For the differential equation s′′+bs′+6s=0, find all the values of b that make the general solution overdamped, those that make
it underdamped, and those that make it critically damped. (For each, give an interval or intervals for b for which the equation is as indicated. Thus if the the equation is overdamped for all b in the range 2
1 answer:
You might be interested in
All of given options contain quadratic functions. One way to determine the extreme value is squaring the expression with variable x.
Option B contain the expression where you can see perfect square. Thus, equation (choice B) reveals its extreme value without needing to be altered.
To determine the extreme value of this equation, you should substitute x=2 (x-value that makes expression in brackets equal to zero) into the function notation:
The extreme value of this equation has a minimum at the point (2,5).
Let be the cat's speed just as it leaves the edge of the table. Then taking the point 1.3 m below the edge of the table to be the origin, the cat's horizontal position at time
is given by
and its height is
where is 9.8 m/s^2, the magnitude of the acceleration due to gravity.
The time it takes for the cat to hit the ground is with
(Unfortunately, this doesn't match any of the given options...)
The cat lands 0.75 m away (horizontally) from the edge of the table, so that its speed was
(Again, not one of the answer choices...)
I'm guessing there's either a typo in the question or answers.