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attashe74 [19]
3 years ago
7

Consider the geometric sequence 1/64, 1/16, 1/4, 1, …. What is the common ratio?

Mathematics
2 answers:
marta [7]3 years ago
8 0

Answer:

4

Step-by-step explanation:

<u>Sequence: </u>

  • 1/64, 1/16, 1/4, 1

<u>Common ratio is the ratio between the next term and the previous term:</u>

  • 1/16 : 1/64 = 1/16 * 64 = 64/16 = 4

or

  • 1/4 : 1/16 = 1/4 * 16 = 16/4 = 4

or

  • 1: 1/4 = 1* 4 = 4
kompoz [17]3 years ago
3 0

Answer:

Identify the Sequence 1, 1/4, 1/16, 1/64 11, 1414, 116116, 164164 This is a geometric sequencesince there is a common ratiobetween each term. In this case, multiplying the previous termin the sequenceby 1414gives the next term.

Step-by-step explanation:

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Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
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Answers:

  • Total equation:  x+y = 80
  • Legs equation:  2x+4y = 248
  • How many ducks? 36
  • How many cows? 44

====================================================

Further explanation:

  • x = number of ducks
  • y = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

  • 2x = number of legs from all the ducks only
  • 4y = number of legs from all the cows only
  • 2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

------------

Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

-2x = -72

x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

There are 44 cows.

------------

Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.

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