fractions you multiply by the reciprocal

2 x 7/1= 1/7× 7/1

14/1=14

4 0

3 years ago