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3 years ago

What is the 11th term of the geometric sequence 178, 106.8, 64.08, ...?

Mathematics

1 answer:

Anna [14]3 years ago

5 0

Step-by-step explanation:

step 1. A geometric sequence is found by multiplying subsequent term by a number r.

step 2. 106.8/178 = 0.6. 64.08/106.8 = 0.6. a = 0.6. note that a geometric series must have the same number when dividing successive terms.

step 3. an = ar^(n - 1) = a(0.6)^(n - 1)

step 4. given a1 = 178. an = 178(0.6)^(n - 1)

step 5. therefore a11 is the 11th term!

step 6. a11 = 178(0.6)^10 = 1.0763 = 1.08.

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Mike wants to fence in part of his backyard. He wants the length of the fenced-in area to be at least 20 feet long, l ≥ 20. He h

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I added a screenshot of the complete question along with the given choices.

Answers:

w = 10 ft and l = 50 ft ................> second option

w = 20 ft and l = 60 ft ...............> third option

w = 50 ft and l = 40 ft ...............> fifth option

Explanation:

We are given that:

length should be at least 20 ...........> length ≥ 20

equation for perimeter is : 2l + 2w ≤ 200

We will check each option as follows:

Option 1:

w = 50 ft and l = 10 ft

This option is incorrect as the proposed length is less than 20.

Option 2:

w = 10 ft and l = 50 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(10) = 100 + 20 = 120 ≤ 200

The second condition is also satisfied.

This option is correct

Option 3:

w = 20 ft and l = 60 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(60) + 2(20) = 120 + 40 = 160 ≤ 200

The second condition is also satisfied.

This option is correct

Option 4:

w = 90 ft and l = 30 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(30) + 2(90) = 60 + 180 = 240 > 200

The second condition is not satisfied.

This option is incorrect

Option 5:

w = 50 ft and l = 40 ft

Since the length is greater than 20, the first condition is satisfied.

Now, we check the second condition:

2l + 2w = 2(50) + 2(40) = 100 + 80 = 180 ≤ 200

The second condition is also satisfied.

This option is correct

Hope this helps :)

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