Is that the exact question? because the last part doesn't really make sense to me
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Answer:
2.30 years
Step-by-step explanation:
The number of fish tripled in the first year, making a total of 240 * 3 = 720 fishes.
(a) The formula for logistic equation is as the following
where P0 = 240 is the number of fishes initially, we can plug in P = 720 and t = 1 to calculate the constant k
b) Using the following formula
with P = 3000, P0 = 240, k = 1.1, we can calculate the number of years it takes to get to 3000 fishes
The ribbon would be 9 yards long
Answer:
ten thousands/thousands/hundreds/tens/ones
7 / 0 / 0 / 0 / 0
Explanation:
10 x 7,000 = 70, 000
<span>Position at t=0.35s is 0.2 m
Velocity at t = 0.35s is -0.2 m/s
Since this is college level mathematics, the use of the word "acceleration" should indicate to you that you've been given the 2nd derivative of a function specifying the location of point a. And since you've been asked for the velocity, you know that you want the 1st derivative of the function. And since you've also been asked for the position, you also want the function itself. So let's calculate the desired anti-derivatives.
f''(t) = -1.08 sin(kt) - 1.44 cos(kt)
The integral of f''(t) with respect to t is:
f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k + C
In order to find out what C is, we know that at time t=0, v = 0.36 m/s. So let's plug in the values and see what C is:
f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k + C
0.36 = (1.08 cos(3*0) - 1.44 sin(3*0))/3 + C
0.36 = (1.08 cos(0) - 1.44 sin(0))/3 + C
0.36 = (1.08*1 - 1.44*0)/3 + C
0.36 = 0.36 + C
0 = C
So the first derivative will be f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k
Now to get the actual function by integrating again. Giving:
f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2 + C
And let's determine what C is:
f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2 + C
0.16 = (1.08 sin(3*0) + 1.44 cos(3*0))/3^2 + C
0.16 = (1.08 sin(0) + 1.44 cos(0))/9 + C
0.16 = (1.08*0 + 1.44*1)/9 + C
0.16 = 1.44/9 + C
0.16 = 0.16 + C
0 = C
So C = 0 and the position function is: f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2
So now, we can use out position and velocity functions to get the desired answer:
Position:
f(t) = (1.08 sin(kt) + 1.44 cos(kt))/k^2
f(t) = (1.08 sin(3*0.35) + 1.44 cos(3*0.35))/3^2
f(t) = (1.08 sin(1.05) + 1.44 cos(1.05))/9
f(t) = (1.08*0.867423226 + 1.44*0.497571048)/9
f(t) = (0.936817084 + 0.716502309)/9
f(t) = 1.653319393/9
f(t) = 0.183702155
So the position of point a at t=0.35s is 0.2 m
Now for the velocity:
f'(t) = (1.08 cos(kt) - 1.44 sin(kt))/k
f'(t) = (1.08 cos(3*0.35) - 1.44 sin(3*0.35))/3
f'(t) = (1.08 cos(1.05) - 1.44 sin(1.05))/3
f'(t) = (1.08*0.497571048 - 1.44*0.867423226)/3
f'(t) = (0.537376732 - 1.249089445)/3
f'(t) = -0.711712713/3
f'(t) = -0.237237571
So the velocity at t = 0.35s is -0.2 m/s</span>
