Which inequality is true for x = 20?
1 answer:
The question is incomplete. Here is the complete question:
Which inequality is true for x = 20?
A. x + 30 < 3x
B. x - 5 < 2x - 35
C. x divided by 4 < x - 12
D. 2x < x + 22
Answer:
Options A, B and D.
Step-by-step explanation:
Given:
The value of 'x' is 20.
In order to find which options are correct, we need to plug in 20 for 'x' in each of the given inequalities and check which of them hold true.
Option A:
Substitute 20 for 'x' in the above inequality. This gives,
The given inequality is true as 50 is less than 60.
Option B:
Substitute 20 for 'x' in the above inequality. This gives,
15 < 5
The given inequality is false as 5 is less than 15.
Option C:
Substitute 20 for 'x' in the above inequality. This gives,
5 < 8
The given inequality is true as 5 is less than 8.
Option D:
Substitute 20 for 'x' in the above inequality. This gives,
40 < 42
The given inequality is true as 40 is less than 42.
Therefore, the correct options are A, B and D.
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Answer:
The answers for your two questions are the following
a)11.606 m
b) As the number of swings approaches infinity
Step-by-step explanation:
We are dealing with an exponential equation series, where the length of each swing can be represented as
l = [ 15 *(0.95)^(n-1) ]
n is the corresponding number of the swing.
So, for the first swing, n = 1
[ 15 *(0.95)^(1-1) ] = 15 m
a) How far with the pendulum travel on its 6th swing?
We just need to evaluate the previous formula for n = 6
[ 15 *(0.95)^(6-1) ] =
[ 15 *(0.95)^(5) ] =
[ 15 *(0.7737) ] =
[ 15 *(0.7737) ] = 11.606 m
b) How far will the pendulum swing before it essentially stops? Hint: This is an infinite geometric series.
We previously stated that the length of the arc of each swing can be represented as
l(n) = [ 15 *(0.95)^(n-1) ] , for n>=1
Since the function approaches zero if and only if n approaches infinity, we can say that the pendulum never stops.
Of course, this only happens mathematically, we can always fin a threshold for which the movement cannot be registered anymore.
Please see attached graph for a representation of the function
