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Soloha48 [4]
3 years ago
9

Which is bigger? 92^7 or 3^81? Hint: can you write 9^27 as an exponential expression with a base of 3?​

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
7 0

Answer:

{3}^{81} is bigger.

Step-by-step explanation:

{9}^{27}  = ( {3}^{2} )^{27}  =  {3}^{2 \times 27}  =  {3}^{54}  \\

If we compare the exponents of {3}^{54} and {3}^{81} it can be concluded that:

{3}^{81} > {3}^{54}

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Anika [276]

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

<h3>The recursive rule</h3>

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:

\sum\limits^{12}_{n=1} {18 + 8n}

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:

brainly.com/question/6561461

7 0
2 years ago
What is the difference between 6 2/4 and 1/6????? PLEASE HELP ME
VashaNatasha [74]

Answer:

6 2/4 is a mixed fraction and 1/6 is not.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
last summer, at camp okey-fun-okey, the ratio of the number of boy campers to girl campers was 8:7. If there were a total of 195
Evgen [1.6K]

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>

\frac{8}{15} =\frac{x}{195}

<em>*Cross multiply*</em>

15x=1560

<em>*Divide both sides by 15*</em>

x=104

There are 169 boy campers.


<u>For girls:</u>

\frac{7}{15} =\frac{x}{195}

<em>*Cross multiply*</em>

15x=1365

91=x

There are 91 girl campers.


Hope this helps!!

7 0
3 years ago
Read 2 more answers
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