Question
Consider, The motion of a a damped harmonic oscillator is described by x′′
x
″
+ bx′
b
x
′
+ kx=0
k
x
=
0
, where b is greater than or equal to 0
A) Rewrite as a two dimensional linear system.
x′=y
x
′
=
y
y′
y
′
= - (by+kx)
(
b
y
+
k
x
)
B) Sketch the analogue of the trace-determinant plane in the bk-plane. That is, identify the regions in the relevant portion of the bk-plane where the corresponding system has similar phase portraits.
I have cut out most of my answer etc as it seems to of merely confused people, how does one answer this question?
Answer:
12
Step-by-step explanation:
The equation would be 2 (3+3). You would distribute the 2 to both threes and get 6+6. Then you would add them to get 12.
Answer:
The answer is last option
As we know 1 + tan^2 = sec^2
95% of red lights last between 2.5 and 3.5 minutes.
<u>Step-by-step explanation:</u>
In this case,
- The mean M is 3 and
- The standard deviation SD is given as 0.25
Assume the bell shaped graph of normal distribution,
The center of the graph is mean which is 3 minutes.
We move one space to the right side of mean ⇒ M + SD
⇒ 3+0.25 = 3.25 minutes.
Again we move one more space to the right of mean ⇒ M + 2SD
⇒ 3 + (0.25×2) = 3.5 minutes.
Similarly,
Move one space to the left side of mean ⇒ M - SD
⇒ 3-0.25 = 2.75 minutes.
Again we move one more space to the left of mean ⇒ M - 2SD
⇒ 3 - (0.25×2) =2.5 minutes.
The questions asks to approximately what percent of red lights last between 2.5 and 3.5 minutes.
Notice 2.5 and 3.5 fall within 2 standard deviations, and that 95% of the data is within 2 standard deviations. (Refer to bell-shaped graph)
Therefore, the percent of red lights that last between 2.5 and 3.5 minutes is 95%
Answer:
B is correct.
Step-by-step explanation:
Quadratic Expression (Standard Form) is:
To say it simply, the expression must have 2 as the highest degree.
This means that if there are any higher or lower degrees than 2 then they are not quadratic expression.
A choice is not quadratic expression because it has 1 as the highest degree.
B choice is correct because 2 is the highest degree.
C choice is wrong because 3 is the highest degree.
D choice is wrong because it is not a polynomial.
Therefore, B is correct.
