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defon
3 years ago
8

PLEASE ANSWER RIGHT AWAY

Mathematics
1 answer:
Tcecarenko [31]3 years ago
4 0

Answer:

The sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is t2 = 4 and recursive definition is tn+1 = 2 tn - 2 ⇒ 4th answer

Step-by-step explanation:

* Lets revise the recursive formula

1. Determine if the sequence is arithmetic (Do you add, or subtract, the

  same amount from one term to the next?)

2. Find the common difference. (The number you add or subtract.)

3. Create a recursive formula by stating the first term, and then stating

   the formula to be the previous term plus the common difference.

   a1 = first term;

   an+1= an + d

- Where:

# a1 = the first term in the sequence

# an = the nth term in the sequence  

# an+1 = the term after the nth term  

# n = the term number

# d = the common difference.

* Now lets solve the problem

∵ The recursive definition is tn+1 = 2 tn - 2 and t2 = 4

- Look to the answer we have three answer with second term = 4,

 1st , 2nd and 4th

- Lets find the 1st term

∵ t2 = 2 t1 - 2

∵ t2 = 4

∴ 4 = 2 t1 - 2 ⇒ add 2 to the both sides

∴ 6 = 2 t1 ⇒ divide the two sides by 2

∴ t1 = 3

- We have two answer with first term = 3, 2nd and 4th answers

* Lets find the third term

∵ t3 = 2 t2 - 2

∵ t2 = 4

∴ t3 = 2 (4) - 2 = 8 - 2 = 6

∴ The 4th answer has the third term = 6

* The 4th sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is

 t2 = 4 and recursive definition is tn+1 = 2 tn - 2

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Read 2 more answers
4. The directrix of the parabola 12(y + 3) = (x-4)2 has the equation y=-6. Find the coordinates of
Sveta_85 [38]

The coordinates of the focus of the parabola are (4 , 0)

Step-by-step explanation:

The standard form of the equation of the parabola is  

(x - h)² = 4p(y - k), where

  • The vertex of the parabola is (h , k)
  • The focus is (h , k + p)
  • The directrix is at y = k - p

∵ The equation of the parabola is 12(y + 3) = (x - 4)²

 - The form of the equation is (x - h)² = 4p(y - k), compare

    between them to find h, k and p

∴ h = 4

∵ - k = 3

- Multiply both sides by -1

∴ k = -3

∵ 4p = 12

- Divide both sides by 4

∴ p = 3

∵ The coordinates of the focus are (h , k + p)

∵ h = 4 , k = -3 , p = 3

∴ k + p = -3 + 3

∴ k + p = 0

∴ The focus is (4 , 0)

The coordinates of the focus of the parabola are (4 , 0)

Learn more:

You can learn more about the equation of the parabola in brainly.com/question/9390381

#LearnwithBrainly

5 0
3 years ago
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