A quadratic pattern has a second term equal to 1,a third term equal to -16 and a fifth term equal to -14 1.1.1.calculate the second difference of this quadratic pattern

1.1.2.hence or otherwise, calculate the first term of term

1.1.1. The common difference is 12

1.1.2. The first term is 30

Step-by-step explanation:

1.1.1. The given quadratic pattern is presented as follows;

The 2nd term = 1

The 3rd term = -16

The 5th term = -14

Let 'd' represent the second difference, we have;

1 + 2d + a =  -16

2·d + a = -16 - 1 = -17

2·d + a = -17...(1)

-16 + 3d + a + 4d + a = -14

7·d + 2·a = -14 + 16 = 2

7·d + 2·a = 2...(2)

Making 'a' the subject of both equation (1) and (2) gives;

a = -17 - 2·d

a = 1 - 7/2·d

∴ -17 - 2·d = 1 - 7/2·d

(7/2)·d - 2·d = 1 + 17

(3/2)·d = 18

d = (2/3) × 18 = 12

The common difference, d = 12

a = -17 - 2·d = -17 - 2 × 12 = -41

1.1.2. Let 'x' represent the first term, we have;

x + a + d = 1

x = 1 - (a + d)

x = 1 - (-41 + 12) = 30

The first term, x = 30

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.