Explain how the triangular difference process is related to the rate of change of your sequence function.

3rd differences of the cubes = 6

Step-by-step explanation:

Given function is,

f(x) = a

If x = 3 (sequence of cubes)

Sequence formed will be,

1           8            27         64         125           216         343  

    7            19           37          61           91             127

           12            18          24          30             36

                   6            6             6             6

Therefore, 3rd differences of the cubes will be 6.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15