Answer: c=5.4
The two roots are 3/5 and 9/5
Step-by-step explanation:
assume 5x2−12x c=0 is supposed to be 5x^2 - 12x + c = 0
p = (12 + sqrt(144-20c))/10
q = (12 - sqrt(144-20c))/10
p-3q=0,
1.2 + 0.1sqrt(144-20c) +
-3.6 + 0.3sqrt(144-20c) = 0
-2.4 + 0.4sqrt(144-20c) +2.4 = 2.4
sqrt(144-20c) = 2.4/0.4 = 6
144-20c=36
144-36=20c
c = 108/20 = 5.4
5x^2-12x+5.4=0
x = 3/5 or x = 9/5
ANSWER
4 ft
EXPLANATION
The velocity equation of the oscillating spring is given by the function.

To find the displacement function, we need to to Integrate the velocity function.


At time t=0, there was no displacement.
This implies that,




The displacement function then becomes,

To find the displacement over the first π seconds, we put

into the equation for the displacement to get,



Lets get the negative reciprocal of the slope so we get

Now the equation that is perpendicular is

Lets solve for b by plugging in the point (x,y)=(6,1)

Now plug that into the equation. So the equation of the line that is perpendicular and
passes through the point (6, 1) is
Is there a picture to go with this?