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
Answer:
sparky 4 years older than cookie
Step-by-step explanation:
s=c+4
since there nothing to add or subtract. you are just gonna take that 4 and since there is a plus sign you are gonna say older than.
hope this helps
Answer:
![d(t) = -20t - 260](https://tex.z-dn.net/?f=d%28t%29%20%3D%20-20t%20-%20260)
Step-by-step explanation:
The depth function is:
![d(t) = mt + b](https://tex.z-dn.net/?f=d%28t%29%20%3D%20mt%20%2B%20b)
After 3 minutes, a submarine had descended to −320 feet.
This means that
. So
![d(t) = mt + b](https://tex.z-dn.net/?f=d%28t%29%20%3D%20mt%20%2B%20b)
![-320 = 3m + b](https://tex.z-dn.net/?f=-320%20%3D%203m%20%2B%20b)
After 8 minutes, the submarine had descended to −420 feet.
This means that
. So
![d(t) = mt + b](https://tex.z-dn.net/?f=d%28t%29%20%3D%20mt%20%2B%20b)
![-420 = 8m + b](https://tex.z-dn.net/?f=-420%20%3D%208m%20%2B%20b)
From the first equation:
![b = -320 - 3m](https://tex.z-dn.net/?f=b%20%3D%20-320%20-%203m)
So
![-420 = 8m + b](https://tex.z-dn.net/?f=-420%20%3D%208m%20%2B%20b)
![-420 = 8m - 320 - 3m](https://tex.z-dn.net/?f=-420%20%3D%208m%20-%20320%20-%203m)
![5m = -100](https://tex.z-dn.net/?f=5m%20%3D%20-100)
![m = \frac{-100}{5}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-100%7D%7B5%7D)
![m = -20](https://tex.z-dn.net/?f=m%20%3D%20-20)
And
![b = -320 - 3*(-20) = -260](https://tex.z-dn.net/?f=b%20%3D%20-320%20-%203%2A%28-20%29%20%3D%20-260)
So
![d(t) = -20t - 260](https://tex.z-dn.net/?f=d%28t%29%20%3D%20-20t%20-%20260)
Answer:
B ∩ (A ∪ C)'
Step-by-step explanation:
It's the B part excluding A and C union. Hence,
(A ∪ C)' ∩ B
5a - 10*3 = 45
5a - 30 = 45
5a = 45 + 30
5a = 75
a = 15