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Answer:

-10, 40, -240, 1,920 and -19, 200

Step-by-step explanation:

Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.

when n= 1;

aₙ₊₁ = -2naₙ

a₁₊₁ = -2(1)a₁

a₂ = -2(1)(5)

a₂ = -10

when n = 2;

a₂₊₁ = -2(2)a₂

a₃ = -2(2)(-10)

a₃ = 40

when n = 3;

a₃₊₁ = -2(3)a₃

a₄ = -2(3)(40)

a₄ = -240

when n= 4;

a₄₊₁ = -2(4)a₄

a₅ = -2(4)(-240)

a₅ = 1,920

when n = 5;

a₅₊₁ = -2(5)a₅

a₆ = -2(5)(1920)

a₆ = -19,200

Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200

Answer:

0

Step-by-step explanation:

Hope this helps

Answer:

( 5 , 10 )

Step-by-step explanation:

Solution:-

- There are two ships, A and B, currently located by their respective coordinates in the cartesian coordinate system:

          Position of ship A: ( - 1 , -2 )

          Position of ship B: ( -4 , 1 )

- Both ships try to locate a lifeboat. The spotlights used by each ship are modelled as straight line functions of cartesian coordinate originating from their respective ships.

- Spot lights for each ship were able to locate the same lifeboat. The respective spotlights are modelled by the following functions:

         Spotlight Ship A: y = 2x

         Spotlight Ship B: y = x + 5

- To locate the position of the lifeboat with respect to the origin ( 0 , 0 ) we will use the spotlight model functions and equate them. This is because the spotlights must converge or meet at the position of lifeboat provided the lifeboat is found by both ships.

- Therefore,

         Spotlight A = Spotlight B

         y = 2x = x + 5

         2x = x + 5

         x = 5 , y = 10

Answer:The two spotlight meet at the coordinates ( 5 , 10 ). This is also the position of the lifeboat located by both the ships.

Modeling the data in the table is done via the equation y = 4 sine (pi/6x) + 6.

What is a cyclic pattern?

Over a period of years, a cyclical pattern recurs with considerable regularity. Cyclical patterns are distinct from seasonal patterns in that they last across a number of years as opposed to only one year for seasonal trends.

Given, The table shows the height of water in feet at different times. The water rises and falls in a cyclical pattern.

Table:

12 AM                      6  

3 AM                        10

6 AM                        6  

9 AM                        2  

12 PM                       6  

from the general formula of wave

y = A sin(bx + c)

Substituting values in the equation from the graph attached below:

6 = A sin(0*b + c)......(1)

10 = A sin3b + c...(2)

6 = A sin6b + c......(3)

2 = A sin9b +c........(4)

Since -c/b is a phase shift of the graph

Thus

-c/b = 6

c = -6b

from equations 2 and 1

2* 6 = Asin(-3b) = -Asin3b

2 * 6 = Asin(-6b) = -Asin6b

2* 6/6 =sin6b/sin3b

1 = Cos3b

Thus b = π/6

from substitution in equations 3

6 = A sin6b + c

=> 6 = Asin 6* pi/6  + c

=> c = 6

from substitution in equations 2

10 = A sin3b + c

A = 4

therefore, The equation that models data in the table is y = 4 sine (pi/6x) + 6.

Learn more about cyclic patterns here:

brainly.com/question/15223077

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Answer:

c

Step-by-step explanation: