Determine whether each of the following LTIC systems is i) BIBO stable, ii) asymptotically stable, and iii) marginally stable. E
xplain why or why not. (a) d 3y dt3 − 3 dy dt − 2y(t) = df dt − f(t) (b) d 3y dt3 − 3 dy dt − 2y(t) = df dt − 2f(t) (c) d 2y dt2 + 3 dy dt + 2y(t) = df dt + f(t) (d) d 2y dt2 + 2 dy dt + 2y(t) = f(t) (e) d 2y dt2 + 2y(t) = f(t)
1 answer:
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Answer:
129.996 cubic feet
Step-by-step explanation:
Assuming that the barrel is a perfect cylinder, we can use the formula to find the volume:
First, we have to find the radius, which is:
D = 2r
So the radius is 3 feet, since it is half of the diameter. Then, we plug in the values.
Now, we solve. Exponents are first...
3.14(9)(4.6)
Now multiply left to right.
28.26(4.6)
129.996 cubic feet
Therefore, the barrel can hold 129.996 cubic feet of oil. Hope this helps you!
Answer:
Step-by-step explanation:
Slope can be represented as rise over run (change y-values over change in x-values). Since the y-value is changing by -2 every time the x-value is changing by 2, the slope of the line must be .
In slope-intercept form ,
represents the slope of the line,
represents the y-intercept, and
represent the coordinates of any point the line passes through.
To find , substitute
and any point the line passes through.
Using (1, 0) from the table:
Thus, the equation of this line is