Answer:
$10,000
Step-by-step explanation:
-12,000+23,200-1,200= 10,000
Answer:
144
Step-by-step explanation:
First: 6x
Second: 6x+6
Third: 6x+12
Fourth: 6x+18
- Since they're multiples of 6


Subract 36 from each side give us...


Hope this helped! Please mark brainliest :)
Answer :

step-by-step explanation :

This can be rewritten as:

Now,

The law of indices states that:

It implies that, when dividing two expressions with the same bases, repeat one of the bases and subtract the exponents.
Therefore,


Note: Any non-zero number exponent zero is 1
Also

Hence:
Answer:
See below
Step-by-step explanation:
a) 43.8 - 38 = 5.8 yrs
b) SD = 8.9 yrs 5.8 / 8.9 = .6517 SD <u> below</u> the mean
(A z score merely shows how many standard deviations a score (age) is above or below the mean in SD units)
c) Z = - .6517 Negative because it is <u>BELOW</u> the mean ( FYI from z-score table: this is .2578 in percentage )
d) usual ( it (-.6517) is between -2 and + 2 )
Answer:
![x(t) = e ^{-3t} [-cos (4t) - \frac{3}{4}sin (4t)]](https://tex.z-dn.net/?f=x%28t%29%20%3D%20e%20%5E%7B-3t%7D%20%5B-cos%20%284t%29%20-%20%5Cfrac%7B3%7D%7B4%7Dsin%20%284t%29%5D)
Step-by-step explanation:
A force of 5 pounds stretches a spring 1 foot.
This implies that, the string constant (K) = 5 lbs? ft
Mass (m) = 
= 
The damping force 
The negativity of the damping force is due to the fact that it opposes the motion.
Then the force due to the spring is :
where;
x = the mass distance from the equilibrium point.
Total Force F = 
⇒ F = -1.2v - 5.0 x
⇒ mx = -1.2v - 5.0 x
where v = x' and a = x"
Hence, the equation becomes mx" = -1.2x' - 5.0 x
⇒
= 0
⇒ 
The auxiliary equation is can be written as:

⇒ r = 
r = 
r =
OR 
Now,the general equation of motion is :


Initial Conditions are:
x(0) = -1 and x' (0) = 0
x(0) = -1
⇒ -1 = 
x' (0) =0 ⇒ 0 = -3(-1) + (4
)
⇒
= 
Thus:
![x(t) = e ^{-3t} [-cos (4t) - \frac{3}{4}sin (4t)]](https://tex.z-dn.net/?f=x%28t%29%20%3D%20e%20%5E%7B-3t%7D%20%5B-cos%20%284t%29%20-%20%5Cfrac%7B3%7D%7B4%7Dsin%20%284t%29%5D)