Step-by-step explanation:
Let the height above which the ball is released be H
This problem can be tackled using geometric progression.
The nth term of a Geometric progression is given by the above, where n is the term index, a is the first term and the sum for such a progression up to the Nth term is
To find the total distance travel one has to sum over up to n=3. But there is little subtle point here. For the first bounce ( n=1 ), the ball has only travel H and not 2H. For subsequent bounces ( n=2,3,4,5...... ), the distance travel is 2×(3/4)n×H
a=2H..........r=3/4
However we have to subtract H because up to the first bounce, the ball only travel H instead of 2H
Therefore the total distance travel up to the Nth bounce is
For N=3 one obtains
D=3.625H
-2/5=-.4
-7=-7
These two are repeating decimals.
3/9=.3333334
11/12=.9166667
Answer:
Expand: x² + 11x + 11x + 121
Simplify: x² + 22x + 121
Step-by-step explanation:
To expand this, you can use the FOIL technique:
First terms
Outer terms
Inner terms
Last terms
(x+11)(x+11)
F - x*x = x²
O - x*11 = 11x
I - 11*x = 11x
L - 11*11 = 121
Put these numbers together (expanded) to get:
x² + 11x + 11x + 121
Put the common terms together (simplify) to get:
x² + 22x + 121
Note:
Not sure if you need this info, but (x + 11)(x + 11) is the same as (x + 11)².
The numbers need to be in the order I put them in because you are supposed to place them in order greatest to least degree.
Hope it helps!
Answer:
120 blocks total
Step-by-step explanation:
All of the little cubes have side length 2" Thus, the 11" height of the box cannot be used entirely: we waste the top 1" because the five layers of little cubes reach only to 10" from the bottom.
Start at the bottom of the box. The dimensions of the bottom are 12" by 8". Along the longer side we can lay 6 blocks (which add up to 12" and are 2" wide. We can add 3 more such rows to fill the available 8" width of the box bottom. That's 6*4, or 24 blocks.
We can add 4 more 6 block by 4 block layers before we have the maximum 5 layers stacked in the box.
5 layers times 24 blocks per layer comes to 120 blocks total.
Use a app called photo math it works good.
