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lisabon 2012 [21]
3 years ago
7

1. The sum of first n terms of an arithmetic sequence is 3n²+4n

Mathematics
1 answer:
valentina_108 [34]3 years ago
5 0

Answer:

<h3>           a.  a₁=7,     b.  a_n=7n+1,    c.  a₂₀=141</h3>

Step-by-step explanation:

a.

 a_1=S_1=3\cdot1^2+4\cdot1=3+4=7

b.

   a_1+a_2=S_2\\\\a_1+a_1+d=3\cdot2^2+4\cdot2\\\\7+7+d=3\cdot4+8\\\\14+d=12+8\\\\d=6\\\\\\a_n=a_1+d(n-1)\\\\a_n=7+6(n-1)\\\\a_n=7+6n-6\\\\\underline{a_n=7n+1}

c.

 a_{20}=7\cdot20+1=141

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given a polynomial function f(x) = -x^2 + 2x + 1 and an exponential function g(x) = 2x, what key features do f(x) and g(x) have
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<h3>Polynomial and exponential functions</h3>

Given the following functions as shown:

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Time intervals measured with a stopwatch typically have an uncertainty of about 0.2 seconds, due to human reaction time at the s
Yakvenalex [24]

Answer:

a) 2,650%

b) 27,400%

c) 164,900%

Step-by-step explanation:

We want to measure the percentage we would have to increase the typical value to obtain the values given in a), b) and c).  

But 0.2 increased in x% equals  

0.2 + 0.2(x/100) =0.2(1+x/100)

So, if we want to increase 0.2 in x%, we must multiply it by (1+x/100)

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We need to find the value of x such that

0.2(1+x/100) = 5.5 ⇒ (1+x/100)=5.5/0.2 ⇒  1+x/100=27.5

⇒  x/100=26.5 ⇒ x=2,650%

b)

0.2(1+x/100) = 55 ⇒ (1+x/100)=55/0.2 ⇒  1+x/100=275

⇒  x/100=274 ⇒ x=27,400%

c)

5.5 min = 5.5*60 s = 330

0.2(1+x/100) = 330 ⇒ (1+x/100)=330/0.2 ⇒  1+x/100=1,650

⇒  x/100=1,649 ⇒ x=164,900%

4 0
3 years ago
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