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))
In order to make this easier, let us convert the fraction into a mixed number. 2 2/3 would become 8/3. Now, let us divide 8 pints by 8/3 cups and we get 24/8 or 3 cups. Therefore, the amount of water that Cary has to use when she makes barbecue sauce with 1 pint of tomato is 3 cups.
The club members would have to buy 2 to have the same amount as one non club members
Answer:
V = 678.24cubic cm
Step-by-step explanation:
Volume of a cylinder
V = πr^2h
V - volume of a cylinder
π - pie
r - radius of a cylinder
h - height of a cylinder
Given:
π - 3.14
h - 6
d = 12
d = 2r
Divide both sides by 2
d/2 = 2r/2
d/2 = r
r = d/2
r = 12/2
r = 6
Insert the values into the formula
V = πr^2h
V = 3.14 * 6^2 * 6
= 3.14 * 36 * 6
= 678.24cubic cm
Answer:
Linearly, because the table shows that the sunflowers increased by the same amount each month
Step-by-step explanation:
Given the table
Note that months change one-by-one (21-1, 3-2=1, 4-3=1).
Also
![17.2-15=2.2\ [\text{from month 1 to month 2}]\\ \\19.4-17.2=2.2\ [\text{from month 2 to month 3}]\\ \\21.6-19.4=2.2\ [\text{from month 3 to month 4}]](https://tex.z-dn.net/?f=17.2-15%3D2.2%5C%20%5B%5Ctext%7Bfrom%20month%201%20to%20month%202%7D%5D%5C%5C%20%5C%5C19.4-17.2%3D2.2%5C%20%5B%5Ctext%7Bfrom%20month%202%20to%20month%203%7D%5D%5C%5C%20%5C%5C21.6-19.4%3D2.2%5C%20%5B%5Ctext%7Bfrom%20month%203%20to%20month%204%7D%5D)
This means the number of sunflowers increases linearly, because the table shows that the sunflowers increased by the same amount each month
