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andreev551 [17]
3 years ago
6

logs are stacked in a pile on the bottom row and 15 on the top row . there are 10 rows in all with each row having one more log

that the one above it. how many logs are in the stack?
Mathematics
2 answers:
WITCHER [35]3 years ago
8 0
Since there is a common difference of one, this is an arithmetic sequence of the form a(n)=a+d(n-1) which in this case is:

a(n)=15+1(n-1)

All arithmetic sequences have a sum which is equal to the average of the first and last terms time the number of terms, mathematically:

s(n)=(2an+dn^2-dn)/2  (that is just the result of ((a+a+d(n-1))(n/2)) )

Since a=15 and d=1 this becomes:

s(n)=(30n+n^2-n)/2

s(n)=(n^2+29n)/2 so

s(10)=(100+290)/2

s(10)=195 logs
Lady_Fox [76]3 years ago
4 0
There are 195 logs in total.

If the top row has 15 logs, and each row below it has one more log than the one above it, then 15 • 10 (since there are 10 rows in total) plus 9+8+7+6+5+4+3+2+1 ( minus the top layer, starting from the 2nd layer down, deducting 1 each time since every time the number gets add to it, a row's requirement that each row below it has one more log gets satisfied.)
(15 • 10) + (9+8+7+6+5+4+3+2+1) = 150 + 45 = 195.
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Read 2 more answers
3x+6y=36 and -3x-6y=0​
Anastasy [175]

Answer:

No solution

Step-by-step explanation:

3x + 6y  =36

-3x - 6y =0​

------------------add

0 ≠ 36

No solution

4 0
3 years ago
the combined area of two squares is 45 square centimetres each side is twice as long as a side of the other square what length o
Ostrovityanka [42]

Answer:

Let the side of  one square be x.    Area = x*x = x²

Then the side of other square  would be 2x ,   Area = 2x*2x = 4x²

Combined area = x² + 4x²  = 5x²

This combined area = 45 cm²

you simplify

Therefore  5x²  = 45   Divide both sides by 5

                 x²  =  45/5

                 x²  = 9        Take square root of both sides

                 x   =  √9

                 x  = 3

Length of larger square is 2x  = 2*3 = 6 cm

Length of larger square = 6cm

Step-by-step explanation:

4 0
2 years ago
7) What is the slope-intercept form of this equation? Show all your work. 6x + 2y = 12​
mariarad [96]

Answer:

3

Step-by-step explanation:

6x+2y=12

2y=6x-12

y=6x/2- 12/2

y=3x-6

7 0
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