Which is bigger? 92^7 or 3^81? Hint: can you write 9^27 as an exponential expression with a base of 3?
1 answer:
You might be interested in
The chairs in the auditorium illustrates an arithmetic sequence
- The recursive rule is: an = an-1 + 8; a1 = 26
- The explicit rule is: an = 18 + 8n
- There are 74 seats in the 7th row
- 840 chairs can fit the auditorium
From the question, we have the following sequence:
Seats: 18, 26, 34
Rewrite as:
26 = 18 + 8
34 = 26 + 8
The above means that:
The number of seats on a row is 8 added to the the number of seats on the previous row.
Hence, the recursive rule is:
an = an-1 + 8; a1 = 26
<h3>The explicit rule</h3>In (a), we have:
a1 = 26 and d = 8
The explicit rule is calculated using:
an = a1 + (n -1) * d
This gives
an = 26 + (n - 1) * 8
Expand
an = 26 - 8 + 8n
Evaluate the difference
an = 18 + 8n
Hence, the explicit rule is:
an = 18 + 8n
<h3>The number of seats in the row 7</h3>This means that n = 7.
So, we have:
a7 = 18 + 8 * 7 = 74
Hence, there are 74 seats in the 7th row
<h3>The sigma notation</h3>We have the maximum number of rows to be 12.
So, the sigma notation would be:
The total number of seats is:
Sn = n/2(2a + (n -1) * d)
This gives
S12 = 12/2(2 * 26 + (12 -1) * 8)
S12 = 840
Hence, 840 chairs can fit the auditorium
Read more about arithmetic sequence at:
The ration of boy campers to total campers is 8:15, and the ratio of girl campers to total campers is 7:15. Using this information, we can answer this question by setting up proportions.
<u>For boys:</u>
<em>*Cross multiply*</em>
15x=1560
<em>*Divide both sides by 15*</em>
x=104
There are 169 boy campers.
<u>For girls:</u>
<em>*Cross multiply*</em>
15x=1365
91=x
There are 91 girl campers.
Hope this helps!!