Answer:
(P(t)) = P₀/(1 - P₀(kt)) was proved below.
Step-by-step explanation:
From the question, since β and δ are both proportional to P, we can deduce the following equation ;
dP/dt = k(M-P)P
dP/dt = (P^(2))(A-B)
If k = (A-B);
dP/dt = (P^(2))k
Thus, we obtain;
dP/(P^(2)) = k dt
((P(t), P₀)∫)dS/(S^(2)) = k∫dt
Thus; [(-1)/P(t)] + (1/P₀) = kt
Simplifying,
1/(P(t)) = (1/P₀) - kt
Multiply each term by (P(t)) to get ;
1 = (P(t))/P₀) - (P(t))(kt)
Multiply each term by (P₀) to give ;
P₀ = (P(t))[1 - P₀(kt)]
Divide both sides by (1-kt),
Thus; (P(t)) = P₀/(1 - P₀(kt))
Answer:
<em>t=60</em>
Step-by-step explanation:
3/2t-16=4/3t-6
(subtract 4/3t from both sides)
3/2t-16-4/3t=-6
(add 16 to both sides)
3/2t-4/3t=-6+16
(simplify)
1/6t=10
(divide by 1/6 (or multiply by 6 on both sides)
t=60
Answer: (27- 4/3 pi) r^3
Step-by-step explanation: 1. Volume of a cube: V= a^3, V= 3^3 , V=27
2. Volume of a sphere: V=4/3 pi r^3 ......
For this case, the parent function is given by:
We apply the following transformations:
Vertical translations:
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units upwards:
For k = 9 we have:
Horizontal translations:
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right
For h = 4 we have:
Answer:
The function g (x) is given by:
