How many sides does a regular dodecagon have?
2 answers:
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Answer: a = 4, b = 163,422
<u>Step-by-step explanation:</u>
P is the new population, P₀ is the initial population, k is the growth rate, t is the time elapsed.
Part a) What do we know?
P = 7003
P₀ = unknown
k = .21 <em>(converted 21% into a decimal)</em>
t = 36 yrs <em>(2006 - 1970) </em>
<em>need to solve for P₀</em>
7003 = P₀ (1920)
3.6 = P₀
rounded to the nearest whole number = 4
Part b) What do we know?
P = unknown
P₀ = 7003
k = .21 <em>(converted 21% into a decimal)</em>
t = 15 yrs <em>(2021 - 2006) </em>
<em>need to solve for P₀</em>
P = 7003(23.33)
P = 163,422.46
rounded to the nearest whole number = 163,422
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Answer: 2, -1
<u>Step-by-step explanation:</u>
eˣ² = eˣ * e²
eˣ² = eˣ⁺²
x² = x + 2
x² - x - 2 = 0
(x - 2)(x + 1) = 0
x - 2 = 0 or x + 1 = 0
x = 2 or x = -1
Check both answer for validity:
eˣ² = eˣ⁺²
e⁴ = e⁴ or e¹ = e¹
TRUE TRUE
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Answer: 0 = ln 1
<u>Step-by-step explanation:</u>
-10 = ln 1 - 10 <em>log rules say division is subtraction</em>
0 = ln 1
For the given geometric series the value of the common ratio(r) is 3, while the value of a₁ is 1.
<h3>What is geometric series?</h3>A series of numbers whose any two consecutive numbers are always in a common ratio of that series.
Given to us
Series, 1 3 9 27 81
To find the value of the common ratio(r), we will simply find the ratio of any two consecutive numbers, therefore,
As we can see the common ratio of the given series is 3, therefore, every next number will be thrice the number before.
We need to find the value of a₁ for the given series, and as we know that a₁ is the first number of the series with which the series is starting, therefore,
a₁ = 1
Hence, for the given geometric series the value of the common ratio(r) is 3, while the value of a₁ is 1.
Learn More about Geometric Series: