The length of a rectangular park is twice its width.
1 answer:
Answer:
Step-by-step explanation:
<u>Quadratic Function</u>
It's given the length of a rectangular park is twice its width.
Let's call:
x = width of the rectangular park
2x = length of the rectangular park
The park is surrounded by a 3-foot-wide path. This path adds 3 ft twice to both dimensions, i.e.:
x+3+3=x+6 width of the park and the path
2x+3+3=2x+6 length of the park and the path
The total area is:
A=(x+6)(2x+6)
Operating:
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Answer for the first box: 20
Answer for the second box: 6
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Explanation:
The notation a(1) represents the first term of the sequence given. The first term is 20, so thats why a(1) = 20.
The notation a(n) = a(n-1) + ____ means we add some term to the previous term to get the next. This process happens over and over. In this case, we add 6 to each term to get the next
- term1 = 20
- term2 = term1 + 6 = 20 + 6 = 26
- term3 = term2 + 6 = 26 + 6 = 32
- term4 = term3 + 6 = 32 + 6 = 38
and so on...
So we write a(n) = a(n-1) + 6
This value of 6 can be found by selecting any term and subtracting off the previous term, so we could say any of the following below
- term2 - term1 = 26 - 20 = 6
- term3 - term2 = 32 - 26 = 6
- term4 - term3 = 38 - 26 = 6
That's how we end up with
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Extra info:
The common difference is d = 6 and the first term is a = 20
We can use these two facts to find the nth term a(n)
a(n) = a + d*(n-1)
a(n) = 20 + 6*(n-1)
a(n) = 20 + 6n - 6
a(n) = 6n + 14
Then note how plugging in n = 1 leads to
a(n) = 6*n + 14
a(1) = 6*1 + 14
a(1) = 20
and n = 2 leads to
a(n) = 6*n + 14
a(2) = 6*2 + 14
a(2) = 26
and so on
This allows us to plug in any value of n we want, without having to generate the previous terms before it. So for instance, you could plug in n = 100 to jump directly to the 100th term. If you use the recursive definition in the last section, then you have to generate the first 99 terms first before you can get to the 100th term.