Answer:
c=80
Step-by-step explanation:
Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.
So let's see that characteristic equation:
20r^2+cr+80=0
The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.
a=20
b=c
C=80
c^2-4(20)(80)
We want this to be 0.
c^2-4(20)(80)=0
Simplify:
c^2-6400=0
Add 6400 on both sides:
c^2=6400
Take square root of both sides:
c=80 or c=-80
Based on further reading damping equations in form
ay′′+by′+Cy=0
should have positive coefficients with b also having the possibility of being zero.
Answer: t= -0.799
This can also be written as t= -0.8
How to do it :
4.74t+ 5 = 13.5t + 12
first, subtract 4.74t from both sides
5= 8.76t + 12
next, subtract 12 from each side
-7 = 8.76t
next, divide 8.76 from each sides
-0.799 = t
The lines y = 2x - 1 and y = -2x + 3 intersect at exactly one point which means this system has exactly one solution. so the system is consistent and independent
Answer:
16 crates
Step-by-step explanation:
-This is a division problem.
-Let x be the number of crates that will fit in to the box car.
-To solve x, we divide the volume of the boxcar by the volume of one crate:
Hence, 16 crates will fit in the boxcar.
Answer:
$17.85
Step-by-step explanation:
Let the dollar amount per shirt be represented by s.
Let the dollar amount per pants be represented by p.
You have the following system:
3s+2p=104.81
2s+1p=61.33
If I multiply the bottom equation by -2, I can set the system up for elimination since the equations are already and the same form and I will have 2p and -2p in the same column there. 2p+(-2p)=0
Multiplying equation 2 by -2:
3s+2p=104.81
-4s-2p=-122.66
-----------------------Add the equations:
-1s =-17.85
Multiply both sides by -1:
s=17.85
So one shirt cost $17.85
