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:
<h3>
1) 7x - 5
</h3><h3>
2) 9y - 18
</h3><h3>
3) 0.5n + 4n
</h3><h3>
4) 2(w³+23)</h3><h3>
Step-by-step explanation:</h3>
1)
The product of seven and a number x: 7·x = 7x
<u>Five less than the product of seven and a number x:</u>
<h3>
7x - 5
</h3>
2)
nine times a number y: 9·y = 9y
<u>The difference of nine times a number y and eighteen:</u>
<h3>
9y - 18
</h3>
3)
half a number n: 0.5n
four times the number: 4·n = 4n
<u>Half a number n increased by four times the number:</u>
<h3>
0.5n + 4n
</h3>
4)
a number w cubed: w³
the sum of a number w cubed and twenty-three: w³+23
<u>Twice the sum of a number w cubed and twenty-three:</u>
<h3>2(
w³+23)</h3>
I believe it’s 100 hopefully it helps
Step-by-step explanation:
$20/hr carpenter pay
$25/hr blacksmith pay
Let c = hours working carpentry
Let b = hours working as blacksmith
c + b = 30 {equation 1}
20c + 25b = 690 {equation 2}
In equation 1 solve for one variable in terms of the other.
c = 30-b
Substitute that into equation 2:
20(30-b) + 25b = 690
600 - 20b + 25b = 690
5b = 90
b = 90/5
b = 18 hours working as a blacksmith
c = 30-b = 30-18 = 12 hours as a carpenter
Answer:
3^2/5
Step-by-step explanation:
