This grid follows two rules. Rule 1 The sums of each row are equal.
Rule 2 The products of each column are equal.
The grid below follows the same two rules.
Work out the missing numbers.
a =
b =
c =
d =

a = 4,

b = 12

c = 10

d = 15

Step-by-step explanation:

Since the product of each column is equal, therefore,

b*5 = 60

b = 60 ÷ 5 = 12

c*6 = 60

c = 60 ÷ 6 = 10

Since the sum of each column are equal, therefore,

12 + 10 + a = 5 + 6 + d

22 + a = 11 + d

Think of a number you can add to 22, and another number you can add to 11, which will make both sides equal. Add both numbers, whenmultiplied together should give you 60.

Factors of 60 are:

(a, d)

(1, 60) => 22 + a = 11 + d => 22+1 = 11+60 (incorrect)

(2, 30) => 22 + a = 11 + d => 22+2 = 11+30 (incorrect)

(3, 20) => 22 + a = 11 + d => 22+3 = 21+20 (incorrect)

(4, 15) => 22 + a = 11 + d => 22+4 = 11+15 => 26 = 26 [CORRECT]

(5, 12) => 22 + a = 11 + d => 22+5 = 11+12 (incorrect)

(6, 10) => 22 + a = 11 + d => 22+6 = 11+10 (incorrect)

Therefore,

a = 4,

d = 15

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

32

step-by-step explanation: