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?
I believe it’s 18 because you find 5 then another 4 which is 9 and you guys already had 9, 9 plus 9 equal 18
Answer:
Step-by-step explanation:
a.
first number is 1000-1+9=1008
9)1000(1
9
-------
10
9
-----
10
9
----
1
----
last number is 9999
9| 9999
---------
1111 |0
--------
9999=1008+(n-1)9
9999-1008=(n-1)9
n-1=8991/9=999
n=999+1=1000
b.
first digit=1000
last digit=9999-1=9998
2 |9999
---------
|4999|1
9998=1000+(n-1)2
(n-1)2=9998-1000=8998
n-1=4499
n=4499=1=5000
c.not sure
d.
total numbers=9000
9999=1000+(n-1)1
9999-1000=n-1
n=8999+1=9000
numbers divisible by 3=3000
first number=1002
last number=9999
9999=1002+(n-1)3
(n-1)3=9999-1002=8997
n-1=2999
n=2999+1=3000
numbers not divisible by 3=9000-3000=6000
e.
numbers divisible by 5=1800
first number=1000
last number=9995
9995=1000+(n-1)5
(n-1)5=9995-1000=8995
n-1=1799
n=1799+1=1800
numbers divisible by 7=1286
7 | 1000
---------
| 142-6
1000-6+7=1001
7 | 9999
|---------
1428-3
9999-3=9996
first digit=1001
last digit=9996
9996=1001+(n-1)7
(n-1)7=9996-1001=8995
n-1=1285
n=1285+1=1286
numbers divisible by 35=257
first digit=1015
35 ) 1000 ( 28
70
----
300
280
------
20
---
1000-20+35=1015
35)9999(285
70
----
299
280
-----
199
175
----
24
----
last digit=9999-24=9975
9975=1015+(n-1)35
(n-1)35=9975-1015=8960
n-1=8960/35=256
n=257
reqd. numbers=1800+1286-257=3019
Answer:
y<-2x-3
Step-by-step explanation:
Your first step is to find the equation of the line. You can see that the y-intercept is -3, therefore your b is -3. So now your formula looks like this:
y=mx-3
To find m, you substitute in an x value and its corresponding y value. When you do this you will get -2.
Now it looks like this:
y=-2x-3.
Now that you have the equation of the line, you can look at the inequality. Since the line is dotted, that means it is not included in the inequality. That mean it cannot contain an equal to. So the only options we have are < and >. Since the shaded area is to the left, which is the negative side, we can conclude that y<-2x-3 is the correct equation.
HOPE THAT THIS IS HELPFUL!
Wait what
I don’t see anything
