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nikklg [1K]
3 years ago
8

~I ~ need ~ help ~ once ~ again~

Mathematics
1 answer:
ruslelena [56]3 years ago
8 0
A. 12pi meters.

Circumference = pi x diameter (pi x 12 = 12pi)
Diameter = 2 x radius (2 x 6 = 12)

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If s is a sequence of consecutive multiples of 3, how many multiples of 9 are there in s? (1) there are 15 terms in s. (2) the g
Luba_88 [7]

\it a_{15} =126=3\cdot42
\\\;\\a_1=3n=?
\\\;\\
3, 6, 9, 12, ... , 3n, ..., 3\cdot42

\it 42-(n-1) =15 \Rightarrow n-1=42-15=27 \Rightarrow n=28 \Rightarrow 
\\\;\\
\Rightarrow  a_1=3\cdot28= 84

Now, we have the sequence :

\it a_1= 3\cdot28 = 84 \notin M_9
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a_2= 3\cdot29 = 87 \notin M_9
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\it a_{15} =3\cdot42=126 \in M_9
\\\;\\
90\leq9\cdot k\leq126 |:9 \Rightarrow 10\leq k\leq14 \Rightarrow k \in \{10, 11, 12, 13, 14\}

It implies 5 multiples of 9

At a glance :  {90,  99,  108,  117,  126}


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3 years ago
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