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2 years ago

Consider the sequence -2, 6, -18, 54,

Mathematics

1 answer:

hram777 [196]2 years ago

6 0

Answer: The sequence is geometric

Step-by-step explanation:

In an arithmetic sequence, the consecutive terms differ by a common difference and this difference is linear.

Common difference = given term - the term before it

In geometric progression, the consecutive terms differ by a common ratio this difference is exponential.

Common ratio = given term/the term before it

Looking at the given sequence,

1) d = 6 - - 2 is not equal to - 18 - 6

Therefore, it is not an arithmetic sequence

2) r = 6/- 2 = - 18/6 = - 3

Therefore, it is a geometric sequence.

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A backyard pool has a concrete walkway around it that is 3 feet wide on all sides. The total area of the pool and the walkway is

Gnoma [55]

Answer:

<h2>29.4 length and 21.4 width.</h2>

Step-by-step explanation:

To fin the dimensions of the pool we need to use the total area of the pool plus the concrete walkway. Lets say that W is the width and L the length. We know that, the walkway has 3 ft wide, this means that the width and length are increased by 6ft (3ft on each side). So, the total area can be expressed like this: $A_{total} = (L+6)(W+6)$ .

In addition, we know that the total area is 970 and the length is 8 ft longer than the width ( $L=W+8$ ). So:

$A_{total} = (L+6)(W+6)\\970 = (W+8+6)(W+6)\\970=W^{2}+20W+84\\W^{2}+20W-886=0$

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Therefore, the dimensions of the pool are 29.4 length and 21.4 width.

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