Cans collected in a recycling project are displayed against a wall and are arranged in a pyramid with 2 cans in the top row, 4 cans in the second row, six cans in the third row, and so on. How many rows are in the pyramid if it contains 1,190 cans?
a. 68 rows b. 70 rows c.34 rows
Can you show me the equation or steps to do that?
a. 68 rows b. 70 rows c.34 rows
Can you show me the equation or steps to do that?
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This works but I can't explain it very well. It says you're building a pyramid but really its a triangle since it is only one can deep. The area of a triangle is base * height / 2. So if you know that each row has 2R cans (the base) and the height is the number of rows then the area is R*2R/2 or R*R. The area isn't quite the same as the number of cans in the pyramid but the difference is the number of rows so the number of cans is R*R+R.
So if you know you have 1190 and you have R*R+R, or R^2+R then you can solve 1190=R^2+R using the quadratic equation. a=1 b=1 c=-1190.
R=(-1+sq(1^2-4*1*-1190))/2
R=(-1+sq(1+4760))/2
R=(-1+69)/2
R=68/2
R=34
So if you know you have 1190 and you have R*R+R, or R^2+R then you can solve 1190=R^2+R using the quadratic equation. a=1 b=1 c=-1190.
R=(-1+sq(1^2-4*1*-1190))/2
R=(-1+sq(1+4760))/2
R=(-1+69)/2
R=68/2
R=34
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a. 68