Find the area of each shaded region.
1 answer:
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81 a² - 25 is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)
Step-by-step explanation:
The difference of two squares is a binomial of two terms each term is a square and the sign between the two terms is (-), its factorization is the product of two identical binomials with different middle signs
- a² - b² is a difference of two squares
- a² - b² = (a + b)(a - b)
∵ The binomial is 81 a² - 25
∵ = 9
∵ = a
∴
∵ = 5
∵ = z³
∴
- The two terms have square root
∵ The sign between them is (-)
∴ 81 a² - 25 is a difference of two squares
∵ Its factorization is two identical brackets with different
middle signs
∵ 81 a² = 9a × 9a
∵ 25 = 5z³ × 5z³
- The terms of the two brackets are 9a and 5z³
∴ 81 a² - 25 = (9a + 5z³)(9a - 5z³)
81 a² - 25 is a difference of two squares and its factors are (9a + 5z³) and (9a - 5z³)
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Answer:
a) k=2.08 1/hour
b) The exponential growth model can be written as:
c) 977,435,644 cells
d) 2.033 billions cells per hour.
e) 2.81 hours.
Step-by-step explanation:
We have a model of exponential growth.
We know that the population duplicates every 20 minutes (t=0.33).
The initial population is P(t=0)=58.
The exponential growth model can be written as:
For t=0, we have:
If we use the duplication time, we have:
Then, we have the model as:
The relative growth rate (RGR) is defined, if P is the population and t the time, as:
In this case, the RGR is k=2.08 1/h.
After 8 hours, we will have:
The rate of growth can be calculated as dP/dt and is:
For t=8, the rate of growth is:
(2.033 billions cells per hour).
We can calculate when the population will reach 20,000 cells as: