For the function F defined by F(x) = x2 – 2x + 4, find F(| — 4|).
1 answer:
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Answer:
We have the system of equations:
y=1/3x+5
y=2/3x+5
To solve it graphically, we need to graph both lines and see in which point the lines intersect.
You can see the graph below, and you can see that the lines intersect in the point (0, 5)
Now, we can also solve this analytically.
We can use the fact that for the solution, we need y = y.
Then we can write:
(1/3)*x + 5 = (2/3)*x + 5
First, we can subtract 5 in both equations to get:
(1/3)*x = (2/3)*x
This only has a solution when x = 0.
Replacing x = 0 in one of the equations, we get:
y = (1/3)*0 + 5 = 5
Then the solution is x = 0, and y = 5, as we already could see in the graph.
Answer:
The maximum amount of red kryptonite present is 33.27 g after 4.93 hours.
Step-by-step explanation:
dy/dt = y(1/t - k)
separating the variables, we have
dy/y = (1/t - k)dt
dy/y = dt/t - kdt
integrating both sides, we have
∫dy/y = ∫dt/t - ∫kdt
㏑y = ㏑t - kt + C
㏑y - ㏑t = -kt + C
㏑(y/t) = -kt + C
taking exponents of both sides, we have
when t = 1 hour, y = 15 grams. So,
(1)
when t = 3 hours, y = 30 grams. So,
(2)
dividing (2) by (1), we have
taking natural logarithm of both sides, we have
-2k = ㏑(2/3)
-2k = -0.4055
k = -0.4055/-2
k = 0.203
From (1)
Substituting A and k into y, we have
The maximum value of y is obtained when dy/dt = 0
dy/dt = y(1/t - k) = 0
y(1/t - k) = 0
Since y ≠ 0, (1/t - k) = 0.
So, 1/t = k
t = 1/k
So, the maximum value of y is obtained when t = 1/k = 1/0.203 = 4.93 hours
<u>So the maximum amount of red kryptonite present is 33.27 g after 4.93 hours.</u>