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Answer:
The number of people that received copies of the letter at the twentieth stage is<em> 9.537 × 10¹³ </em>.
Step-by-step explanation:
Using the discrete model,
a_k = r a_(k-1) for all integers k ≥ 1 and a₀ = a
then,
aₙ = a rⁿ for all integers n ≥ 0
Let a_k be equal to the number of people who receive a copy of the chain letter at a stage k.
Initially, one person has the chain letter (which the person will send to five other people at stage 1). Thus,
a = a₀ = 1
The people who received he chain letter at stage (k - 1), will send a letter to five people at stage k and thus per person at stage (k - 1), five people will receive the letter. Therefore,
a_k = 5 a_(k - 1)
Thus,
aₙ = a rⁿ = 1 · 5ⁿ = 5ⁿ
The number of people that received copies of the letter at the twentieth stage is
<em>a₂₀ = (5)²⁰ = 9.537 × 10¹³ copies</em>
Answer:
theta = all real values
Step-by-step explanation:
sec theta + tan theta = cos theta / (1-sin theta )
sec theta = 1/cos theta
tan theta = sin theta/cos theta
1/cos theta + sin theta /cos theta= cos theta/ (1-sin theta)
(1+ sin theta) / cos theta = cos theta /( 1-sin theta)
using cross products
(1+sin theta) * (1-sin theta) = cos theta * cos theta
1 +sin theta - sin theta- sin^2 theta= cos ^2 theta
1 - sin ^2 theta= cos ^2 theta
cos ^2 theta= cos ^2 theta
this is an identity so it is true for all theta
Answer:
600
Step-by-step explanation:
